ຄະນິດສາດ_Math

• 0Ao8vodko7yfw]jD 7jkoE,ao]qf 7jk0hk,0q; 7jkvkskomjP’ 7kj xUg0Qk-q,l;olaf ^70 # 2h ' 10 # 8200 + ^2000 # 2h + 52000 + ^5000 # 2h + ^3000 # 2h 140 4000 10000 6000 14 180800 186800 114800 118800 170800 @D 9qj’c8j’39f[aosk8k,37’Ijk’]j5,oUD ]k7k0kpma’\\qf &@ WWW du[ ສະຫງສ.ວວນ.ລິສຂະສິດ ]k7k\\kddhP’ + ]k7k\\kdmao $W WWW du[ !@ WWW du[ x x ]k7k\\kd oE|ad\\kd ]k7k\\kd oE|ad\\kd dhP’ ! kg dhP’ mao ! kg mao & WWW du[ ) kg # WWW du[ $ kg #D vu’8k,37’Ijk’.o0=h @ 9q’j 0Po8n,j .lj[vj o9Eg,af0v’ltg\\uzqo]5j,oUD 52 000 = . . . + . . . 52 000 = ( . . . x . . . ) + ( . . . x . . . ) II. .97;k,D { djvo9tcdh39f[aosk.f|b’j 8hv’;yg7kt7e39f c]t lhk’0Ao8vodkocdh[ao sk 9kdoAofegouodkocdh8k,0Ao8voD { dvj o9tlhk’39f[aosk|bj’0Bowfh 8hv’gda[de0=h,6omu,j u.sh4nd8hv’D 98

III. [qfg/udsafD !D 16j3I’]t7vocs’j |b’j D { g[nhv’0;k0v’mk’zkj odk’,u8aj’oaj’ !) c4;M]t !& |j;pD { g[nhv’-hkp0v’mk’zkj odk’,u8aj’oaj’ !) c4;M]t @W |j;pD 8voc]’,nhohu,u7qog0Qk-q, $!W 7qoD 4k,;jk9t,u8a’j s;jk’9ad[jvoD dD 9qj’lhk’37’Ijk’cdh39f[aoskD 0D 9qj’0Poltg\\uzqo8k,37’Ikj ’.o0=h dD @D 9qj’c8’j 39f[aosk8k,37’Ijk’cdh39f[aosk]j5,oU G g’yogs^nv,kc8j8ts^kf !$ WWW du[ _ g’yo4nwx8ts^kf ]kp9kj pma’\\qf &@ WWW du[ #) WWW du[ + -N\\kdg]ajo -Nxk -Ndh;p ສະຫງສ.ວວນ.ລິສຂະສິດ @$ WWW du[ _ WWW du[ & WWW du[ x x ]k7kxk oE|adxk ]k7kdh;p 9eo;os;u ! kg @ kg ! s;u dh;p # s;u !@ WWW du[ # WWW du[ #D xhkmv’fuwx8ts^kf]k;-nhlyj’0v’8jk’Mfa’j oUG -nhxk $ dy3]dik,F dy3]dik,]t !@ WWW du[S -nh-Uo’q; @ dy3]dik,F dy3]dik,]t @& WWW du[F -nh\\kdc8’ # dy3]dik, F dy3]dik,]t & WWW du[S -nhw0jgxaf !W |j;pM]t ! @WW du[ c]t -nhzadlts^af @ dy3]dik,F dy3]dik,]t ( WWW du[D 4k,;jk]k;9kj pg’yoma’ \\qfgmqkj .f L 99

