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Bai-tap-toan-lop-4-nang-cao-theo-chu de

Published by THƯ VIỆN TRƯỜNG TIỂU HỌC ĐỒNG TÂM - NINH GIANG, 2023-05-04 02:52:49

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BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ 1. Sè tù nhiªn - D·y sè tù nhiªn Bµi 11: T×m x , biÕt: a) x lµ sè trßn chôc vµ 28 < x < 48 b) x lµ sè tù nhiªn vµ 145 < x < 150 c) x lµ sè ch½n vµ 200 < x < 210 d) x lµ sè tù nhiªn vµ x < 3 e) x lµ sè tù nhiªn vµ 2 < x < 5 ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 12: Sè tù nhiªn x gåm mÊy ch÷ sè, biÕt sè ®ã: a) Cã ch÷ sè hµng cao nhÊt thuéc líp ngh×n? b) Cã ch÷ sè hµng cao nhÊt thuéc líp triÖu? c) BÐ h¬n 10? d) BÐ h¬n 1 000 000 vµ lín h¬n 1 00 000? e) §øng liÒn sau mét sè cã ba ch÷ sè? f) §øng liÒn tr-íc mét sè cã ba ch÷ sè? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 13: ViÕt sè tù nhiªn nhá nhÊt, biÕt sè ®ã: a) Gåm cã: - Mét ch÷ sè - Ba ch÷ sè - Ba ch÷ sè lÎ kh¸c nhau 1

b) Cã ®ñ n¨m ch÷ sè 5, 4, 7, 0, 1 c) Cã ba ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 20. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 14: T×m sè tù nhiªn x, biÕt: a) x lµ sè tù nhiªn bÐ nhÊt; b) x lµ sè liÒn sau sè 999; c) x lµ sè liÒn tr-íc sè 1001; d) x lµ sè võa lín h¬n 99 võa bÐ h¬n 1000; e) x lµ sè cã hai ch÷ sè vµ lín h¬n 15; f) x lµ sè cã ba ch÷ sè vµ bÐ h¬n 105; g) x lµ sè ë gi÷a sè 1 vµ sè 11; h) x lµ sè gi÷a sè tù nhiªn a vµ sè (a + 1) ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 16: H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 3. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 17: Cho 3 ch÷ sè 1; 2; 3. 2

a) H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 3 ch÷ sè ®· cho. b) TÝnh nhanh tæng c¸c sè võa viÕt ®-îc. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 18: Víi bèn ch÷ sè 1,2,3,4; a) H·y viÕt tÊt c¶ c¸c sè cã ®ñ bèn ch÷ sè Êy. b) TÝnh tæng cña tÊt c¶ c¸c sè ë c©u a. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 19: Cho 5 ch÷ sè 0, 1, 2, 3, 6. a) H·y lËp tÊt c¶ c¸c sè cã bèn ch÷ sè kh¸c nhau tõ 5 ch÷ sè trªn? b) TÝnh nhanh tæng c¸c sè võa lËp ®-îc? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 22: Cho d·y sè: 2, 3, 4, 5, ..., 30, 31, 32, 33, 34. a) D·y sè trªn cã bao nhiªu sè h¹ng? b) TÝnh nhanh tæng cña d·y sè trªn? ..................................................................................... ..................................................................................... 3

..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 25: Cho d·y sè ch½n liªn tiÕp 2, 4, 6, 8, 10, ... , 2468. Hái d·y cã: a) Bao nhiªu sè h¹ng? b) Bao nhiªu ch÷ sè ? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 2. BÀI TOÁN LIÊN QUAN DÃY SỐ THEO QUY LUẬT Cho các số 1;4;7;10;..................... a.Số 2221;2234 có thuộc dãy số đó không ? b.Số thứ 134 ,số thứ 205 là số nào ? c.Tính tổng của 50 số đầu của dãy số. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 3/CẤU TẠO SỐ D¹ng 1: ViÕt sè TN tõ nh÷ng ch÷ sè cho tr-íc Bµi 2 : Cho 5 ch÷ sè : 0; 1; 2; 3; 4. a) H·y viÕt c¸c sè cã 4 ch÷ sè kh¸c nhau tõ 5 ch÷ sè ®· cho ? b) T×m sè ch½n lín nhÊt, sè lÎ nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 5 ch÷ sè ®· cho ? ..................................................................................... ..................................................................................... 4

..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 1 : Cho bèn ch÷ sè : 0; 3; 8 vµ 9. a) ViÕt ®-îc tÊt c¶ bao nhiªu sè cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho ? b) T×m sè lín nhÊt, sè nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho? c) T×m sè lÎ lín nhÊt, sè ch½n nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho ? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... D¹ng 2: C¸c bµi to¸n gi¶i b»ng ph©n tÝch sè : Bµi 1: T×m 1 sè TN cã 2 ch÷ sè, biÕt r»ng nÕu viÕt thªm ch÷ sè 9 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp 13 lÇn sè ®· cho ? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 2: T×m mét sè cã 3 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã th× nã t¨ng thªm 1112 ®¬n vÞ. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 3: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm sè 21 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp 31 lÇn sè ph¶i t×m. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 5

Bµi 4: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã ta ®-îc sè míi lín h¬n sè ph¶i t×m lµ 230 ®¬n vÞ. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... D¹ng 3: Nh÷ng bµi to¸n vÒ xÐt c¸c ch÷ sè tËn cïng cña sè aBbc)))µ(2i( 11119:99K811h2+«+3n11g99l982µ22m5++tÝ..n....2h++7, 11h–99·9y8199c1h))o–b1i((Õ311t 91c9h+1÷115+s2è1+t9Ë91.n.27.c..+ï+n..1g..9+c)ñ1.a99m9ç)i kÕt qu¶ sau : ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 2 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ? a) 136  136 – 42 = 1960 b) ab  ab - 8557 = 0 ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 3 : Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau : a) ( 19996+6 237786+458465–+ 759156 )6–1 ( 37115+ 58918 + 736 + 89 ) b. ). .5.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 4 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ? a) abc  abc - 853467 = 0 b) 11  21  31  41 – 19  25  37 = 110 6

..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 4. C¸c bµi to¸n vÒ dÃy sè I. §iÒn thªm sè h¹ng vµo sau, gi÷a hoÆc tr-íc mét d·y sè Bµi 1. ViÕt tiÕp ba sè h¹ng vµo d·y sè sau : a) 1; 3; 4; 7; 11; 18;... b) 0; 2; 4; 6; 12; 22;... c) 0 ; 3; 7; 12;... d) 1; 2; 6; 24;... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 2 : T×m sè h¹ng ®Çu tiªn cña c¸c d·y sè sau : a). ...; 17; 19; 21. b). .: 64; 81; 100. BiÕt r»ng mçi d·y cã 10 sè h¹ng. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 7

..................................................................................... ..................................................................................... ........... ......................................................................... Bµi 3 : ViÕt tiÕp hai sè h¹ng cña d·y sè sau : a) 100; 93; 85; 76;..... b) 10; 13; 18; 26;... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... II. X¸c ®Þnh sè a cã thuéc d·y ®· cho hay kh«ng Bµi 1: H·y cho biÕt: a) C¸c sè 50 vµ 133 cã thuéc d·y 90; 95; 100;...hay kh«ng ? b) Sè 1996 thuéc d·y 2;5;8;11;... hay kh«ng ? c) Sè nµo trong c¸c sè 666; 1000; 9999 thuéc d·y 3; 6; 12; 24;... hay kh«ng ? Gi¶i thÝch t¹i sao ? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... III. T×m sè sè h¹ng cña d·y Bµi1. Cho d·y sè 11; 14; 17;.....;65; 68. a) H·y x¸c ®Þnh d·y sè trªn cã bao nhiªu sè h¹ng? b) NÕu ta tiÕp tôc kÐo dµi c¸c sè h¹ng cña d·y sè ®ã th× sè h¹ng thø 1996 lµ sè mÊy? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 2 . Trong c¸c sè cã ba ch÷ sè, cã bao nhiªu sè chia hÕt cho 4? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 8

