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Multiplication using Grids Example 2: Multiply 13 by 42. You can also multiply using grids. We know that, 13 = 10 + 3 and Example 1: Multiply 34 by 6. 42=40+2 We know that, ste p 1: 40 34=30+4 2 Step 1: I 30 Step 2; Step 2: 40 Step 3: 180 + 24 = 204 2 Thus,34x6=204 Step 3: 13 x 42 = 40O + L20 + 20 + 6 = 546 Thus, 13 x 42 = 546 L. N4 ultiply using multiplication tables. a. L2xL1 b. 23x16 c. 62xt9 f. 82xL2 d. 34x18 e. 61 x20 i. 37 xIs l. 26xL9 8. 25xt3 h. 56x14 j. 65x17 k. 72x16 c. 31x 14 f. L4xL6 /. Multiply using grids. b. 54x6 i. 3L2 x 2t a. 29x8 e. L2x18 l. 524 x 52 d. 81 x23 h. 93x17 k. 762 x 62 9 87x11 i' 4I4x3

Multiplication of a 3-digit Number By a 3-digit Number Example: Multiply 432 bY 222. ir';'16fEf 432 222 864 Step 1: Multiply by ones. 432 x 2 = 864 8640 Step 2: Multiply by tens. 432 x 20 = 8640 +86400 Step 3: Multiply by hundreds.432 x 200 = 86400 9 5 9 0 A Add: 864 + 8640 + 86400 = 95904 Thus, 432 x 222 = 959Q4 Multiplication of a 4-digit Number By a l-digit Number EltETExample 2: Multiply 3216 bY 2. 6 Example 1: Multiply 22u by 3. 2 6432 EINEIil 7 fhus,3216x2--6432 3 Step 1: Multiply by ones. 3342 x 4 = 13368 665r. Ste p fhus,2ZL7 x 3 = 6651 Add: 13368 + 66840 = 80208 By a 2-digit Number ETETExample: Multiply 3342 by 24. 3342 24 133 68 +668 40 802 08 Ft Thus, 3342 x 24 = 8O,2O8 -r#

1. Find the product. \" EEEEE. trEtrEtr 5 62 4 46 43 1 52 L J5 7 EEd. trtrEtrEtr 38 254 V b4 ' II@EITEE - E@EtrEE 558 969 548 L22 ^EEEtrEtr rl@trr|Etr 684 7453. 97 91 The rent of a deluxe room in a resort is { 2250 per day. Compute the rent if Sneha and her family stay in the resort for a. 4 days b. l week c. 10 days

Word Problems Example 1: There are 524 pages in a novel. How many pages are there in j.43 novels with the same number of pages? @Etrlttr Number of pages >24 Number of novels r43 1572 . (s24x3=7s72J 20960 +(524x+O=29969; +52400 + (524 x 100 = 52400) Total number of pages 7 A 9 3 2 <-Add: 1572 + 20960 + S24OO = 74932 Thus, there are 74,932 pages in 143 novels. Example 2: lfa petrol pump sells 2318 L of petrol ina day, then how much petrol will it sell in 6 days? Amount of petrol sold in a day EEtrtrEtr 18 Number of days Amount of petrol sold in 6 days 1, 9 08 Thus, L3,908 L of petrol will be sold in 6 days. 1. Abhijeet has a coconut farm in which 246 trees are planted in a row and there are 2j.3 such rows. How many coconut trees are there in the farm? 2. Mr Lee has a pineapple orchard consisting of 1653 plants. tf he has 1.5 such orchards, then how many plants are there in all? 3. 278 ice cream parlours in a city sold 9gO ice creams each. How many rce creams were sold in all? 4. 300 schools sent 225 students each, to participate in a district marathon race. How many students participated .FGFl in the marathon? | 44 tf

5. Every day about 250 chilcjren visit a water park. Find out how many children visited the water park in April. 6. lf Ragini pays < 375 every month for her music lessons, then how much will she pay for the whole year? 7. 1245 people visited the Taj Mahal in the first week of February. lf the same number of people visited the Taj Mahal in every week of February, then find the total number of people who visited the Taj Mahal in the month of February. 8. Make appropriate questions with the clues given. a. There are 243 rows with 12 seats in each row. Question: b. 235 students from each ofthe 32 schools participated in National Sports Day. Qu estio n: lEypl On the occasion of Diwali, the students of Ridge Valley School decided to donate clothes to Blue Bells Home for homeless children. lf there are 5624 students in the school and each student donates 3 pairs of clothes, then find the number of pairs of clothes donated in all to the Blue Bells Home. What value of students is depicted here? Present in your class at least 5 lines on the topic'Help people in need'. Complete the table. ---_{ti.\"na 26 30 28 31 29 Multiplier =--- 9 234 12 1,4 392 15 13 403

MrcrHS Find 11 x3x10: 23x614=6\\4x ]' Compute 12 x 70: 3. What is 27 x 1000? l1:,li!. rll ;:., i Egyptian method of multiplying by doubling and halving numbers: Keep dividing the multiplicand by 2 until you reach L. Multiply the multiplier by 2, the same number of times. lf the multiplicand is an odd numbet then subtract 1 before halving it. Everytime when you subtract l from the multiplicand, note the corresponding doubled numbers, and add them to the final number as shown. You get the answer without using multiplication tables at alll Exa mple 1: Multiply 8 x 25. Example 2: Multiply 42 x 33. Half Double Half Double 8 25 42 33 4 50 2L l-1,1 66 2 100 L 200 10 r32 s (-1) 264 Step 1: 8 is halved to 4 and 25 is doubled to 50. 2 528 1 1056 Step 2: When you reach 1 in the half column, you get your answer in the double 66+264+1056=1386 column as 200. Thus,42x33=1386 Thus,8x25=200 Find the product using doubling and halving method. 1,. 7 x24 2. 54x5L 3. 65x44 n 73x53 5. 82xL4 6. L28 x 82

Estimating the Product Estimating a product is a way to get an approximate value of the product. We can get the estimated product by rounding off each number to the nearest L0 or 100 and then multiplying the rounded values. ExampleL: Estimatethe product of665 and 211 by roundingoffthe numberstothe nearest 100. To find the estimated product, round off 665 to 700 and 211 to 200 and then multiply. Estimated product = 700 x 200 = 140000 Thus, the product is 1,40,000 approximately. Example 2: Estimate the product of 731 and 350 by rounding off the numbers to the nearest 100. ro Trno tne esumateo orooufi, rouno oIT /5r to /uu ano 55u to 4uu. Estimated oroduct = 700 x 400 = 280000 Thus, the product is 2,80,000 approximately. 1. Estimate the following products by rounding off to the nearest 100. a. 168 x 230 b. 277 x L66 c. 567 x 244 d. 2O8 x 425 2. Estimate the total number of books by rounding off to the nearest 10 if there are 143 rows with 109 books in each row. 3. One can of juice costs { 158. Ritu wants to buy 45 such cans. Compute an estimated amount of money Ritu would spend by rounding off to the nearest L0. 4. A jar of toffees costs { 256. A jar of chewing gums costs { 402. Estimate which is cheaper by rounding off to the nearest 10-28 jars of toffees or L5 jars of chewing gums? / Mental Maths ,RN Fill in the empty boxes a by finding the products. a