[qfmu 35 dko;afcmd];’pk; I. dyf9tdeD !D 9q’j ;afcmd];’pk;0v’I6[]5,j oUfh;pc4[g9hp s^n g-nvd A BA B E C DD C E FF I6[ dD I6[ 0D { ];’pk;0v’I6[.fpk;d;jkdao L @D mhk; o;omv’ c]t mhk; cf’ wxmjP;r6F r;dg0qkc8h,glAomk’pjk’0v’ .z]k; .lcj zomuDj 9q’j .-hg-nvdglAo|b’j pk;8k,.9grnjvcmdw]ptmk’pjk’0v’ c8]j t7qoD ສະຫງສ.ວວນ.ລິສຂະສິດ mk’pjk’0v’mhk;cf’ mk’pkj ’0v’ mhk; o;omv’ 95fg]uj,8Qo { .zpkj ’mPj ;r6wdd;jkdao L 95fg]u,j 8Qo II. .97;k,D dko;afcmd];’pk;c,oj dko-vdsk];’pk;0v’lyj’.fly’j |b’j D gryoj oe .-hly’j .flyj’|bj’grnvj .-hgxaog7njv’,n.odko;afcmdg-ajoG mvj ow,Fh c4[g9ph F gloA g-nvd ;k’8+MdaowxD 100

III. [qfg/ydsafD a !D 9qj’cmdmvj o-njG AB, CD, EF, GH fh;pmjvo-nj c]t mjvo-nj b GH BD AC EF @D 9qj’xP[mP[mvj o-nj8+wxoU c]h;9af]Po8k,]efa[c8jlAoskpk;D AB . . . < . . . < . . .<. . . <. . . C D E FJ G ສະຫງສ.ວວນ.ລິສຂະສິດ H I #D 9q’j .-h]6ddtc9oUgxaosq;|;j p;afcmdI6[ly’j 0v’8jk’MD $D 9q’j oe.-h];’pk;0v’c4[g9hp s^n glAofhkpgrnjv;afcmd];’pk;0v’I6[]5,j oUG A BA B DC D C F E F E I6[ @ I6[ ! { ];’pk;0v’I6[.fpk;d;kj dao L 101

[qfmu 36 dko;afcmd];’pk; X8+? I. dyf9tdeD !D 9qj’cmd];’Iv[0v’I6[]5,j oU3fp.-h[aomafc]h;8v[7e4k,D d0 I6[.f,u];’Iv[pk;d;jk L pk;d;kj gmqkj .f L @D 9qj’.-hglAofhkpcmd8k,Ivp37h’0v’gxnvdsvpgfnjvoU;jk ,u7;k,pk;gmqjkda[ 9ad-a’8uc,af L ສະຫງສ.ວວນ.ລິສຂະສິດ II. .97;k,D sq;|j;p;afcmd];’pk;.-hle]a[;afcmdG ];’pk;F ];’d;hk’F ];’l6’F ];’Iv[F 7;k,g]ydF 7;k,|kF w]ptmk’F D D D D sq;|j;p;afcmd];’pk;c,oj c,af X , s^n m ?F v5xt76o0v’c,af,u gf-uc,af X f- s^n dm ?F -a’8uc,fa X -8 s^n cm ?F ,yo]uc,af X ,, s^n mm ?F mt;u7o6 0v’c,fa ,u gfdkc,af X fd, s^n dam ?F gIad38c,afX I, s^n hm ?F dy3]c,af X d, s^n km?D 102

mt;u76o sq;|;j p v5xt76o d, I, fd, , f, -, ,, km hm dam m dm cm mm 130 2 403 0 50 1 km 3hm = 1300 m 4dm 3 mm = 403 mm 2 m 5dm = 25 cm III. [qfg/ydsafD !D ];’pk;0v’I6[ lujc9lkd cmdwfh $ cm c]t # mmD ];’dh;k’cmdwfh @ cm c]t ( mm . 9q’j 7yfw]j];’Iv[ 0v’I6[lujc9lkdgxao mm. @D mkh ; lvo 8fa ;’q ,oq ( ;’q ,oq F ];’pk;0v’gloA zkj o.9dk’]f5 Mdoa @ mm ]q’wx8k,]efa[grnjv8yf8+ .ljdao.shgxaoI6[[Q’D ;q’,qomu ! muj.-hgIaf sq;[Q’oAopk; !F_ cm I6[[Q’oAo9tpk; gmqkj .f L ສະຫງສ.ວວນ.ລິສຂະສິດ 1 2 3 4 5 67 #D 9q’j 8n,j .lj8k8t]k’]5j,oUG ' 100 x 100 ];’pk; ];’pk; ];’pk; ];’pk; cm m m cm 43 800 4 38 42 4 200 27 000 . . . . . 6 ..... . . . . . 2 28 . . . . . 2 400 . . . . . 42 70 . . . . . 4 ..... 300 . . . . . ........ ' 100 103