..................................................................................... ..................................................................................... Bµi 3: Cã bao nhiªu sè : cã 3 ch÷ sè khi chia cho 5 d- 1? D- 2 ? ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... IV. T×m tæng c¸c sè h¹ng cña d·y sè Bµi 1 . TÝnh tæng cña 50 sè lÎ ®Çu tiªn . ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... Bµi 2: T×m tæng cña : a) C¸c sè cã 2 ch÷ sè chia hÕt cho 3. b) C¸c sè cã 2 ch÷ sè chia cho 4 d- 1. ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... ..................................................................................... 5. Bèn phÐp tÝnh víi sè tù nhiªn 5.1. PhÐp céng Bµi 1: T×m hai sè cã tæng b»ng 1149, biÕt r»ng nÕu gi÷ nguyªn sè lín vµ gÊp sè bÐ lªn 3 lÇn th× ta ®-îc tæng míi b»ng 2061. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè thø nhÊt, gÊp sè thø hai lªn 6 lÇn th× ®-îc tæng míi b»ng 6789. H·y t×m hai sè h¹ng ban ®Çu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 9

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: T×m hai sè cã tæng b»ng 140, biÕt r»ng nÕu gÊp sè h¹ng thø nhÊt lªn 5 lÇn vµ gÊp sè h¹ng thø hai lªn 3 lÇn th× tæng míi lµ 508. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 4: T×m hai sè tù nhiªn cã tæng lµ 254. NÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt vµ gi÷ nguyªn sè thø hai th× ®-îc tæng míi lµ 362. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: T×m hai sè cã tæng b»ng 586. NÕu viÕt thªm ch÷ sè 4 vµo bªn ph¶i sè thø hai vµ gi÷ nguyªn sè thø nhÊt th× tæng míi b»ng 716. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 36: Khi céng mét sè tù nhiªn víi 107, mét häc sinh ®· chÐp nhÇm sè h¹ng thø hai thµnh 1007 nªn ®- îc kÕt qu¶ lµ1996. T×m tæng ®óng cña hai sè h¹ng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 37: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè h¹ng thø nhÊt, gÊp sè h¹ng thø hai lªn 6 lÇn th× ®-îc tæng míi b»ng 65789. H·y t×m hai sè h¹ng ban ®Çu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 40: Cho sè cã hai ch÷ sè. NÕu viÕt sè ®ã theo thø tù ng-îc l¹i ta ®-îc sè míi bÐ h¬n sè ph¶i t×m. BiÕt tæng cña sè ®ã víi sè míi lµ 143. T×m sè ®· cho. 10

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 41: Tæng cña hai sè thay ®æi thÕ nµo nÕu mét sè h¹ng cña nã t¨ng thªm 300 ®¬n vÞ vµ gi÷ nguyªn sè h¹ng kia? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 42: Chu vi h×nh ch÷ nhËt sÏ thay ®æi thÕ nµo nÕu ta t¨ng chiÒu dµi thªm 3 mÐt vµ gi¶m chiÒu réng cña nã ®i 3m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 43: Tæng cña hai sè lµ 69, nÕu gÊp 3 lÇn sè thø hai vµ gi÷ nguyªn sè thø nhÊt th× tæng míi lµ 87. T×m hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.2. PhÐp trõ Bµi 1: T×m hai sè cã hiÖu lµ 23, biÕt r»ng nÕu gi÷ nguyªn sè trõ vµ gÊp sè bÞ trõ lªn 3 lÇn th× ®-îc hiÖu lµ 353. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: T×m hai sè cã hiÖu lµ 383, biÕt r»ng nÕu gi÷ nguyªn sè bÞ trõ vµ gÊp sè trõ lªn 4 lÇn th× ®-îc hiÖu míi lµ 158. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 11

.......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: HiÖu cña hai sè tù nhiªn lµ 4441, nÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè trõ vµ gi÷ nguyªn sè bÞ trõ th× ®-îc hiÖu míi lµ 3298. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 4: HiÖu cña hai sè tù nhiªn lµ 134. ViÕt thªm mét ch÷ sè vµo bªn ph¶i cña sè bÞ trõ vµ gi÷ nguyªn sè trõ th× hiÖu míi lµ 2297. T×m ch÷ sè viÕt thªm vµ hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 45: TÝnh nhanh a) 32 - 13- 17 c) 1732 - 513 - 732 b) 45 - 12 - 5 - 23 d) 2834 - 150 -834 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 50: T×m tæng hai sè, biÕt hiÖu cña hai sè ®ã lµ 37 vµ hiÖu ®ã b»ng nöa sè bÐ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 51: HiÖu cña hai sè thay ®æi thÕ nµo nÕu ta cïng t¨ng thªm (hay bít ®i) hai sè ®ã cïng mét sè. Cho vÝ dô? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 52: HiÖu cña hai sè lµ 27, nÕu ta cïng gÊp lªn ( hay gi¶m ®i) mçi sè ®ã 3 lÇn th× hiÖu míi lµ bao nhiªu? 12

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 53: Kh«ng thùc hiÖn phÐp tÝnh, cã thÓ nãi ngay gi¸ trÞ biÓu thøc sau ®-îc kh«ng? a) A= 621 – ( 621 – 58) b) B = x- ( x- 60) c) C= 720 + ( 3927 – 720) d) D = x + ( 390 – x) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 54: T×m sè tù nhiÖn x, biÕt: a) 35- x < 35 – 5 b) x – 10 < 35 – 10 c) x – 10 < 45 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.3. PhÐp nh©n Bµi 1: T×m tÝch cña 2 sè, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø 2 lªn 4 lÇn th× ®-îc tÝch míi lµ 8400. Bµi gi¶i .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 13

Bµi 2: T×m 2 sè cã tÝch b»ng 5292, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø hai thªm 6 ®¬n vÞ th× ®-îc tÝch míi b»ng 6048. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: T×m 2 sè cã tÝch b»ng 1932, biÕt r»ng nÕu gi÷ nguyªn mét thõa sè vµ t¨ng mét thõa sè thªm 8 ®¬n vÞ th× ®-îc tÝch míi b»ng 2604. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 58: Trong mét phÐp nh©n cã thõa sè thø hai lµ 64, khi thùc hiÖn phÐp nh©n mét ng-êi ®· viÕt c¸c tÝch riªng th¼ng cét víi nhau nªn kÕt qu¶ t×m ®-îc lµ 870. T×m tÝch ®óng cña phÐp nh©n? Bµi 59: Kh«ng tÝnh tæng, h·y biÕn ®æi tæng sau thµnh tÝch cã hai thõa sè . a) 462+273+315+630 c) 5555+6767+7878 b) 209+187+726+1078 d) 1997,1997+1998,1998+1999,1999 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 59: . So s¸nh A vµ B biÕt: a. A=73 x 73 B=72 x 74 b. A=1991 x 1999 B=1995 x 1995 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 60: TÝch cña hai sè thay ®æi thÕ nµo nÕu ta gÊp mét thõa sè lªn 2 lÇn vµ gi¶m thõa sè kia ®i 2 lÇn. Cho vÝ dô? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 61: TÝch cña hai sè thay ®æi thÕ nµo nÕu mçi thõa sè ®Òu gÊp lªn 3 lÇn. Cho vÝ dô? 14