D[srus] A-uIIUV Objective: To learn estimation in multiplication Materials required: Bits of paper and pencil Method: The teacher writes different 3-digit numbers on the bits of paper and puts them as a stack. Each student comes and picks up two paper bits randomly and estimates their product and then performs the actual calculation. Suppose a student picks up 1.43 and 257. Their estimated product will be 100 x 300 = 30000 and their actual oroduct will be I43 x 257 = 3675L Students who cannot find the nearest estimate, should repeat the process. Make multiplication tables of numbers between 20 and 30 bY adding numbers to 20. Asz!=20+L So, the multiplication table of 21 is equal to the sum of the multiplication tables of 20 and 1' Ft _Eis

1. Multiple Choice Questions. a. _lfthere are 156 mangoes in a crate, the number of mangoes in L00 crates is i. 15,600 ii. L560 iv. 15006 iii. 16,500 b. lf 225 students each from 25 schools participated in a rally, then the total strength of the rally is i.5225 ii.5625 iii.6250 iv 5265 c. Value of 6 x 99 is equal to iii. 600 - 1 iv. 600 - 6 i.600-60 ii. 6 - 600 d. 18 x 200 is equalto i. 360 ii. 3600 iii.36,000 iv. 3060 e. Value of 56 x 10 x 0 ts iii. 0 iv 5600 i. 560 ii. 56 lf a car travels 462 km in a month, the total distance travelled by the car In a year rs 5015 km i. 4267 km ii. 5310 km iii. 5544 km 2. Given below is a chart giving airfare between two cities. Cities Airfare ({) Delhi-Mumbai 4500 Mumbai-Kolkata 6200 Chennai-Delhi 6700 Bengaluru-Kolkata 1200 Chennai-Bengaluru 2750 Based on the above data, answer the following questions. a. Rahul and his friend are to attend a science exhibition for which thev have to travel from Delhi to Mumbai. What is the airfare for both of them? b. Mr Lal and his wife travelled from Chennaito Bengaluru and then from Bengaluru to Kolkata. Find the total airfare. c. lf Mr lmran along with his 2 colleagues is required to travel from Chennaito Delhi, Delhi to Mumbai and then from Mumbai to Kolkata, find the total airfare. 3. Estimate the product by rounding off the numbers to the nearest hundred. ooa. 352 x L72 o. 542 x tl42 ooc. 250 x 265

t. 250 students from different city schools visited a science museum every day during the months of'January to May. Using this information, complete the table given below. Months I Number of Students January February Ma rch April May a. lf the museum was closed for renovation work for 15 days in the month of May, how many students visited in the remaini ng part of the month? b. lf the museum had 1.0 more students every day in the month of April, then how manv students visited in this month? c. lf the museum was closed for 5 days in January and 8 days in March, then how many students visited the museum altogether in the months of January and Ma rch ? 2. Fitl in the missing numbers. One has been done for you. Number of I Number of b. Number of I Number of Cars I Wheels Ants I Legs 14 16 10 20 25 100 50 250

4 Let us revise the terms involved in division. Divi sor For Checking: pn <-J 24 <- Quotient +rQuotient x Diviso Remainder = Dividend Dividend -10t vI I II '2. z- +20 24x 722 2 Remainder What do the monkeys want to say? Choose the correct answer, and write the corresponding letter in the box given. One has been done for you. EE Et. 426+6 = 71 80 5. 120+6 = 20 40 tBl EE N2. 405+9 = 46 45 6. 387+9 = 43 84 3. 981 +9 = 104 109 7. 205+5 = T407-'l4-t;- f--;-- f-=-- ME4. 98+2 = 49 46 8. 25+25 = L T--1t-T-l

EE9. 928+4 = 312 232 EfR-lL2. 848+8 = 567 106 15. 100+5 = t5il0fo2-0 l EITI10.70+10 = 6 , EE13. 54+9 = 96 EE16. 51 +3 = 77 16 EtilL4. 78+6 = 13 tL 56+7 = EfB_l EEL7. 84+7 = t2 .L5 Answer T 8 10 17 L2 73 14 75 L6 t7 Moths Around Us A saint organized a yoga camp in a town. The total number of people who attended the yoga camp was 4608. There were 18 teachers of the saint who taught yoga at the camp. Seeing such a large gathering, the yoga teachers were wondering that how they can conduct the class effectively. They decided to divide the number of people into groups, so that it is easy for them to manage and conduct the classes. They divided the total number of people by the number of yoga teachers available, to see the number of groups formed. They found that 4608 + 18 = 256. Hence, they concluded that each teacher will teach a group of 256 people. Division ' Dividing a 3-digit Number by a 2-digit Number We divide a 3-digit number by a 2-digit number in the same way as we divide a 3-digit number by a l-digit number.

Example 1: Divide 962 by 15. 64 Step 1: Since 9 cannot be divided by 15, divide 96 by 15. 15 x 6 _ 90. Write lcL A, -_o-n! :a tI 6 in the quotient and 90 below 96, and subtract. 62 Step 2: Bring down 2. Djvide 52 by 15. 15 x 4 = 60. Write 4 in the quottent -_ 9_0 and 60 below 62, and subtract. Thus, Quotient = 64 and Remainder = 2 To check the division, apply the following formula. Divisor x Quotient + Remainder = Dividend Here, Dividend = 962, Divisor =15, euotient = 64 and Remainder = 2 So, 15 x 64 + 2 = 962 = Dividend Thus, the answer is correct. Example 2: Divide 834 by L8. 46 Stepl: Since 8 cannot be divided by 18, divide 83 by Ia. 1-8 x 4 = 72. 16lE 3 4 -72+ Write 4 in the quotient column and 72 below 83, and subtract. The difference is 11. 1. 1,4 Step 2: Bring down 4. Divide 114 by 18. 18 x 6 = 199. _1O8 Write 6 in the quotient and 108 below 114, and subtract. Thus, Quotient = 46 and Remainder = 6 Here, Dividend = 834, Divisor = 18, euotient = 46 and Remainder = 6 To check the division, apply the following formula. Divisor x Quotient + Remainder = Dividend 18 x46.. 6 = g2t * 6 = 834 = Dividend Thus, the answer is correct, Dividing a 4-digit Number by a 1-digit Number 62t Example 1: Divide 4352 by 7. TFlsz Step 1r Since 4 cannot be divided by 7, divide 43 by 7. - 42l Since 7 x 6 = 42, write 5 in the quotient column and If, subtract 42 from 43, and write 1as the difference. I2 Step 2: Bring down 5. The new divjdend is 15.