[qfmu 37 g]dlj;o I. dyf9tdeD !D 9q’j la’gdfI6[]5,j oU c]h;8v[7e4k, D 1111 4444 I6[c[’j vvdgxao9adlj;ogmqkj dao L ສະຫງສ.ວວນ.ລິສຂະສິດ 9q’j 0uf]kp.lj ! lj;o 0v’I6[ D lj;omu0j uf]kpvkj o;jkco;.f L @D 9qj’la’gdfI6[]5,j oU c]h;8v[7e4k, D I6[c[’j vvdgxao9adl;j ogmqkj dao L 9q’j 0uf]kp.lj # lj;o0v’I6[ D lj;omuj0uf]kpvkj o;jkco;.f L lj;omu[j +0uf]kpvjko;jkco;.f L lj;omu0j uf]kp c]t lj;omuj[+0uf]kp];,daovjko;kj co;.f L 104

II. .97;k,D c4[g9hppk; !W cm c[’j vvdgxao & l;j o ltg\\udaoc8j]tlj;o ,u];’pk; @ cm g-ajo G 9eo;or6f0v’g]dl;j o 11111 1 vkj o;jk|b’j lj;oshk 55555 5 r6f0v’g]dl;j o II. [qfg/ydsafD !D 9q’j vkj og]dlj;o]5j,oU D 1 24 3 ; 7 6 7 ; ; ; ; ; ; 2 35 6 8 7 11 54 8 6 15 32 ສະຫງສ.ວວນ.ລິສຂະສິດ41 ; ; ;; ; ; . 69 10 13 20 50 49 @D 9qj’0Pogxaog]dl;j o D shklj;ocxf S ly[l;j oly[lk, S |bj’l;j ogdQk S g9afl;j oly[ S sqdlj;o-k; S ly[g9afl;j o-k;shk S -k;gvaflj;olk,ly[S shkly[g9afl;j oIhvp S gdQkly[sqdlj;oIhvpS Ihvpshkly[lj;olv’Ihvp D #D 9qj’0Pog]dl;j ocmolj;omu0j uf]kp0v’I6[]5j,oU .lj[voj 9Eg,afD DDDDDDD DDDDDDD DDDDDDD 105

[qfmu 38 g]dl;j oly[ I. dyf9tdeD !D I6[lucj 9lkd X dF 0F 7F CF 9F lF - ? xtdv[fh;p I6[9t85]af muj,u0t|kf ! cm x ! cm c]t ];’pk;0v’c8]j tI6[gmqjkda[ !W 8k D dD 9q’j la’gdfI6[c]h; 0Po8nj,.lj8k8t]k’D 7 I6[ 9eo;o8kdk3i ];’pk;0v’I6[luj ];’d;hk’ c8]j tI6[lucj 9lkd c9lkdXgxao8kdk3i? Xgxao8kdk3i? 0 d d 10 10 10 ' 10 = 1 0 15 10 15 ' 10 = 1, 5 ];’pk; 7 35 10 35 ' 10 = 3, 5 C 40 10 9 25 10 ສະຫງສ.ວວນ.ລິສຂະສິດ l 52 10 - 46 10 cm 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0S 9q’j \\kp];’dh;k’0v’c8]j tI6[.ljcdo9eo;o]5j,oUS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 cm d0 @D 9qj’la’gdfI6[]j5,oUc]h;8v[7e4k,S \\ \\ 3 7 = 0,3 = 0,7 10 10 106