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 62: T×m x ( Kh«ng thùc hiÖn phÐp tÝnh) a) 5  x = 5 195 b) ( x + 5)  2009 = ( 19 + 5)  2009 c) 35  x < 35  6 d) ( 15 – x)  79 < ( 15 – 2)  79 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 63: TÝch cña hai sè tù nhiªn lµ 65. NÕu mét sè t¨ng thªm 30 ®¬n vÞ vµ gi÷ nguyªn sè kia th× tÝch míi lµ 215.T×m hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 64: Khi nh©n mét sè víi 245, mét häc sinh ®· ®Æt c¸c tÝch riªng th¼ng cét nh- trong phÐp céng nªn t×m ra kÕt qu¶ lµ 4257. T×m tÝch ®óng cña phÐp nh©n ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 65: TÝnh gi¸ trÞ cña biÓu thøc sau b»ng c¸ch hîp lÝ: a) 54  113 + 54 113 + 113 b)( 532  7 - 266 14)  ( 532  7 + 266) c) 117  ( 36 + 62) - 17 ( 62 + 36) d)( 145  99 + 145) – ( 143  101 – 143) 21. T×m 3 sè lÎ liªn tiÕp mµ tÝch cña chóng lµ 105. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 15

.......................................................................................................................................................................... .......................................................................................................................................................................... 22. Cho A= 1  2 + 2 3 + 3 4 + …+ 19  20 TÝnh A 3 = ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 66: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) 2009  867 + 2009  133 b) 2008 867 + 2009 133 TÝch cña hai sè tù nhiªn liªn tiÕp tõ 1 ®Õn 76 tËn cïng b»ng bao nhiªu ch÷ sè 0? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 67: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) A = 1 + 1 + 1 + ...+ 1 – 999( cã 1000 sè 1) b) 4 113 25 - 5  112  20 c) ( 100 – 99 + 97 – 80 + 15)  ( 16 – 2  8) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 69: TÝnh b»ng c¸ch thuËn tiÖn b) 123 15 - 123 5 a) 3  17 + 3  25 - 3  2 c) 246  4 - 246 3 – 246 d) 789 9 - 789 8 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.4. PhÐp CHIA Bµi 73: §Æt tÝnh råi tÝnh a) 256075 : 5 b) 369090 : 6 c)498479: 7 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 16

Bµi 74: T×m x: a) x 5 = 106570 b) 450906 : x = 6 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 76: TÝnh ( Theo mÉu) MÉu: 60 : 30 = 60 : ( 10  3) = 60 : 10 : 3 = 6:3 =2 a) 90 : 30 b) 180 : 60 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 77: §Æt tÝnh råi tÝnh 552 : 24 450 : 27 540 : 45 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 79: §Æt tÝnh råi tÝnh 4725 : 15 8058: 34 5672 : 42 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 80: Ng-êi ta xÕp c¸c gãi kÑo vµo c¸c hép, mçi hép 30 gãi. Hái cã thÓ xÕp 2000 gãi kÑo vµo nhiÒu nhÊt bao nhiªu hép vµ cßn thõa bao nhiªu gãi kÑo? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 81: §Æt tÝnh råi tÝnh 3621: 213 8000 : 308 1682 : 209 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 17

Bµi 84: Mua 52 bót bi hÕt 78 000 ®ång. Hái nÕu mçi bót bi ®ã gi¶m gi¸ 300 ®ång th× víi sè tiÒn 78 000 ®ång sÏ mua ®-îc bao nhiªu bót bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 85: Nam lµm mét phÐp chia cã d- lµ sè d- lín nhÊt cã thÓ cã. Sau ®ã Nam gÊp c¶ sè bÞ chia vµ sè chia lªn 3 lÇn. ë phÐp chia míi nµy, sè th-¬ng lµ 12 vµ sè d- lµ 24. T×m phÐp chia Nam thùc hiÖn ban ®Çu? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 86: Sè A chia cho 12 th× d- 8. NÕu gi÷ nguyªn sè chia th× sè A ph¶i thay ®æi thÕ nµo ®Ó th-¬ng t¨ng thªm 2 ®¬n vÞ vµ phÐp chia kh«ng cã d-? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 87: Mét phÐp chia cho 18 d- 8. §Ó phÐp chia kh«ng cßn d- vµ th-¬ng gi¶m ®i 2 lÇn th× ph¶i thay ®æi sè bÞ chia nh- thÕ nµo? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 88: Th-¬ng cña hai sè thay ®æi thÕ nµo nÕu ta gÊp sè bÞ chia vµ sè chia lªn cïng mét sè lÇn? Cho vÝ dô. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 89: Kh«ng thùc hiÖn phÐp tÝnh, t×m x: a) 2009 : x = 2009 : 2 b) ( x + 2) : 2009 = (2345 + 2) : 2009 c) x : 5 < 15 : 5 d) 35 : x > 35 : 5 .......................................................................................................................................................................... .......................................................................................................................................................................... 18

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Bµi 89: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) 1875 : 2 + 125 : 2 b) 0 : 36 ( 32 + 17 + 99 – 68 + 1) c) ( m : 1 - m  1) : ( m 2009 + m + 1) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... B...µ..i..9..0..:...H...·.y...®..Æ..t..d..Ê..u...n..g..o..Æ..c...v..µ.o...b..i.Ó..u...t.h..ø..c...:..3.....1..5...+....1..8...:..6..+...3...®..Ó...g..i.¸...t.r.Þ..c..ñ..a...b..i.Ó..u...t.h..ø..c...l.µ..:............................... a) 47 b) Sè bÐ nhÊt cã thÓ cã c) Sè lín nhÊt cã thÓ cã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 91: TÝnh gi¸ trÞ biÓu thøc sau víi x = 1 vµ y = 0: a) A = ( 15 : x + 15  x) + 2009  y b) B = y : ( 119  x + 4512) + (756 : x – y) c) C = ( 10 + y) : ( 10 – y) – x + 10 x – 10 : x + y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 6. DẠNG TOÁN TRUNG BÌNH CỘNG 4. Trong c¸c sè, nÕu cã mét sè lín h¬n møc trung b×nh céng cña c¸c sè n ®¬n vÞ th× trung b×nh céng cña c¸c sè ®ã b»ng tæng c¸c sè cßn l¹i céng víi n ®¬n vÞ råi chia cho sè l-îng c¸c sè h¹ng cßn l¹i ®ã. 19