Divide 15 by 7. Since 7 x 2 = 74, write 2 in the quotient column and subtract 14 from 15, and write 1as the difference. Step 3: Bring down 2. The new dividend is 12. Divide 12 by 7. since 7 x 1= 7, write 1 in the quotient column and subtract I tfom 12. Thus, Quotient = 621 and Remainder = 5 Here, Dividend = 4352, Divisor = 7, Quotient = 621 and Remainder = 5 check the division, 7 x 62L + 5 = 4347 + 5 = 4352 = Dividend Thus, the answer is correct. 2:Example Divide 8756 bY 2. 437 8 1:step Divide 8 by 2. 218 7 56 since 2 x 4 = 8, write 4 in the quotient column and subtract 8 from 8. The difference is zero. -8 Step 2: Bring down 7. The new dividend is 7. Divide 7 by 2. o7 Since 2 x 3 = 6, write 3 in the quotient column and l- as the -6 difference. 15 Step 3: Bring down 5. The new dividend is 15. Divide 15 by 2. -L4 Since 2 x 7 = 14, write 7 in the quotient column and to L as the difference. 4rStep Bring down 6. The new dividend is 16. Divide 16 by 2. Since 2 x 8 = 16, write 8 in the quotient column and 0 as the remainder. Thus, Quotient = 4378 and Remainder = 0 Here, Dividend = 8756, Divisor = 2, Quotient = 4378 and Remainder = 0 Check the division, Divisor x Quotient + Remainder = Dividend 2 x 4378 + 0 = 8756 = Dividend Thus, the answer is correct.

Dividing a 4-digit Number by a 2-digit Number ExamDle 1: Divide 7435 by 72. 619 Step 1: Since 7 cannot be divided by 12, divide 74 by 12. LZ x 6 = 72. Write 6 in the quotient column and 2 as the 1, -zfl;I-l;5-t;-- diffe rence. -72+l Step 2: Bring down 3. The new dividend is 23. Divide 23 by 12. 23 L2 x 'J- = !2. Write 1 in the quotient column and 11 as the -t2 difference. 115 Step 3: Bring down 5. The new dividend is 115. Divide 115 by 12. -108 12x9=108. Write 9 in the ouotient column and 7 as the remainder. Thus, Quotient = 61.9 and Remainder = 7 Here, Dividend = 7435, Divisor = 12, Quotient = 619 and Remainder = 7 Check the division, Divisor x Quotient + Remainder = Dividend So, L2 x 619 + 7 = 7428 + 7 = 7435 = Dividend Thus, the answer is correct. Example 2: Divide 5246 by 25. Step 1: Divide 52 by 25. The quotient is 2 and the difference is 2. 246 Step 2: Bring down 4. Divide 24 by 25. Since, 24 cannot be divided by -221 25, bring down 6 and write 0 in the quotient column. 2t Step 3: Divide 246 by 25. The quotient is 9 and the remainder is 21. Thus, Quotient = 209 and Remainder = 2L Here, Dividend = 5246, Divisor = 25, Quotient = 209 and Remainder = 21 Check the division, Divisor x Quotient + Remainder = Dividend So, 25 x 2Og + 27 = 5225 + 2L = 5246 = Dividend Thus, the answer is correct.

1. Divide and check your answer. b. tlosrl.t-tr l=---__-l a. d. f4%l*(-1Tl=[----__-l c. f. e. ts8?al+[D=t-l n. t73rol.Tt-l=[-__-l tlrrl.ail=---__-l 2. In a library,4608 books are packed in 12 cartons. How many books are packed in each carton? 3. In a school assembly, 256 students are asked to stand in 15 rows. Each row should have the same nu mber of students. How many students are there in each row? How many students are left? 4. Five paper strips together make a design. How many similar designs can be made with 2645 paper strips? 5. Fin d the quotient and remainder One has been done for you. a. [Ts4F1+[-t'= Q = 569; R= 11 o. *@= c. o. I rz+s-l+[-i-l=------___l e. t Igs7a-l+[-6-l=---l t---__ltr. I grgz-l + [-r7l = [8rs6-]-[-8*-l=t---__-] 6. Fill in the blanks. a. 633 + Quotient = 15 Remainder = 3 Quotient = 1957 Remainder = l- b. 9786 + Quotient = 4356 Remainder = 5 7. 4606 earthen lamps were arranged in such a way that 20 lamps were packed in each box and 6 were left. Use this information to answer the questions below. a. 4606 + 20 gives Quotient = and Remainder = b. 20x = 4606 c. 23Ox20=

llEypl l tur eatet Oecided to distribute 643 tree saplings equally among 16 houses in his localitv on the occasion of World Environment Day. How many saplings will each house get and how many will be left with him? Discuss in groups of four and present in your class, a skit on the topic'Growing deforestation and its consequences'. Division by 10, 100 and 1000 , I . lf a number is divided by 10, then the digit at ones place becomes the remainder and the remaining digits form the quotient. Example 1: Divide 3425 by 10. Here, Quotient = 342 and Remainder = 5 Example 2: Divide 73632 by 10. Here, Quotient = 7363 and Remainder = 2 . lf a number is divided by 100, then the digits at ones and tens places together form the remainder and the rest of the digits form the quotient. Example 1.: Divide 26245 by 100. Here, Quotient = 262 and Remainder = 46 Example 2: Divide 4353 by L00. Here, Quotient = 43 and Remainder = 53 . If a number is divided by 1000, then the digits at ones, tens and hundreds places together form the remainder and the rest of the digits form the quotient. Fxample 1: Divide 73253 by 1000. Here, Quotient = 73 and Remainder = 253 Example 2: Divide 83635 by 1000 Here, Quotient = 83 and Remainder = 635 Example 3: Divide 97654 by 1000. Here, Quotient = 97 and Remainder = 654

L. Find the quotient and the remainder. b. Fooo-l'Fooo-l=(----__-l \".@*@=t----__l d. F827.[1ooO={-----_--l c. foooo0+Fol=t----l [--__]f. [ 3s?s?-] - Fooo-l = e. [2764t]+Foo-j=(----__-l h. t586r8l-,tlool=[---l e Is7318]+FO=t----__l 2. Divide the numbers given below by 10, 100 and 1OOO and fill in the taore. Number Divide by 10 Divide by 100 Divide by 1000 a. 61056 aR aR aR b. 86044 c. 1L638 d. 2906s 3. A group of 4383 children went for trekking. There they formed groups of 100 for doing group activities. How many groups did they form? How many children were left? 4. A club collected a fee of 172800 from 1OO students. How much did each student pav to the club? 5. A farmer has 220 apple saplings. tf he sows 10 saplings in a row, how many rows of apple trees will be there? 6. Fitl in the blanks. a, 698 + 100 gives Quotient = and Remainder = b. 706 + L00 gives Quotient = and Remainder = c. + 100 gives Quotient = 3 and Remainder = 51 . d. 9684 + 1000 gives Quotient = and Remainder = e. 5123 + 1000 gives Quotient = and Remainder = f. + 1000 gives Quotient = 8 and Remainder = 206.