{ .oI6[oUc[’j vvdgxaoma’\\qf9adl;j o L { l;j omuj0uf]kp0Pogxaog]dlj;ogmqjk 3 c]tgxao9eo;omqfltoypq,gmqkj 10 WF#D 9qj’[vdrkdlj;omu[j +0uf]kpgxaog]dlj;o c]t gxao9eo;omqfltoypq,D II. .97;k,D 9eo;omugj Iqkrq[.\\gj -ajoS !F& S #F& S DDD gvhuo;jk9eo;omqfltoypq,g-y’j wfh9kd dkosko9eo;o4h;o.sh !WD 8q;1kj ’ G 15 ' 10 = 1, 5 35 ' 10 = 3, 5 { 4hk1kd\\kp.lcj do9eo;o 8hv’c[’j s;kj ’mu1j 6]ts;jk’ @ 9eo;o4h;ogxao !W l;j ogmqkj daoD 2 1 c8]j tlj;ogvuho;jk|b’j l;j oly[ gIqk0Po 1 s^n WF ! 10 \\kp7;k,;jk G 1 ' 10 = 1 = 0, 1 10 ສະຫງສ.ວວນ.ລິສຂະສິດ 8q;1jk’G ;ymuvkj o $#F& vjko;jklujly[lk, c]t shklj;oly[ s^n lulj y[lk,95fshk gIqk.lj95f X F ? 0Ao]ts;jk’rkdlj;o4h;oda[rkdl;j omqfltoypq, III. [qfg/ydsafD !D 9q’j vkj o0uf\\kpc]h;0Pogxao9eo;omqfltoypq,16jc8]j t95fD _ d 0 !W 7 C 9 l !! _F$ 0 7C &( &* d @D 9qj’0Pog]dl;j oly[]5j,oUgxao9eo;omqfltoypq, D 8 25 157 126 218 185 109 10 10 10 10 10 10 10 107

[qfmu 39 g]dl;j oIhvp I. dyf9tdeD !D 9qj’la’gdfc]h;0Po8n,j .lj8k8t]k’]5,j oU D ' 100 100 ' 10 ' 10 100 1 128 10 1 128 1,28 245 12,8 1,28 245 2,45 160 160 253 253 138 138 149 149 200 200 @D 9q’j la’gdf8q;1jk’c]h;7yfw]j[A’8+wxD ສະຫງສ.ວວນ.ລິສຂະສິດ 228 = 2 + 2 + 8 = 2, 28 393 =....................... . =............ 100 10 100 100 754 =....................... . =............ 100 II. .97;k,D gryoj wfh9eo;omqfltoypq,.\\jvudg,nvj gvqk9eo;o4h;osko.sh !WW Ɣ 9eo;ooU0Pofh;p8q;g]d0v’9eo;o4h;ooAo c]t 0Aofh;p95f]ts;kj ’ @ 8q; g]dmhkpD248 ' 100 = 2, 48 ; 1700 ' 100=17, 00 s^n 17 160 ' 100 = 1, 60 s^n 1, 6 Ɣ 4hk0Po.ljcdo9eo;o8hv’c[’j s;jk’lj;oly[gxao !W l;j o ltg\\udaoD 1,47 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 lj;oc[j’c8]j tmvj oohvpMoAoc,jo|b’j lj;oIhvp 108

0Po 1 s^n WF W! \\kp7;k,;jk G 1 ' 100 = 1 = 0, 01 100 100 100 # 1 = 100 # 0, 01 = 1 100 5 # 1 = 5 = 0, 05 100 100 Ɣ !F(# vkj o;jk |bj’95fg9afly[lk, s^n |b’j 95fg9aflk, s^n |b’j 95fg9afl;j oly[ c]t lk,l;j oIhvpD III. [qfg/ydsafD !D 9q’j la’gdfc]h;0Po8n,j .l[j jvos;kj ’G sq;Ihvp sq;ly[ sq;|j;p |b’j l;j oly[ |b’j l;j oIhvp 0Po !WW !W # ! 1 1 34,2 10 100 $ $ 6,25 * @ & ... & @ ( 5,70 # 0,25 ... !@ ) @ ( ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9q’j 8n,j .l[j jvos;kj ’0v’8k8t]k’]5j,oU D 400 650 465 10 12 sko!WW sko!W 40 46,5 sko!W 4 6,5 58 17,20 6,37 #D 9qj’0Po9eo;o8+wxoUgxao8q;g]d D 8q;1kj ’G lv’95f-k;lk, @F @# DDDDD lk,95fl6oluj DDDDD DDDDD sqdsq;|;j plk,lj;oIhvp 9876 sqdly[lk, c]t |bj’l;j oly[ 100 $D 9qj’0Pog]dlj;oIhvp]5j,oUgxao9eo;omqfltoypq, D 752 1254 2349 6103 100 100 100 100 109