VD: An cã 20 viªn bi, B×nh cã sè bi b»ng 1 sè bi cña An. Chi cã sè bi h¬n møc trung b×nh céng cña ba 2 b¹n lµ 6 viªn bi. Hái Chi cã bao nhiªu viªnn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5. Trong c¸c sè , nÕu mét sè kÐm trung b×nh céng cña c¸c sè ®ã n ®¬n vÞ th× trung b×nh céng cña c¸c sè ®ã b»ng tæng c¸c sè cßn l¹i trõ ®i n ®¬n vÞ råi chia sè c¸c sè h¹ng cßn l¹i. VD: An cã 20 bi, B×nh cã 20 bi. Chi cã sè bi kÐm trung b×nh céng cña c¶ ba b¹n lµ 6 bi. Hái Chi cã bao nhiªu bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 6. Bµi to¸n cã thªm mét sè h¹ng ®Ó møc trung b×nh céng cña tÊt c¶ t¨ng thªm n ®¬n vÞ, ta lµm nh- sau: VD: Mét « t« trong ba giê ®Çu, mçi giê ®i ®-îc 40km, trong ba giê sau, mçi giê ®i ®-îc 50 km. NÕu muèn t¨ng trung b×nh céng mçi giê t¨ng thªm 1 km n÷a th× ®Õn giê thø 7, « t« ®ã cÇn ®i bao nhiªu km n÷a? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô 1: H·y t×m sè trung b×nh céng cña 1, 2, 3, 4, 5, 6, 7, 8, 9. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô3: An cã 20 nh·n vë, B×nh cã 20 nh·n vë. Chi cã sè nh·n vë kÐm trung b×nh céng cña ba b¹n lµ 6 nh·n vë. Hái Chi cã bao nhiªu n·nh vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô 4: 20

Cã bèn b¹n An, B×nh, Dòng, Minh cïng ch¬i bi. BiÕt An cã 18 viªn bi, B×nh cã 16 viªn bi, Dòng cã sè bi b»ng trung b×nh céng sè bi cña An vµ B×nh. Minh cã sè bi b»ng trung b×nh céng sè bi cña c¶ bèn b¹n. Hái B¹n Minh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 1: T×m sè trung b×nh céng cña c¸c sè c¸ch ®Òu nhau 4 ®¬n vÞ : 3, 7, 11, …,95, 99, 103. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: T×m sè trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12, 14, 16, 18. Em cã c¸ch nµo tÝnh nhanh sè trung b×nh céng cña c¸c sè trªn kh«ng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè. mÑ vµ Lan lµ 28 tuæi. T×m tuæi cña mçi ng-êi, biÕt tuæi B×nh gÊp ®«i tuæi Lan, tuæi Lan b»ng 1 tuæi mÑ. 6 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: Hai ng-êi ®i xe m¸y khëi hµnh cïng mét lóc tõ hai đ Þa ®iÓm c¸ch nhau 216km vµ ®i ng-îc chiÒu nhau. Hä ®i sau 3 giê th× gÆp nhau. Hái trung b×nh mét giê mçi ng-êi ®i ®i ®-îc bao nhiªu ki- l«- mÐt? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 21

Bµi 6: Con lîn vµ con chã nÆng 102kg, con lîn vµ con bß nÆng 231kg, con chã vµ con bß nÆng 177kg. Hái trung b×nh mçi con nÆng bao nhiªu ki-l«-gam? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 7: T×m sè cã ba ch÷ sè, biÕt trung b×nh céng ba ch÷ sè cña sè ®ã b»ng 6 vµ ch÷ sè hµng tr¨m gÊp ba ch÷ sè hµng chôc, ch÷ sè hµng chôc kÐm ch÷ sè hµng ®¬n vÞ lµ 2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 8: Ba sè cã trung b×nh céng lµ 60. T×m ba sè ®ã, biÕt nÕu viÕt thªm mét ch÷ sè ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt th× ta ®-îc sè thø hai vµ sè thø nhÊt b»ng 1 sè thø ba. 4 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 12: ViÖt cã 18 bi, Nam cã 16 bi, Hoµ cã sè bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã sè bi kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 13: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung b×nh céng cña 2 b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn. Hái Cóc mua bao nhiªu quyÓn vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 14: Tuæi trung b×nh 11 cÇu thñ cña mét ®éi bãng ®¸ lµ 22 tuæi . NÕu kh«ng kÓ thñ m«n th× tuæi trung b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................2..2.

Bµi 103: T×m trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12 14, 16, 18. Em cã c¸ch nµo tÝnh nhanh sè trung b×nh céng cña c¸c sè trªn kh«ng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 104: T×m sè cã ba ch÷ sè, biÕt truug b×nh céng ba ch÷ sè cña nã b»ng 5 vµ ch÷ sè hµng tr¨m gÊp ba ch÷ sè hµng chôc, ch÷ sè hµng chôc h¬n ch÷ sè hµng ®¬n vÞ lµ 1. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 105: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè, mÑ vµ Lan lµ 28 tuæi. T×m tuæi mçi ng-êi, biÕt tuæi B×nh gÊp ®«i tuæi Lan, tuæi Lan b»ng 1 tuæi mÑ. 6 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 106: Cã 4 b¹n An, B×nh, Dòng, Minh ch¬i bi. An cã 18 viªn, B×nh cã 16 viªn, Dòng cã sè bi b»ng TBC sè bi cña An vµ B×nh, Minh cã sè bi b»ng TBC sè bi cña c¶ 4 b¹n. Hái Minh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 107: TBC sè tuæi cña «ng , bè vµ ch¸u lµ 36 tuæi, TBC sè tuæi cña bè vµ cña ch¸u lµ 23, «ng h¬n ch¸u 54 tuæi. T×m tuæi mçi ng-êi. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 108: T×m 3 sè cã TBC b»ng 60, biÕt r»ng nÕu viÕt thªm 1 ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt th× ®-îc sè thø hai vµ sè thø 3 gÊp 4 lÇn sè thø nhÊt. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 23

.......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 109: ViÖt cã 18 viªn bi, Nam cã 16 bi, Hßa cã s« bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã sè bi kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 110: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung b×nh céng cña hai b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn vë. Hái Cóc mua bao nhiªu quyÓn vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 112: Tuæi trung b×nh cña 11 cÇu thñ cña ®éi bãng ®¸ lµ 22 tuæi. NÕu kh«ng kÓ thñ m«n th× tuæi trung b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 113: Mét th¸ng ®iÓm cã 20 lÇn kiÓm tra, sau 10 lÇn kiÓm tra b¹n An thÊy ®iÓm trung b×nh cña m×nh lµ 7 ®iÓm. Hái cßn 10 lÇn kiÓm tra n÷a b¹n An ph¶i ®¹t ®-îc tÊt c¶ bao nhiªu ®iÓm ®Ó ®iÓm trung b×nh cña th¸ng lµ 8 ®iÓm. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 1: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 2: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... 24

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 3: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 4: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 5: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 6: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 7: Trung bình cộng của n số là 80 biết 1 trong các số đó là 100 .Nếu bỏ số 100 thì trung bình cộng các số còn lại là 78 tìm n. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 8: Có ba con ; gà, vịt, ngan . Hai con gà và vịt nặng tất cả là 5 kg . Hai con gà và ngan nặng tất cả là 9 kg . Hai con ngan và vịt nặng tất cả là 10 kg . Hỏi trung bình một con nặng mấy kg ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 25

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 10: Trung bình cộng của ba số là 50 . Tìm số thứ ba biết rằng nó bằng trung bình cộng của hai số đầu . Hướng dẫn giải .Dùng sơ đồ .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 11: Trung bình cộng của ba số là 35 . Tìm ba số đó biết rằng số thứ nhất gấp đôi số thứ hai, số thứ hai gấp đôi số thứ ba? Gợi ý Dùng sơ đồ .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 12: Tìm sáu số chẵn liên tiếp biết tổng của chúng là 90. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 13: Tìm trung bình cộng của tất cả các số có hai chữ số , mà chia hết cho 4 . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 14: Trung bình cộng số tuổi của hai anh em ít hơn tuổi anh là 4 tuổi . Hỏi anh hơn em mấy tuổi ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 15: Lớp 4 A có 40 học sinh , lớp 4B có 36 học sinh . Lóp 4 C có số học sinh ít hơn trunh bình cộng số học sinh của cả ba lớp là hai bạn . Tính số học sinh lớp 4 B. 26