Fill in the empty boxes, L. 4873+ 11 =[]. 2. 1e836+e=f---l 3. The product of two numbers is 110. lf one of them is 11, the other number is 3ee3o+3=(----__-l s. sooo*roo=a---l and Remainder = [--*-_l zzse + zz =[---_) 462 + L00 gives Quoti\"nt = (----l Complete the following problems of division by filling in the boxes. a. tlLJ JI] -'l2n6 s 13 n s 2 -3 o ,l t l1 -25 - |4);zl Properties of Division 1. When a non-zero number is divided by 1, the quotient is the number itself and the remainder is zero. Examples: 25+I=25 728 + 1,= 728 5329 + 1,= 5329 2. When a number is divided by itsell the quotient is l and the remainder is zero. 1,Exa mples: 310+310= 8762+8762=! I786L2 + 78672 = 3. Division by zero has no meaning. 4. When 0 is divided by any number, the quotient is always 0. Examples: 0+56=0 0+2340=0 0 + 45941 =0

1. Divide the following using the properties of division. \".@*@=r---__-l b @.@ a c. Izrzsl+@=[--__=l @.@=t----__-l r \" @*@=(-] @.@=---__-l Estlmating Quotient Estimating a quotient is a way to get an approximate value of the quotient. We can get estimated quotient by dividing the rounded values of dividend and divisor. Examplel: A classroom of 28 students used 613 pencils in a year. lf all the students used the same number of pencils, find the estimated number of pencils used by each student. Round the divisor to the nearest ten and the dividend to the nearest hundred. 613 rounded off to the nearest 100 becomes 600 and 28 rounded off to the nearest 10 is 30. 600+30=20 5o, each student used approximately 20 pencils in a year. Example 2: Estimate 756 + 81. 756 rounded off to the nearest 100 is 800 and 81 rounded off to the nearest 10 is 80. 800+80=1.0 Thus, the estimated quotient is 10. 1. Estimate the quotient. (Rou nd off the dividend to the nearest 100 and the divisor to the nearest 10.) . @*@=[---__-l b. F-ra=a2t=f---l . r--;;- a _- r---------------l L \"11_J = t_________J -;-r ':Jtd.

\\ e. *[-1t= i ,442-l= n. +fs4-l= A box contains 572 g ofsugar. lf we need 12 equal servings ofsugar, estimate the amount of sugar in each serving rounded off to the nearest 10. 3. There are 23 fish tanks and 643 goldfish are to be placed equally in these fish tanks. Estimate the number of goldfish in each tank rounded off to the nearest L0. Sami has collected 643 stamps and wants to place them in an album. The album has 82 pages. Estimate the number of stamps that can be placed on each page rounded off to the nearest 10. Make cards with numbers from 1to 20 written on them. Distribute them into 3 piles such that the total in each pile is the same. Mixed Bag 1. Mr Krishna has 15,848 in his bank account. lf he withdraws I 1956, how much money is left in his account? 2. In a school assembly, 725 students are standing in rows and columns. lf there are 25 rows, find the number of columns. VE students of class lV have put up an exhibition on 'Global Warming'. 750 parents visited the exhibition on the first day and 289 parents on the second day. How many parents visited the exhibition in the two days? Present a short report on'Global Warming-lts Causes and Consequences'. As part of the Environment Club activity, a group of students collected 32 -l<-- n\"*rp\"p\"rs from each block of an apartment. lf there are 112 blocks in the apartment, how many newspapers were collected in all? lf 8 newspapers can be recycled into one notebook which is to be donated to needy children, how manv notebooks were donated? What value is seen in this action of the students? Create an interesting ob.iect with recvcled material.

L5 Shashank and two of his friends went to buy notebooks. The shopkeeper said, 'lf you buy one notebook, it will cost you { 46 each but if you buy a bundle of 5 notebooks, it will cost vou ( 22 each'. Shashank and his friends decide to buy a bundle of 5 notebooks and 1 notebook separately so that they 8et 2 notebooks each. How much will each child has to pay? What is the cost of 1 notebook in this transaction? Do vou think it was a right decision on their part? What quality do You observe in this action of Shashank and his friend? a. Patriotism b. Team spirit c. Decision making and cooperation zMental Maths Who am l? 1-. I am a number greater than 20 and less than 25. When lam divided by 11, I leave a remainder 2. I am I am a number less than 60, but greater than 48. When I am divided by 6, the remainder is 0. lam 3. I am a number greater than 56 and less than 66. I leave 2 as remainder when divided by 7. I am 4. I am a number greater than 50 and less than 60. I leave I' as remainder when divided by 9. I am 5. lam a number greater than 14 x 5 and less than 15 x 5. When I am divided by 5, lleave a remainder 1. lam ry[atugj A-u4n7 obiective: To reinforce the understanding of remainder in division Materials required: Shells, slips containing simple division problems with remainder Method: Teacher distributes slips with 5 Dividend Divisor Quotient Remainder division problems to pairs of students. one student picks up the first problem, a' say 29 + 5; divides 29 shells into groups b. of 5. The other student observes the number of groups formed, number of shells left, and records the observations' _ilFl62t l-4

Multiple Choice Questions 1. Rishi has t 195 and he wants to buy pens. Each pen costs { 15. How many pens can i he buy? b. L5 c. 13 d. 12 a. 1,4 2. The oroduct of two numbers is 2000. lf one of them is 40, the other number is a. 1600 b. 40 c. 50 d. 80000 is3. Sahana paid { 3960 towards half-yearly membership in a gym. The monthly fee i a. (600 b. {660 c. {400 d. ?350 i 4. 8019divided by1000givesquotientand remainderas-and- : respectively : a.t.. 860v;i 1LJ9 bP.. 8o;' 1Lr9 c. 8;190 d. 80;20 : 5. The money collection towards a one-day trip amounted to { 6000. lf 30 students are i : going for the trip, then the contribution of each student is a. ? 300 b. t 250 c. { 400 d. { 200 6. 1.2 bags weigh 480 kg. The weight of one bag is a. 30 kg b. 60 kg c. 40 kg - d. 35 kg 7. 60000 Daise amounts to a. {6 b. {600 c. {-6000 d. {50 8. steve took 6005 sweets to his class on his birthdav. He distributed them equallv among his 30 friends. The number of sweets leftt with him is I a.3b.2c.5d.4: g. Sammytyped 25 linesinonepage. lf thereare3T5 lines to be typed, the number of i pages that he will need is c. 15 - d. L6 : : a.25 b. L7 : rs10. Tlhhe number otf hourss iIn 4z2b6u0 mrinnuutteess is : u. +- r a. t! .-tt d. 48 i 11. Rohini bought a box of mangoes in which 2 were rotten. The rest she placed in 51 i .: bags with 6 mangoes in each bag. The number of mangoes she bought is a. 308 b. 302 c. 303 d. 300 i 12. The smallest number that can be added to 4L7 so that it is divisible bV 11 without i -lear\\vnings 2a raemtalninadtper tiss : a. 5 b.4 c. L :

1. The number of students in each class of a school is given below in the table. IClass Number of Students I 129 L32 ]:;ll 1 1qn lll I I I'rv, -tou how many students will be there in each section? b. lf the number of students of Class ll are divided equally into four sections, then how many students will be there in each section? lf the number of students of each of Classes t, lV and V are divided into five sections, then how many students will be there in each section of each class? Class I Number in each section l lf students of Classes I and ll go for a picnic in five buses (equally distributed), then how many students will go in each bus? How many students will be left who cannot be accommodated in the buses? e. lf students of Classes lll, lV and V watch a documentary on animals in 5 halls, then how many students will watch the documentary in each hall?