[qfmu 40 g]dlj;orao I. dyf9tdeD !D 9q’j 7yfw]jc]h;0Po8n,j .l8j k8t]k’]5,j oU D ' 10 5147 6284 7543 7614 8362 8104 x 0,1 ' 100 514,7 x 0,01 ' 1000 51,47 x 0,001 5,147 @D 9q’j 0Po8nj,.lj.o8k8t]k’]5j,oU D |b’j lj;o |bj’l;j o |b’j lj;oສະຫງສ.ວວນ.ລິສຂະສິດ sq;Ihvp sq;ly[ sq;|;j p ly[ Ihvp rao 345,086 # $ & W ) * 426,83 59,5 24,601 6,710 II. .97;k,D grnjv.shzqowfhIa[-afg9ogryjo.-h9eo;omqfltoypq,muj,us^kp8q;g]ds^a’9kd95fD 5 5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6 gryoj c[’j 1 gxao 1 10 5,5 5,51 5,52 5,53 5,54 5,55 5,56 5,57 5,58 5,59 5,6 100 5,55 5,551 5,552 5,553 5,554 5,555 5,556 5,557 5,558 5,559 5,56 1 gxao 1 1000 gryoj c[’j 100 110

!W ! ! ! ! vkj o;kj G !W !WW !WWW lk,95fsqdIhvpshkly[lv’ s^n lk,95fsqdshklv’ |b’j lj;o |bj’lj;o |bj’l;j o 0Po G #F*&@ sq;ly[ sq;|;j p ly[ Ihvp rao !W ! WF! WFW! WFWW! #*&@ III. [qfg/ydsafD !D 9qj’la’gdfc]h;0Po8nj,.lj[vj o9Eg,afD sq; sq; sq; |bj’lj;o |b’j l;j o Ihvp ly[ |j;p ly[ Ihvp 235 2 5 (2x100)+(3x10)+5+(2x0,1)+(5x0,01)ສະຫງສ.ວວນ.ລິສຂະສິດ 46 3 7 (...x...) + (...x...) + (...x...) + (... x...) ... ... (3 x 100 ) + 6 + ( 7 x 0,1 ) + ( 1 x 0,01 ) ... ... ... 10 x 0,001 = @D 9qj’7eo;og]d]j5,oU G 1 217 x 100 = 0,017 x 1 000 = 10 x 0,01 = 17 x 10 = 1 217 x 10 = 1 217 ' 1000 = 0,017 x 10 = 0,1 ' 10 = 12,17 x 10 = 0,001 x 100 = 17 ' 100 = #D 9q’j 0Po8nj,.l8j k8t]k’ G sq; sq; |b’j lj;o |bj’lj;o |b’j l;j o ly[ |;j p ly[ Ihvp rao 12,735 0,304 (3 x 10) + (5 x 0,01) + (6 x 0,001) ly[shk95f|bj’Ihvp-k;shk 111

[qfmu 41 ]efa[9eo;omqfltoypq, I. dyf9tdeD !D 9qj’0Po9eo;o]5j,oU.ljcdo9eo;o 4,1 6,101 6,21 6,1 5,30 5,7 6,001 6,8 6,959 4,40 4,04 5,03 4 5 6 7 4,1 3,4 @D 9qj’la’gdfc]h;0Po9eo;o8nj,.lj.o 3 3,2 ສະຫງສ.ວວນ.ລິສຂະສິດ3,8 II. .97;k,D grnvj 1kd9af]Po9eo;omqfltoypq,8k,]efa[gIqkxt8y[affa’j oUG dD la’j gdfg[y’j rkdl;j o4h;o G 9eo;omqfltoypq,musj ^kpd;kj c,jo9eo;omu,j urkdl;j o4h;os^kpd;kj D 8q;1kj ’G *F) > $F_&_ phvo * > $ 0D 4hkrkdl;j o4h;oskdgmqjkdao gIqkla’gdfg[y’j 8q;g]dmu ! 0v’rkdl;j omqf ltoypq, s^n .o8ec|’j |b’j l;j oly[ Xs^a’95f?D 9eo;omusj ^kpd;kj c,oj 9eo;o muj,u8q;g]dmu ! s^a’9kd95foAos^kpd;kj D 8q;1jk’G *F) > *F ! phvo ) > ! 112