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 16: Hai lớp 3A và 3B có tất cả 37 h/s .Hai lớp 3B và 3B có tất cả là 83 h/s. Hai lớp 3C vàg 3A có tất cả là 86 h/s . Hỏi: trung bình mỗi lớp có bao nhiêu học sinh ? Số học sinh của mỗi lớp là bao nhiêu em ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 17: Tuổi trung bình cộng của một đội bóng đá (11 người) là 22 tuổi. Nếu không kể đội trưởng, thì tuổi trung bình của 10 cầu thủ còn lại chỉ là 2. Tính tuổi của đội trưởng ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 18: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 19: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 20: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 27

Bài tập 21: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 22: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 23: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 24: Ba lớp 4a;4b;4c; đi trồng cây . số cây của lớp 4a và 4b trồng được là 41 cây .Số cây của lớp 4b và lớp 4c trồng được là 43 cây . Số cây của 4c và 4a trồng được là 42 cây . Hỏi mỗi lớp trồng được bao nhiêu cây? .BàiGiải. Cả 3 lớp trồng được số cây là: (41+42+43 ): 2 =63 cây Lớp 4c trồng được số cây là 63- 41=22cây Lớp 4 b trồng số cây là: 43 -22= 21(Cây) Lớp 4 a trồng số cây là: 42 – 22 = 20 (cây) Đáp Số: Bài tập 25: An,Bình ,Chi đi câu cá . Cả ba bạn câu được 37 con cá . Nếu An câu thêm được 5 con cá và Bình câu giảm đi 3 con cá thí số cá ba bạn bằng nhau . Hỏi mỗi bạn câu được bao nhiêu con cá? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 1 : Tìm 3 số có trung bình cộng lớn hơn số thứ nhất 540, bé hơn số thứ hai là 1260 và gấp 31 lần số thứ ba. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 28

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 2 : Đội tuyển học sinh giỏi khối 5 của một trường Tiểu học có 16 bạn. Biết rằng 2/5 số bạn nam nhiều hơn 1/2 số bạn nữ là 1 bạn. Hỏi đội tuyển có bao nhiêu bạn nam, bao nhiêu bạn nữ ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 3 : Một trường Tiểu học có số học sinh nam nhiều hơn số học sinh nữ là 40 học sinh. Trong đó 3/4 số bạn nam và 1/2 số bạn nữ đạt danh hiệu học sinh tiên tiến. Tính số học sinh nam và số học sinh nữ của trường đó. Biết số học sinh tiên tiến của trường đó là 530 bạn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 7. DẠNG TÌM HAI SỐ KHI BIẾT TỔNG VÀ HIỆU Bµi 1: Cã mét hép bi xanh vµ mét hép bi ®á, tæng sè bi cña 2 hép lµ 48 viªn bi. BiÕt r»ng nÕu lÊy ra ë hép bi ®á 10 viªn vµ lÊy ra ë hép bi xanh 2 viªn th× sè bi cßn l¹i trong 2 hép b»ng nhau. T×m sè bi cña mçi hép lóc ®Çu. Bµi gi¶i: .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... §¸p sè : 18 vµ 20 Bµi 2: Lan cã nhiÒu h¬n Hång 12 quyÓn truyÖn nhi ®ång. NÕu Hång mua thªm 8 quyÓn vµ Lan mua thªm 2 quyÓn th× 2 b¹n cã tæng céng 46 quyÓn. Hái mçi b¹n cã bao nhiªu quyÓn truyÖn nhi ®ång? ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè : 12 vµ 24 Bµi 3: Hai hép bi cã tæng céng 115 viªn, biÕt r»ng nÕu thªm vµo hép bi thø nhÊt 8 viªn vµ hép thø hai 17 viªn th× 2 hép cã sè bi b»ng nhau. Hái mçi hép cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... §¸p sè 78 vµ 37 Bµi 4: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng víi tæng cña chóng th× ®-îc 2010. .......................................................................................................................................................................... .......................................................................................................................................................................... 29

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: T×m hai sè ch½n cã tæng b»ng 216, biÕt gi÷a chóng cã 5 sè ch½n .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 6: Tæng sè tuæi hiÖn nay cña bµ, cña HuÖ vµ cña H¶i lµ 80 tuæi. C¸ch ®©y 2 n¨m, tuæi bµ h¬n tæng sè tuæi cña HuÖ vµ H¶i lµ 54 tuæi, HuÖ nhiÒu h¬n H¶i 6 tuæi. Hái hiÖn nay mçi ng-êi bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 3 Bµi 7: Hai ®éi trång c©y nhËn kÕ ho¹ch trång tÊt c¶ 872 c©y. Sau khi mçi ®éi hoµn thµnh 4 kÕ ho¹ch cña m×nh, ®éi 1 trång nhiÒu h¬n sè c©y ®éi 2 trång lµ 54 c©y. Hái mçi ®éi nhËn trång theo kÕ ho¹ch lµ bao nhiªu c©y? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 115: T×m hai sè, biÕt tæng hai sè lµ sè lín nhÊt cã hai ch÷ sè. HiÖu hai sè lµ sè lÎ bÐ nhÊt cã hai ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 116: T×m hai sè biÕt tæng hai sè lµ 100 vµ hiÖu hai sè lµ sè bÐ nhÊt cã hai ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 117: T×m hai sè biÕt hiÖu hai sè lµ sè lín nhÊt cã 1 ch÷ sè vµ tæng hai sè lµ sè lín nhÊt cã ba ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 30

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Bµi 118: T×m hai sè ch½n cã tæng b»ng 220, biÕt r»ng ë gi÷a chóng cã 3 sè ch½n. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 119: Tæng cña hai sè ch½n lµ 38. H·y t×m hai sè biÕt r»ng gi÷a chóng chØ cã 3 sè lÎ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 120: Tæng cña ba sè lÎ liªn tiÕp lµ 75,h·y t×m ba sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 121: Anh h¬n em 5 tuæi. BiÕt r»ng 5 n¨m n÷a th× tæng sè tuæi cña hai anh em lµ 25. TÝnh sè tuæi cña mçi ng-êi hiÖn nay? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 122: TÝnh diÖn tÝch cña miÕng ®Êt h×nh ch÷ nhËt cã chu vi lµ 256 m vµ chiÒu dµi h¬n chiÒu réng 32m .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 123: Mét m¶nh v-ên h×nh ch÷ nhËt cã chu vi b»ng chu vi thöa ruéng h×nh vu«ng c¹nh 80m. NÕu gi¶m chiÒu dµi m¶nh v-ên ®i 30m vµ t¨ng chiÒu réng thªm 10m th× m¶nh v-ên sÏ cã h×nh vu«ng. TÝnh diÖn tÝch m¶nh v-ên. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 124: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng tæng cña chóng th× ®-îc 2010 .......................................................................................................................................................................... .......................................................................................................................................................................... 31