Factors t,*. qirlj Anjali has L6 muffins. she wants to arrange them in different ways so that the muffins are equally grouped, and no muffins are left. Muffins can be arranged in one group of 16 muffins or 16 groups with one muffin in eacn group. i0ieTstoe*tTdTet [1 x 16= 16or16x 1= 16] itid i- -- ii Muffins can be arranged into two groups of 8 muffins or 8 groups with two muffins eg ds 60 in each group. [2x8=16or8x2=16] AAAA-t:She cannot make three groups, since 1muffin will be left. tea o\\ 0 * Muffins can be arranged in four groups d a/ * of 4 muffins in each. 4x4=16 \\0/ \\./ \\e/ \\y Thus, the number L6 can be expressed as: L x L6 or 16 x 1; 2x8 or I x2 ; 4x 4. Herc, L,2, 4,8 and 16 are all the numbers we multiplied to get 16. Hence, we can say IhaI L,2, 4,8 and 16 are the factors of 16.

Also, 7,2, 4,8 and 16 are the numbers which can divide 16 without leaving any remainder. Thus, in other words, factors of a given number are the numbers which divide the given number without leaving any remainder. Let us see in how many ways 24 can be w= divided without leaving any remainder. :2.t< 12 = 3x8 = fhus, I,2,3, 4, 6,8,12 and 24 are the 4xG = factors of 24. 1. Fill in the blanks. x36 a. 30=1x 30=2x x10 36=2x x5 36=3x 30= 36=4x 30= 36=6x Factors of 30 are Factors of 36 are c. 56--Lx d. 81 = x81 56=2x 8L=3x 56= xL4 81 = x9 x8 Factors of 81 are Factors of 56 are Factorisation Every number has 1 and itself as its factors. We can find the factors of a number by multiplication or division. Example L: Find the factors of 45 by the method of division. Step 1: 45 + 1= 45; since 45 + l does not leave a remainder, hence l and 45 are the factors of 45. Step 2: 45 + 2; since 45 + 2 will leave a remainder, hence 2 is not a factor of 45. Step 3: 45+ 3 = 15; since45+3 does not leavea remainder, hence3 and 15 are the factors of 45.

Step 4: 45 + 4; since 45 + 4 leaves L as remainder' hence 4 is not a factor of 45' 45 + 5 = 9; since 45 + 5 does not leave any remainder' hence 5 and 9 are the factors of 45. Hence, the factors of 45 are 1, 3, 5, 9' 1\"5 and 45' Example 2: Find the factors of 64 by the multiplication method' Step L: L x 64 = 64 (thus, 1 and 64 are the factors of 64) Step 2: 2 x 32 = 64 (thus, 2 and 32 are the factors of 64) Step 3: 4 x 16 = 64 (thus' 4 and 16 are the factors of 64) Step4:8x8 = 64 (thus' 8 is a factor of 64) Hence, the factors of 64 arc 1,2, 4' 8' L6' 32 and 64' Example 3: Examine whether 2 is a factor of 28 or not' To check whether 2 is a factor of 28' divide 28 by 2' 28 + 2 = !4. so,28 + 2 leaves no remainder' Thus, 2 is a factor of 28. b. 5 is a factor of 35. Example 4: check it a. 3 is a factor of 41' l5t13 7 -e,,fi tt s -3 5 11 -9 2 Here,4l-:3 leaves a remainder 2' Here,35 + 5leaves no remainder' Hence, 5 is a factor of 35' Hence, 3 is not a factor of 4l-' Find the factors of the following numbers' c. 42 '. a. 54: h. 2b\"

1. Write the factors of the given numbers. a. 40i b. 28i c. 5b: o. b6: e. f. 96: 2. Check if the first number is a factor of the second number. lf yes, put a tick (r') or else Put a cross (r). b. 3, L5 t_l c. 9,72 .J 8,36 Oa. 5,60 tlf. 3,22 D7,63 DOh. LlA Oe. 6,32 DDK. 2,73 Di. 6,66 Cj. 4,48 qql t_l 3. Find the factors of the following numbers using division as well as multiplication methods. a. 32 o. bo c. 75 d. 81 e. 93 Factor Tree A factor tree gives information about all the factors of a number. 1 is not there in a factor tree since everv number has L as its factor. Let us draw the factor tree of 24. We can have more than 1 factor tree for a number. Last row in all the factor trees are same, 2x2 x2=

Common Factors A number is said to be a common factor of two or more numbers, if it is a factor of each of the given numbers. Example 1: Find the commonfactors of 12 and 15. thotlisofoctor 12 = lx12 15 = 1x 15 of every number ond = 3x5 = 2x6 every number is a = 3 x4 fqctor of itself The factors of 12 are The factors of L5 are 1, 3, 5 and 15. I,2,3, 4,6 and 72. 1 and 3 are the factors common to both 12 and 15. Thus, the common factors of 1.2 and 15 are 1 and 3. Example 2: Find the common factors of 36 and 48. 36 = 1x36 48 = 1x48 = 2xL8 = 2x24 = 3xL2 = 4x9 = 3x16 = 6x6 = 4xt2 = 6x8 The factors of 36 are 1\", 2, The factors of 48 arc I,2,3, 3,4,6,9,12,18 and 36. 4, 6, 8, L2, 1-6,24 and 48. I, 2,3, 4, 6 and L2 are the factors common to both 36 and 48. Thus, the common factors of 36 and 48 are 1, 2,3, 4,6 and 12. Highest Common Factor Highest common factor (HCF) of two or more numbers is the greatest common factor of the numbers. Example 1: Find the HCF of 66 and 32. 32=lx32 66 =1x66 =2x33 =2xL6 =3x22 =6x11 =4x8 The factors of 66 are L,2,3, The factors of 32 a rc 7,2, 4, 6, 1,7,22,33 and 66. 8, 16 and 32.

2 is the only common factor of 66 and 32. Thus, 2 is the HCF of 66 and 32. Example 2: Find the HCF of 84 and 128. 728 =txL28 =2x64 84 =1x84 =2x42 =4X32 =8x16 =4x2L =6x14 The factors of 1.28 are t,2, 4,I, . =7 xI2 t6,32, 64 and 128. . The factors of 84 are I,2, 4, 6,7, L2, L4,21,42 and 84. The common factors of 84 and 128 are 2 and 4. Thus, the highest common factor or HcF of 84 and 128 is 4. Prime and Composite Numbers The factors of 2 are 1 and 2. similarly, the factors of 5 are 1 and 5. But, factors of 4 are I,2 and 4. Numbers which have only two factors, 1 and the number itself, are called prime numbers. All the other numbers which have more than two factors are called composite numbers. 1 is neither a prime nor a composite number \"s1., Draw factor trees of the following numbers. d. 45 e. 54 a. 80 b. 30 c. L8 i. 42 j. s0 f. 60 h.28 2t,28 2. Find the common factors of the following pairs of numbers. 64,72 a. 24,36 b. 32,8 c. 12,20 d. 48,72 99 f. 10,25 E. 54,26 h. 2s,40 i. 72,8L b4 3. Circle the prime numbers and cross out the composite numbers 13 15 20 23 31 35 L7 47 58 727 81 L95 29 37