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 8. DẠNG TÌM HAI SỐ KHI BIẾT 2 HIỆU SỐ Bài toán: Để chuẩn bị cho năm học mới, hai bạn Vĩnh và Kim đi mua sắm sách vở. Vĩnh mua 15 quyển vở, Kim mua nhiều hơn hơn Vĩnh 5 quyển vở cùng loại và phải trả nhiều hơn Vĩnh 20.000 đồng. Hỏi mỗi bạn phải trả bao nhiêu tiền mua vở? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 3. Bài tập cần luyện: *Bài tập 1: Một hiệu sách, lần thứ nhất bán được 27 quyển vở. Lần thứ hai bán được 40 quyển vở cùng loại và nhận nhiều tiền hơn lần trước 52.000 đồng. Hỏi mỗi lần bán hiệu sách nhận bao nhiêu tiền? (GV phân tích tương tự như bài toán trên). .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Bài tập 2: Hồng mua 3 cái bút và 5 quyển vở hết 39.000 đồng. Hoa mua 3 cái bút và 9 quyển vở cùng loại như Hồng hết 51.000 đồng. Tính giá tiền một cây bút, một quyển vở? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4. Bài tập về nhà: Chị Vĩnh mua 2 mét vải xanh và 6 mét vải hoa. Chị Linh mua 2 mét vải xanh và 9 mét vải hoa cùng loại. Chị Vĩnh phải trả 380.000 đồng. Chị Linh phải trả 530.000 đồng. Tính giá tiền một mét vải mỗi loại? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 32

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Bài 1: Hiện nay, Minh 10 tuổi ,em Minh 6 ,còn mẹ của Minh 36 tuổi .Hỏi bao nhiêu năm nữa tuổi mẹ bằng tổng số tuổi của hai anh em. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2 : Bể thứ nhất chứa 1200 lít nước . Bể thứ 2 chứa 1000 lít nước .Khi bể không có nứớc người ta cho 2 vòi cùng chảy 1 lúc vào 2 bể . Vòi thứ nhất mỗi giờ chảy được 200 lít .Vòi thứ 2 mỗi giờ chảy được 150 lít. Hỏi sau bao lâu số nước còn lại ở 2 bể bằng nhau. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Cùng 1 lúc xe máy và xe đạp cùng đi về phía thành phố xe máy cách xe đạp 60km. Vận tốc xe máy là 40 km/h vận tốc xe đạp là 25 km/h. Hỏi sau bao lâu xe máy đuổi kịp xe đạp. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4 : Một con Chó Đuổi theo một con thỏ .Con chó cách con thỏ 20m.Mỗi bước con thỏ nhẩy được 30cm,con chó nhảy được 50 cm.Hỏi sau bao nhiêu bước con chó bắt được con thỏ ? Biết rằng con thỏ nhảy được 1 bước thì con chó cũng nhảy được 1 bước. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5 Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 60 bộ .Bác thứ 2 nhận 45 bộ . Cứ 1 tuần bác thứ nhất đóng được 5 bộ ,bác thứ hai đóng được 2 bộ . Hỏi sau bao lâu số ghế còn lại của 2 bác bằng nhau. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 33

Bài 6:Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 120 bộ .Bác thứ 2 nhận 80 bộ . Cứ 1 tuần bác thứ nhất đóng được 12 bộ ,bác thứ hai đóng được 4 bộ .Hỏi sau bao lâu số ghế còn lại của bác thứ nhất bằng 1/2 số bộ bàn ghế của bác thứ 2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7: Hai bể nước có dung tích bằng nhau .Cùng 1 lúc người ta cho 2 vòi nước chảy vào 2 bể .Vòi thứ nhất mỗi giờ chảy được 50 lít nước .Vòi thứ 2 mỗi giờ chảy được 30 lít nước . Sau khi bể thứ nhất đầy nước thì bể thứ 2 phải chảy thêm 600 lít nữa mới đầy .Hỏi dung tích của bể là bao nhiêu lít nước? (Tham khảo thêm Đề thi và phần Bài tập mở rộng) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 9. DẠNG TOÁN LIÊN QUAN ĐẾN CHIA HẾT Bµi 1: Tõ 3 ch÷ sè 0, 1, 2. H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau chia hÕt cho 2. ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bµi 2: ViÕt tÊt c¶ c¸c sè chia hÕt cho 5 cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè 0, 1, 2 , 5. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: Em h·y viÕt vµo dÊu * ë sè 86* mét ch÷ sè ®Ó ®-îc sè cã 3 ch÷ sè vµ lµ sè: a) Chia hÕt cho 2 b) chia hÕt cho 3 c) Chia hÕt cho 5 d) chia hÕt cho 9 e) Chia hÕt cho c¶ 2 vµ 5 g) Chia hÕt cho c¶ 3 vµ 9 ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bchµiia4h:ÕHt c·hyot×5mvcµ¸9c. ch÷ sè x, y sao cho 17x8y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 34

........................................................ ........................................................ Bµi 5: T×m x, y ®Ó x765y chia hÕt cho 3 vµ 5. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: Y = 0 ta cã c¸c sè : x= 3, 6 9 Y = 5 ta cã x = 14,7 Bµi 6: T×m x vµ y ®Ó sè 1996xy chia hÕt cho 2, 5 vµ 9. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bµi 7: T×m a vµ b ®Ó 56a3b chia hÕt cho 36. ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: ( Chia hết cho 36 thì tổng của 56a3b chia hết cho 4 và 9) Bµi 8: T×m tÊt c¶ c¸c ch÷ sè a vµ b ®Ó ph©n sè 1a83b lµ sè tù nhiªn. 45 ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: ( Chia hết cho 45 thì tổng của 1a83b chia hết cho 5 và 9) 45 Bµi 9: T×m x ®Ó 37  2x5 chia hÕt cho 3. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: 37 + 2 + 5 = 41 vËy x = 1, 4 , 7 35

Bµi 10: T×m a vµ b ®Ó sè a391b chia hÕt cho 9 vµ chia cho 5 d- 1. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 11: T×m tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau abc , biÕt: ac  2 . b7 3 B= 2 th× ac = 2 x 9 = 18 B= 5 th× ac = 2 x 19 = 39 B= 8 th× ac = 2 x 29 = 54 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 1. ViÕt c©c sè tù nhiªn theo dÊu hiÖu chia hÕt Bµi 2 : Cho 4 ch÷ sè 0; 1; 5; 8. H·y lËp c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho tho¶ m·n ®iÒu kiÖn: a) Chia hÕt cho 3 ? b) Chia hÕt cho 2 vµ 5 ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 2. Dïng dÊu hiÖu chia hÕt ®Ó ®iÒn c¸c ch÷ sè ch-a biÕt. Bµi 2: Cho sè b = xy2008 thay x vµ y sao cho sè b chia hÕt cho 2, 5 vµ 3. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 3.bµi to¸n vÒ vËn dông tÝnh chÊt chia hÕt cña mét tæng vµ mét hiÖu. Bµi 1: Kh«ng lµm phÐp tÝnh, h·y xÐt xem c¸c tæng vµ hiÖu d-íi ®©y cã chia hÕt cho 3 hay kh«ng? a) 240 + 123 b) 240 – 123 c) 459 + 690 + 1236 d) 2454 + 374 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 36