4. List all the prime numbers between l and 20. 5. Which is the smallest prime number? 6. Find the HCF of the following pairs of numbers. e. 88, t2 a. 27,24 b. 50, 100 c. 28,4O j. 93,36 t 55, 11 g. 33,66 h. 49,84 Even and Odd Numbers lf a number leaves no remainder when divided Remember by 2, it is an even number. fhot 2 is o focior of oll the Example: Find whether 52 is an even number or even numbers but not for ony an odd number. of the odd numbers. 52 + 2 = 26. 5o, 52 + 2 leaves no remainder. Thus, 52 is an even number and 2 is a factor of 52. lf a number leaves a remainder when divided by 2, it is an odd number. Example: Find whether 63 is an even number or an odd number. 63+2=31- (quotient) and 1 (remainder) Thus, 63 is an odd number and 2 is not a factor of 63. a. Circle the even numbers. b. Circle the odd numbers. 3, 4, 10, t7, 18, 20 2, 5, 7, II, L6, 2I Multiples The multiples of a number are found by taking the product of that number with anv counting number. ln a residential colony, all thehousesarenumberedZ(2x1,),412x2),6(2x3),...upto 100 (2 x 50). We can see that each house number is the product of 2 with a counting number. Thus, these numbers are multiples of 2. In another residential colony, allthe house numbers follow a different Dattern.

3)The houses are numbered 5 (5 x 1), 10 (5 x 2), 15 (5 x up to 100 (5 x 20) Wecanseethateachhousenumberistheproductof5withacountingnumber. Thus, these numbers are multiples of 5' Similarlv 3, 6, g, L2, f5,18 . . are all multiples of 3' 4,8, L2,76,20 ... are all multiples of 4' 6,12,18,24, 30 ... are all multiples of 6' Note that there are countless multiples of a given number' Example: Find the multiples of 7 and 9' The multiples of 7 arc7,14,2t' 28' 35' 42 ' ' ' The multiples of 9 are 9, 18, 27 ' 36' 45' 54 ' ' ' Common MultiPles Let us consider the multiples of 4 and 6' Multiples of 4: 4,8, L2, L6,20,24,2A,32'16' 40 \"' Muf tipf es of 5: 6, L2, LA, 24, 30, 16, 42, 48' 54' 60 \"' From the above, we can see that 12, 24 and 36 are the multiples common to both 4 and 6' A number is said to be a common multiple of two or more numbers if it is a multiple of each of the given numbers. Example: Find the first three common multiples of 2 and 5' 2:Multiples of 2, 4, 6, 8, LO, 12, 14, 76, L8, 20, 22' 24' 26' 28' 30 \"' 5:Muftiples of 5, LO, 15, 20, 25, 30, 35, 40' 45, 50 \"' The first three common multiples of 2 and 5 are 10, 20 and 30' Least Common MultiPle Least common multiple (LCM) of two or more numbers is the smallest common multiple of the given numbers. Example 1: Find the LCM of L8 and 24' Multioles of 18: 1A'36'54'72'90 ' ' MuftiPles of 24: 24' 4a,72' 96 ' ' ' Here,72 is the smallest common multiple of 18 and 24' Thus, the least common multiple of 18 and 24 is 72'

Example 2: During the summer months, one ice cream vendor visits Maria,s neighbourhood every 3 days and another ice cream vendor visits her neighbourhood everv 6 oays. lf both the vendor3 visited Maria,s neighbourhood today, then which is the next day when the two vendors will visit together? . Multiples of 3: 3, 6, 9, t2, LS, fa, 2L, 24, 27, 30, 33, t6,39,42, . . . Muf tiples of 6: 6, 12, L8, 24, 30, 36, 42, 49, 54, 60, 66, 7 Z, 78, 84, . . . The common multiples of 3and 6 arc 6,12, La,24, - . . The lowest common multiple of 3 and 6 is 6. So, the vendors will visit Maria,s neighbourhood together after 6 days from todav 1. Write down the first ten multiples of 4 and 5. Also circle the common muttiples. 2. Find the first five multiples of the following numbers and circle the common multiples, if any. a. 4and2 b. 5and4 c. 3and9 d. 5and6 3. Find the LCM ofthe following pairs of numbers. a. 9,24 b. 14,32 c. 8,20 d. 9, 15 e. 1,4,24 f. 30,60 h. 78,22 i. 45,72 j. s0,70 4. Find the HCF and LCM of 72 and 27. Raghav and Kunal are playing with marbles. The number of marbles with Raghav rs a multiple of 3, 5 and 15 but not a multiple of 10 or 30. The number of marbles with Kunal is the lowest multiple of 43. lf Raghav shares one marble with Kunal, both will have equal number of marbles. How many marbles does each of them have?

DivisibilitY by another number if the second number is a factor of the first the say that a number is divisible by another number if A number is divisible division of nuti\". ntro, *\" .an first number by the second number leaves no remainder' Example 1: Examine whether 18 is divisible by is o prime number if it is 2 or not. divisible bY 1 ond itselt. on dividing 18 bY 2, we get zero as remainder. A number is comPosite if it con Thus, 18 is divisible bY 2' be divided without o remotnder Example 2: Find whether 21 is divisible by 3 or bv' numl obnedrsiotstheerlft.ho'n/ noT. On dividing 21 bY 3, we get zero as remainder. Thus, 21 is divisible bY 3' Example 3: Find if 24 is divisible by 5' On dividing 24 by 5, we get 4 as the remainder' Thus, 24 is not divisible bY 5' There are certain divisibility rules to find out whether a number is divisible by the other numbers or not. DivisibilitY Rules DivisibilitY bY 2 A number is divisible by 2, if the digit at the ones place of the number is o, 2, 4,6 or 8' Examples:34, 152,278 are divisible by 2' DivisibilitY bY 5 A number is divisible bY 5, if the digit at the ones place of the number is either 0 or 5' Examples: 40, 155, 385 are divisible bY 5. Divisibility bY 10 A number is divisible by 10, if the digit at the ones place of the number is O' ExamPles: 90, 180, 590 are divisible bY 10' 10' 794 ExamPle: Find the numbers which are divisible by 2' 5 and 145 126 235 630 r25 736 Lb5 70 22

The numbers divisible by 2 are 22,70, LZ6, I94,630 and 736. The numbers divisible by 5 are 70, !25, L45,165 and 630. The numbers divisible by 10 are 70 and G3O. 1. Write all the numbers between 3OO and 350 that are divisible bv 5. 2. Find the numbers divisible by 2 and 10. Out of these, which numbers are divisible by both 2 and 10? L32 280 455 904 r)u 505 236 L00 764 749 3. A teacher wants 106 students to sit in columns with 10 students in each column, without any student being left out. Find out by using the divisibility rules, whether it is possible or not. Rohini wants to pair 42 balloons without leaving any balloon unpaired. Find out by using the divisibility rules if she can do that. 5. Akshay wants to pack 50 balls equally in 10 bags without leaving any ball. Find out without dividing if he can pack them. areL. The two fuctors of 13 and 2. Check whether 545 is divisible bv 5 or not. 3. lf6x9=54,then a.54isa_of6and9. b.6andgare of54. 4. The first four multiples of 16 and 32 are The LCM of 16 and 32 is Wo@@ ffi A plant has 3 leaves. They double every day. How many leaves will be there on the fifth dav? *- -...#8_

YY *u Two butterflies want to hide behind the wall to escape a bee attack. They want to hide behind only those bricks that have three-digit numbers, the sum of whose digits is divisible by 5 (for example, I72,1+ 7 +2 = 10 which is divisible by 5) or a two-digit number which is prime. circle the bricks behind which the butterflies can hide. aDtjhurutsrjl!tl7ul objective: To find the factors of a given number, check for prime or composite number and check for divisibility Materials required: Notebook and pencil Method: The teacher assembles the students into groups of three. He/She gives different numbers to the groups. For example, he/she gives 34,44,50, 54,60, 65 and 72 to one group. One student finds the factors of the numbers. As soon as he/she is done, the second student tries to see if each of the numbers is a prime or a composite number and then the third student tests if the numbers are divisible by 2, 5, 10, any two or all the three.