Bµi 2: Tæng kÕt n¨m häc 2007- 2008, mét tr-êng tiÓu häc cã 462 häc sinh tiªn tiÕn vµ 195 häc sinh giái. Ban gi¸m hiÖu dù ®Þnh th-ëng cho mçi häc sinh giái nhiÒu h¬n häc sinh tiªn tiÕn 2 quyÓn vë. C« v¨n phßng nhÈm tÝnh ph¶i mua 1996 quyÓn th× ®ñ ph¸t th-ëng. Hái c« v¨n phßng ®· tÝnh ®óng hay sai? Gi¶i thÝch t¹i sao ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4.C¸c bµi to¸n vÒ phÐp chia cã d-. . H·yChthoaay =x, 5yxby»ng nh÷ng ch÷ sè thÝch hîp ®Ó d-îc mét sè cã 3 ch÷ sè kh¸c nhau chia cho 2,3 vµ 5 ®Òu d- 4. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5. VËn dông tÝnh chÊt chia hÕt vµ phÐp chia cã d- ®Ó gi¶i c¸c bµi to¸n cã lêi v¨n. Bµi 3: Mét cöa hµng då s¾t cã 7 thïng ®ùng 2 lo¹i ®inh 5 ph©n vµ 10 ph©n (mçi thïng chØ ®ùng mét lo¹i ®inh). Sè ®inh trong mçi thïng theo thø tù lµ 24kg, 26kg, 30kg, 37kg, 41kg, 55kg vµ 58 kg. Sau khi b¸n hÕt 6 thïng vµ chØ cßn mét thïng ®inh 10 ph©n, ng-êi b¸n hµng thÊy r»ng trong sè ®inh ®· b¸n, ®inh 10 ph©n gÊp 3 lÇn ®inh 10 ph©n. Hái cöa hµng ®· cã bao nhiªu kil«gam ®inh mçi lo¹i? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 1: Trong giờ tập thể dục của lớp 4a thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8 ,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 vẫn thấy vừa đủ .Các bạn tính xem lớp 4a có bao nhiêu bạn biết biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2:Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả thì cũng vừa hết .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3:ở một bến cảng có ba con tàu A,B,C Tàu a cứ 3 ngày cặp bến 1 lần ,tàu B là 4 ngày cặp bến 1 lần ,tàu C là 5 ngày .Nếu một hôm nào đó cả ba tàu cùng cặp bến thì hỏi sau bao nhiêu ngày ba tàu lại cùng cặp bến. 37

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Bài 4:Trong giờ tập thể dục của lớp 4 b thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8 ,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 đều thấy hàng cuối thiếi 1 người .Các bạn tính xem lớp 4b có bao nhiêu bạn .Biết biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5:Trong giờ tập thể dục của lớp 4C thầy giáo cho các bạn học sinh xếp hàng .lúc thì cho xếp hàng 8, lúc xếp hàng 6, lúc lại xếp hàng 4, hàng 3 hàng 2 đều thấy thừa 1 người .Các bạn tính xem lớp 4c có bao nhiêu bạn biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 6 : Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả thì đĩa cuối đều thiếu 2 quả .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7: Một ông tướng cầm quân đi dẹp giặc .Ông cho quân xép hàng 10 thì thấy hàng cuối thiếu 1 người, thấy vậy ông lại cho quân xếp hàng 9 thì thấy hàng cuối vẫn thiếu 1 người; thế là ông lại cho quân xếp hàng 8 thì hàng cuối vẫn thiếu 1 người. Ông bèn cho xếp hàng 7;6;5;4;3;2 đều vẫn như vậy . Tính hộ xem ông tướng có bao nhiêu quân biết số quân của ông ít hơn 5000 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 38

10. BÀI TOÁN CÓ NỘI DUNG HÌNH HỌC Bài 3:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta tăng chiều dài lên 1/3 chiều dài thì chu vi hình chữ nhật mới là 120m. Tính diện tích thửa ruộng ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta giảm chiều dài đi 1/3 chiều dài thì chu vi hình chữ nhật mới là 80m. Tính diện tích thửa ruộng ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5:Một thửa ruộng hình chữ nhật có chu vi 110m . Nếu tăng chiều rộng 5 m và giảm chiều dài 5 m thì diện tích thửa ruộng không thay đổi .Tính diện tích thửa ruộng 39

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Bài 6:Một thửa đất hình vuông trên thửa đất đó người ta đào một cái ao hình vuông cạnh cái ao cách đều cạnh thửa đất .Chu vi cái ao kém chu vi thửa đất là 64 m.Tính diện tích cái ao biết diện tích phần dất còn lại là 600m2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7:Bác An có một mảnh đất vườn chữ nhật .ở một góc vườn bác đào một cái ao hình vuông có 1 cạnh cách chiều rộng mảnh vườn 33 m còn cạnh kia cách chiều dài mảnh vườn là 17 m .Biết diện tích phần đất còn lại là 1311m2 . Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 8:Một thửa ruộng hình chữ nhật có chu vi 200 m .chiều dài hình chữ nhật hơn 2 lần chiều rộng là 10m.Tính diện tích thửa ruộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 9:Một thửa ruộng hình chữ nhật có chu vi 160 m .chiều dài hình chữ nhật kém 2 lần chiều rộng là 10m.Tính diện tích thửa ruộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 10:Một thửa ruộng hình chữ nhật có chu vi 200 m Dọc theo chiều dài người ta ngăn thửa ruộng thành 2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông nhỏ hơn chu vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... 40

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Bài 11:Một thửa ruộng hình chữ nhật có chu vi 160 m Dọc theo chiều dài người ta ngăn thửa ruộng thành 2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông lớn hơn chu vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 12:Một thửa ruộng hình chữ nhật có chiều dài gấp 3 lần chiều rộng . Nếu tăng chiều rộng 5m và giảm chiều dài 5 m thì diện tích tăng thêm 300m2 . Tính diện tích thửa ruộng ban đầu .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 13: Một hình chữ nhật, nếu tăng chiều rộng để bằng chiều dài của nó thì diện tích tăng thêm 20m2, còn khi giảm chiều dài cho bằng chiều rộng thì diện tích giảm 16 m2. Tính diện tích hình chữ nhật .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 14 Một hình chữ nhật có diện tích 135m2 . Chiều dài bằng 3/5 chiều rộng .Tính chu vi hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 15: Một cái sân hình chũ nhật có chu vi 110m. Người ta tăng chiều rộng lên 5m thì sân trở thành hình vuông . tính diện tích cái sân ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 16 Một mảnh vườn hình chữ nhật có chu vi 180 m nếu giảm chiều dài 10 m thì mảnh vườn trở thành mảnh vườn hình vuông .Tính diện tích mảnh vườn ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 41

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 17 Một mảnh vườn hình chữ nhật có chu vi 150 m .Nếu giảm chiều dài 10m và tăng chiều rộng 5m thì được một hình chữ nhật mới có chiều dài gấp 4 chiều rộng .Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 18 Một hình chữ nhật có chiều dài gấp 3 chiều rộng . Nếu tăng chiều rộng lên 24 m thì được hình chữ nhật mới có chiều dài gấp 3 chiều rộng. Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 19 Một mảnh vườn hình chữ nhật có chiều dài gấp 4 lần chiều rộng . Nếu tăng chiều dài 5m và giảm chiều rộng 5 m thì diện tích giảm đi 256m2. Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 20 Một cái ao hình chữ nhật có chu vi 120 m .Dọc theo chiều dài người ta ngăn cái ao thành 2 ao nhỏ (Hình vẽ). Tổng chu vi 2 ao mới tạo thành la 180 m .Tính diện tích cái ao ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 21 Sân trường em hình vuông .Để tăng thêm diện tích nhà trường đã mở rộng về mỗi phía 3m thì diện tích tăng thêm là 196 m2 . Hỏi trước đây sân trường em có diện tích là bao nhiêu m2? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 42

Bài 22: Bác Hà có hai tấm kính hình chữ nhật. Chiều rộng của mỗi tấm kính bằng 1/2 chiều dài của nó và chiều dài của tấm kính nhỏ đúng bằng chiều rộng của tấm kính to. Bác ghép hai tấm kính sát vào nhau và đặt lên bàn có diện tích 90 dm2 thì vừa khít. Hãy tính kích thước của mỗi tấm kính đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 23: Khu vườn hình chữ nhật có nửa chu vi 108m. Nếu giảm chiều dài 3m và tăng chiều rộng thêm 3m thì được hình vuông . Tính diện tích hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 24: Hình chữ nhật có chu vi 84m. Nếu bớt chiều rộng 5m và bớt chiều dài 7m thì được hình vuông. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 25: Hình chữ nhật có nửa chu vi 86m. Nếu giảm chiều dài 9m và tăng chiều rộng thêm 5m thì được hình vuông . Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 26: Hình chữ nhật có chu vi 216m. Nếu giảm chiều rộng 5m và giảm chiều dài 21m thì được hình vuông. Tính diện tích hình vuông đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 27: Hình chữ nhật có chu vi gấp 10 lần chiều rộng. Chiều dài bằng 88m. Tính chiều rộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 28: Hình chữ nhật có chu vi gấp 12 lần chiều rộng. Chiều dài bằng 120m. Tính diện tích hình chữ nhật. 43

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 29: Hình chữ nhật có chu vi gấp 14 lần chiều rộng. Chiều dài hơn chiều rộng 80m. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 30: Hình chữ nhật có chu vi gấp 16 lần chiều rộng. Chiều dài hơn chiều rộng 198m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 31: Hình chữ nhật có nửa chu vi 99m. Nếu tăng chiều rộng thêm 5m và giảm chiều dài đi 5m thì diện tích không thay đổi. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 32: Hình chữ nhật có chu vi 160m. Nếu tăng chiều rộng thêm 10m và giảm chiều dài đi 10m thì diện tích không thay đổi. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 33: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng bằng 5m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 44

Bài 34: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng kém chiều dài 5m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 35: Hình chữ nhật có chu vi 48m. Nếu tăng chiều dài 6m thì được hình chữ nhật mới có chiều dài gấp 2 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 36: Hình chữ nhật có chu vi 64cm. Nếu giảm chiều rộng 2cm, thêm chiều dài 2cm thì được hình chữ nhật mới có chiều dài gấp 3 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 37: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 18m, chiều dài hơn chiều rộng 6m. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 38: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 32m, chiều dài gấp 3 lần chiều rộng 6m. Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 39: Hình chữ nhật có chiều dài gấp 3 lần chiều rộng. Nếu giảm chiều rộng đi 2m và tăng chiều dài thêm 2m thì diện tích giảm đi 68m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 45

.......................................................................................................................................................................... .......................................................................................................................................................................... Bài 40: Hình chữ nhật có chiều dài gấp 4 lần chiều rộng. Nếu giảm chiều dài đi 3m và tăng chiều rộng thêm 3m thì diện tích tăng thêm 108m2 . Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 41: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu giảm chiều rộng đi 2m và giảm chiều dài đi 2m thì diện tích giảm đi 140m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 42: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu tăng chiều dài thêm 5m và tăng chiều rộng thêm 5m thì diện tích tăng thêm 475m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 43: Một thửa hình chữ nhật có chiều rộng bằng 1/2 chiều dài. Tính diện tích thửa đất. Biết rằng nếu tăng chiều rộng 15m và giảm chiều dài 9m thì thửa đất trở thành hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 44: Nếu bớt một cạnh hình vuông là 7m và bớt một cạnh khác 25m thì được hình chữ nhật có chiều dài gấp 3 lần chiều rộng. Tính chu vi và diện tích của hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 45: Trên một miếng đất hình vuông, người ta đào một cái ao hình vuông để thả cá. Sau khi đào xong thì diện tích còn 1280m2. Tính diện tích miếng hình vuông ban đầu. Biết rằng cạnh ao kém cạnh miếng đất 32m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 46

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 46: Cho hai hình chữ nhật A và B. Diện tích hình A hơn hình B là 300m2, chu vi hình A hơn hình B là 20m. Tính diện tích mỗi hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 47: Một mảnh đất hình chữ nhật có chiều rộng bằng 1/5 chiều dài, nếu tăng mỗi chiều thêm 5m thì mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 300m2. Tính diện tích mảnh đất hình chữ nhật sau khi mở rộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 48: Một mảnh đất hình chữ nhật có chiều dài hơn chiều rộng 15m, nếu tăng mỗi chiều thêm 5m thì mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 600m2. Tính diện tích mảnh đất hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 49: Ở chính giữa một mảnh đất hình vuông người ta đào một cái ao cũng hình vuông. Cạnh ao song song và cách đều đám đất 2m. Tính diện tích cái ao biết diện tích mảnh đất hơn diện tích cái ao là 64m2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 50: Tính diện tích hình chữ nhật biết 3 lần chiều rộng 2 lần chiều dài bằng 62m, 2 lần chiều rộng 3 lần chiều dài bằng 68m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 51: Một khu đất hình chữ nhật có chu vi bằng 286m. CHiều dài hơn chiều rộng 5m. Người ta mở rộng chiều dài và chiều rộng khu đất them một đoạn bằng nhau để được khu đất mới có chiều dài gấp đôi chiều rộng. Tính diện tích khu đất mới. (Tham khảo thêm Đề thi và phần Bài tập mở rộng) 47

.......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 11/®¬n vÞ ®o Bµi 28: C« Mai cã 2kg ®-êng, c« ®· dïng 1 sè ®-êng ®ã ®Ó lµm b¸nh. Hái c« Mai cßn l¹i bao nhiªu gam 4 ®-êng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 48

Bµi 29: ViÕt sè thÝch hîp vµo chç chÊm: 1 phót = ...gi©y 3 phót = . .......gi©y 2 phót 10 gi©y = ...gi©y 1 phót = .......gi©y 1 thÕ kØ = . ...n¨m 6 5 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 30: ViÕt tiÕp vµo chç chÊm: a) N¨m 40, Hai Bµ Tr-ng phÊt cê khëi nghÜa chèng l¹i ¸ch thèng trÞ cña nhµ H¸n, n¨m ®ã thuéc thÕ kØ ... b)Lª Lîi lªn ng«i vua vµo n¨m 1428. N¨m ®ã thuéc thÕ kØ ... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 31: Khoanh vµo ch÷ ®Æt tr-íc c©u tr¶ lêi ®óng: Ngµy 23 th¸ng 5 lµ thø 3. Ngµy 1 th¸ng 6 cïng n¨m ®ã lµ: A. Thø t- B. Thø n¨m C. Thø s¸u D. Thø b¶y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 12. DẠNG TOÁN LIÊN QUAN ĐẾN CHUYỂN TỪ A SANG B ; B SANG C; C SANG ... Bài 1: Ba kho chứa 560 tấn thóc .Nếu chuyển 30 tấn từ kho thứ nhất sang kho thứ 2 Sau đó chuyển 25 tấn từ kho thứ 2 sang kho thứ 3 rồi chuyển 12 tấn từ kho thứ 3 sang kho thứ nhất thì số thóc ở 3 kho bằng nhau .Tính số thóc mỗi kho. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 49


THƯ VIỆN TRƯỜNG TIỂU HỌC ĐỒNG TÂM - NINH GIANG

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