L. Write the common factors of the numbers. a. t5, 20 b. 15,25 c. 18,30 t4,38 e. 25,30 f. 28,24 g. 30,32 56,20 1 Find out if the first number is a factor ofthe second. lf yes, put a (/) or else pur a (x). tl f_-l Da. tla. 5,65 u. a, ro c. e, ss 8,56 C t f_-l Dn. De. 6,30 s,og e. 7,64 4,2A 3. Find the first ten multiples of the following; a. 2and4 b. 6and7 c. 8and9 d. 10 and L1 4. Find the LCM of the following pairs of numbers. a. 9,33 b. 8,20 c. 10, 15 d. 50, 1s0 e. 96,24 5. Fill in the blanks. itsell a. The largest factor of any number is the b. The smallest multiple of 5 is and c. The number of even numbers between 1 and 100 is d. The number of odd numbers between 1 and 1OO is e. The smallest and largest factors of 56 are 6. Find the HCF of the following pairs of numbers. e. 70 85 a. 28,62 b. 66,90 c. 25,70 d. 24,56 7. A piece of cardboard measures 140 cm. lt has to be divided into 35 equal pieces without anything being left. See if it is possible. 8. Find the numbers between 45 and 75 that are divisible by both 5 and 10. 9. Find the numbers between 83 and 91that are divisible by 2. 0. List any four factors of 90 and the first five multiples of 13.



6 When a whole is divided into equal parts, then each equal part is called a fraction. ))pppl ? of the balloons are red. ofthe part _ Number of parts coloured _ 2 <_ Numerator Total number of 5 Denominator ' partsFraction <- coloured 1. Represent the fractions. a. b. Colour 1 of the leaves green. @646@6@6@6@6@6@6@6@6 2. Fill in the blanks. ,D. L .__. c. 1of 32is d. 1of 40 is a. lof L8is -OrZltS 5

jii portion is shaded. In those figures, colour the remaining 3. ldentify the figures in which portion red. a=-=Dh 4. Match the following. One has been done for you. L / One-third offiffi 5 c. ,3p paa ? One-fifth d 1 Two-thirds 5 \\1/ Three-fifths 3 5. jAnita finished of her home assignment having 12 questions. How manV questions has she answered? Representing Fractions Effisrnsldq\\.* Roshni ate half of a pizza. Sameer ate half of the leftover portion. Then Roshni ate half of what was left. How much pizza is left? Let us represent this pictorially. Fraction of pizza, Roshni ate first Fraction of pizza left by Roshni 1\\21, r=1\\ D /1\\ \\' 2t € w Fraction of pizza left by Sameer / 1\\ Fraction of pizza, Sameer ate \\_4/ g I\\/!2,,241=t'2l\\[4n'\"rot 1r

Fraction of pizza, Roshni ate second time (\\1z-1x-+'=l i)6l1H\\tr- atfof.+41is:6tl1- Let us see who ate more pizza. rtf-'\\ Portion of pizza eaten by Roshni [Etn7^ [5 out of 8 portions is !1 (lOh:\",t*\"-i' =EtZ Portion of pizza eaten by Sameer 8 [2 portions out w@\\7i 3[2 out of 8 portions is of 8 portions.j ? 8 lf we observe the portions of the pizza, we can see that Roshni ate more pizza than Sameer. Remember, To find half of something, we divide by 2 or multiply by 1. To find one-third of something, we divide by 3 or multiply by 1. ]To find one-fourth of something, we divide by 4 or multiply by and so on. There are two halves, three one-thirds, four one-fourths and eight one-eighths in a whole.

Fraction of pizza, Roshni ate Fraction of pizza left second time /1\\ /\\12,4.81t='41S\\J[u\"ttot 1 irll \\s/ Let us see who ate more pizza. ELn*7/^ I[5 out of 8 portions is Portion of pizza eaten by Roshni ffin';nm\":i' Portion of pizza eaten by Sameer s f^ pon_r.ons our A\\tIv,A lz out of 8 portions is ?1 LZ of 8 portions] ? 8 lf we observe the portions of the pizza, we can see that Roshni ate more pizza than Sameer. Remember, ].To find half of something, we divide by 2 or multiply by ) ' '3To find one-third of something, we divide by 3 or multiplv bv 1. lTo flnd one-fourth of something, we divide by 4 or multiply by ano so on. There are two halves, three one-thirds, four one-fourths and eight one-eighths in a whole.

Equiva lent Fractions' r.,liw-vffir Ekta has 8 apples. she wants to share a few apples with her four friends' bbbbffi:\",',:i:;;, bbbbffiJ?-x.i+, LASC I: She gives L apple each to her four friends. {.The fraction of apples left with her is 8 Case 2: OOOO Appresrefte\\ She cuts each of the 8 apples into 2 halves and then oooo withEktala gives 2 parts each to her four friends. ].The fraction of apples left with trer is 16 OOOO Appressiven OOOO toherfriend We can see that the portion of apples left with her in each case is the same. 9trl \"'-'' 16 8 2 These are called equivalent fractions. Two fractions are said to be equivalent if they have the same value' To find an equivalent fraction of a given fraction, multiply both the numerator and denominator by the same number observe all the figures carefully. You willfind that though the rectangles have been shaded in different ways, the shaded portion is half of the whole rectangle in each figure. \\te\\2)t /1\\ \\/4t/\\ \\/4-t\\ /\\2;i\\ -tn,us,'2-t2= 4 4 8 Example: Fi nd any three equivalent fractions otZ. 3 Multiply the numerator and the denominator of the fraction by 2,3 and 4. .-tffi

23xx22_46.'23xx33 -69.2'3xx44 _ I L2 69 1,2Thus. 4. 6 and 8 are three eouivalent fractions of 2. 3 What portions of these figures are shaded? Write two equivalent fractions for each. Reducing a Fraction to its Lowest Term A fraction is said to be in its lowest term if the numerator and the denominator have only 1 as the common factor. txamole: S-.imo.li.tv.'2-30-2to. .i.ts lowest term. 32 3ZL6 16 (,D_i.vi.d,.ing the numerator and the denominator by 2.) i= i ,O= ; L.g 8 R 4rr ) 5 There is no common factor between 8 and 5 other than 1. -t,n3u2's28,0 reouceo to tls towest term t5 5 1. Tick the figures which show equivalent fractions. One has been done for you. a. d. .. tri \"AA/:,1'',

) 2.) Colour the following pairs offigures to show equivalent fractions' \\'##..,a'wa fzw 's+ ffiLTr'l '. '. loE*1zFl$qIU/////// r I iI.l 3. Fill in the boxes with suitable numbers to let equivalent f ractions. \" +rrv=Ll+=+=+ b. 1 5 4 .\"8136_32Ll-Ll-_1111 n3 LI . 15 o. 1 LI 16 trl-t 2 L0 5 6 4. Find 5 equivalent fractions of the following: 6 7 ai 21 b'i A o. 5 2 C.-= +\"j--7=14 12 8 5. SimplifY the following fractio ns to the lowest term. q.8 L0 d. 44 a15o'i4 c. 45 60 h. 78 36 e.*te.8q0 55 27 81 Like and Unlike Fractions ryttlt;txq tv Fractions which have the same denominator are called like fractions Itxample, Z and 1 are like fractions since they have the same denominator' that is' 5' Fractions which have different denominators are called unlike fractions' ], ]rxamnle, Z ana are att unlike fractions since they have different denominators'

Comparing Like Fractions Jimmy and Saira painted flower pots in their garden. Jimmy painted 2 out of 5, that is, 3 of the 5 Ipots and Saira painted 3 out of 5, that is, of the pors. ' 5 Who painted more? To compare like fractions, compare the numerators. The fraction with the greater numerator is the greater fraction. >:Hence,\":,)1a. or -a < -. Thus, Saira painted more pots than Jimmy. )555 Example 1: Find the fraction ofcoloured balls in both the groups. Which fraction is greater? er.unr:QOOOOOOO606 er.unz:QOOOOOOOO06 In the first group, 6 balls out of L1 are coloured. Thus, the fraction of 9.coloured balls is 11 In the second group, 10 balls out of 11 are coloured. Thus, the fraction of coloured balls is 19. Lt j11 fand L\\ are like fractions. In like fractions, the fraction with the greater numerator is greater. H\"n.\".'71tot L6Lo,. 5.10 It 7L Thus, the second group has more number of coloured balls. Example2: Arr\"n-\"\" 1. 9. 7. 3 in ascending order' 13- 13 L3 13 On comparingthe numerators, we get 1< 3 < 7< 9.

I 9.Thus, the ascending order of the given fractions is 13. -113. Z13. 13 Z, a Example 3: arr\"ng\" 4, 127, 2t in descendins order. 21 27' On comparing the numerators, we get L1- > 7 > 5 > 4. the ofthe given >'L'J' 7 > 5 >4 21, - 2t 2LThus, is 27 descending order fractions 1. Circle the group of like fractions. One has been done for you. D. L1'13'10 - 222 7'9 11 d.4. ?q ._:._: =^ 5 11 9 555 13', 13 13 L7'17'L? n'19'^ 2. Choose and circle the odd one out in the following groups of like fractions. One has been done for vou. l ^\" ,s'fVs\\T7 ?D. -8. ' 5 18 13't 13' 13 T' 8.9 \"a' 71 23 LO 9 q9 5 41826 E,2523,E t3 13 39 39', 39 38 3. Shade the following figures as per the given fractions and then compare. CC r)Uatt,r) ottt\".CC O 2 rlt- 42 77 c. 4 7 9 9 4. Use >, < or = to compare the given fractions. a.- L 7 /-\\ c c.- 8 .) 11r_J 11 I5 1.3 1o t-o ^ 9 --]t 7 Q /\"\"\"\\ 't 1 1 7 n.4. - 20 r_) 20 zJ \\-----J 2l 33 n 55

5. Arrange the following in ascending order. \"- n53'1n7'i'i Q 2 11 L 11 9 5 13 25 25 25' 25 c. 47' 47'n' 47 .-l 1! !1 e- I? q 1'l 2 f. 22 7 1-1, 8 1-7'L7'17' 17 1=-7::':7: 7' 45' 4( 45' 45 17' 17 6. Arrange the following in descending order. \"_'91rg8' 3Es' 19' rg .- 439 -1, 7 51,1, 1-7 1,7 77'77' 17' c. \"n'59l{3i8'i'i -t -1 LL L n'i'i'nt ^s'21o3--1z1l':9r L0' 1-O' tO' 10 Addition and Subtraction of Like Fractions Addition of Like Fractions To add like fractions, add the numerators and write the sum over the same denominator Examplel: Add'137* 12,7* 4 77 Add the numerators. 3+2+4=9 Write the sum over the same denominator. a. 8168 Thus1,,73*127*41=7917 'rAA Example2: Add' 72 7*73 * 1 D. 'lc o la Add the numerators. aL1 2+3+1,=6 c. Write the sum over the same denominator. (Hint: Make them like l11r fractions first) '7 7 7 7 Example 3: John brought 11 candies to school. He ate 3 candies -i.;t*,.\"1, and his friend ate 2 candies. What fraction of candies did they eat in total? Represent the answer as a fraction. 1Fraction of candies John ate = '1,),

aFraction of candies his friend ate = LI iTotal number of candies eaten = 2 3+2 ) + .l.l 11 11 !Thus. thev ate of the candies. 11 Subtraction of Like Fractions To subtract two like fractions, subtract the numerators and write the difference over the same denominator. txamo'te t: 5ubtrafi.:7-12- 5 txample z: .8 3 5uDrracr: --t -t2 Subtract the numerators. Subtract the numerators. 7 -5=2 Thus, 8 8-3=5 9 Write the difference over the Write the difference over the same denominator. ].same denominator, i.e. q -'','7-'5' 122 L2 72 Example 3: Anshu read 10 pages on Monday and 4 pages on Tuesday. lf there are 21 pages in the book, then on which day did she read more and by what fraction? 'Fraction of pages she read on Monday = 19 21, '21jFraction of pages she read on Tuesday = ' - j2]!1By comparing the fractions, we get > 21, Thus, she read more number of pages on Monday. To find the fraction of pages she read more, subtract the fractions. LO_4 _LO-4 _6 __.62 _2 21 21 21. 21 Zt1 7 i2 Thus, she read I pages more on Monday than Tuesday.

AAoths Around Us Dr Sehgal had to travelto a village to treat an old woman. The village is 36 km away from the city he lived in. He covered half of the distance by train. From there, he boarded a bus and travelled one-third of the total distance by it. He then took an auto for the one-ninth of the total distance to reach the main road of the village. From there, he had to walk as therg was no transportation available. Can you find out how much distance he had to walk? ADistance covered by train = of 3O km = km lDistance covered by bus = of 36 km = km IDistance covered by auto = of 36 km = KM -Distance covered by walking = 36 km Km= KM He knew that the total distance from the city to his destination is 36 km. He had calculated the distance he needed to cover by walking with the use of fractions. The distance came out to be 2 km L. Write an addition fact for each of the followine. One has been done for you. b&a. qD t v,,'O\\7.1 8 14 1-4 t4 -tr6l o. ooooo .CCCC COOCC