7D 4hk;jk8q;g]dmuj|bj’s^a’95fskdpa’gmqjkdao16j8hv’la’gdfg[yj’8q;g]dmu @ s^a’95fF 8q;g]dmuj # sa^’95f c]t 8=jMwxD 8q;1kj ’G 6, 102 > 6,1019 = 1 1 = 0 > 1 0 2 III. [qfg/udsafD !D 9qj’.ljg7jnv’\\kp > ; < s^n = mugj \\ktlq,.lj D 2,4 2,3 5,3 5,42 43,7 43,69 1,61 1,66 8,5 8,50 5,430 5,43 9,62 9,620 52,39 53,39 1,99 2 @D 9q’j 0Po9eo;omqfltoypq,muj,u @ 8q;g]ds^a’9kd95fm5dM8q;muj16j]ts;kj ’ 3,7 c]t 4 ສະຫງສ.ວວນ.ລິສຂະສິດ 99,88 c]t 100,05 0,1 c]t 0,24 #D 9q’j 0Pogru,j 0BoD gmnvj ]t WF@ c8j !@F) sk !$ gmnjv]t WFW& c8j @W sk @! $D 9qj’la’gdfc]h;0Po9eo;o8n,j .l.j o 1,26 1,56 1,86 113

[qfmu 42 dkolhk’I6[.odk’sk; I. dyf9tdeD !D 9qj’la’gdfI6[dhvos^kp|hk dF 0F 7 c]tI6[c[ !F @F # ]5j,oUc]h;8v[7e4k,D dD 0D 7D I6[mkflk,]jP, I6[dhvolkd I6[da[lkd I6[c[ !D I6[c[ #D I6[c[ @D ສະຫງສ.ວວນ.ລິສຂະສິດ { c8j]tI6[ ,u9ad|hk L ,u9ad9v, L ,u9ad]Pj , L { I6[c[.fdq’da[I6[dhvo.f L { 9q’j ]vdc[[I6[c[ !F @F # c]h;lhk’gxaoI6[dhvos^kp|hk II. .97;k,D dkolhk’I6[.odk’sk;7;olhk’gxaoI6[c[djvo c]h;]vdc[[F c8h,F 9kdoAo8af c]t xtdv[gxaoI6[dhvos^kp|hkD 114

ສະຫງສ.ວວນ.ລິສຂະສິດIII. [qfg/udsafD !D 9q’j ]vdc[[I6[c[]5,j oU.ljg9hpc0’D 9kdoAo .sh8afc]h;xtdv[.shgxaoI6[ dhvos^kp|hkD 115

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I6[dhvolkd I6[da[lkd ,u D D D D D D D D D D D D|hk ,u D D D D D D D D D D D D|hk ,u D D D D D D D D D D D D9v, ,u D D D D D D D D D D D D9v, ,u D D D D D D D D D D D D]jP, ,u D D D D D D D D D D D D]jP, #D 9q’j la’gdfg[yj’I6[dhvos^kp|hk]5j,ouhc]h;0Po8bj,.l8j k8t]k’ d0 ສະຫງສ.ວວນ.ລິສຂະສິດ 7 c8]j t|hkgxaoI6[ I6[ 9eo;o|hk 9t85]af lujc9lkd lk,c9mPj ’ dD 0D 7D 117

$D 9qj’0Po-njI6[c[]5j,oU.lj[vj o9Eg,afD dD 0D DDDDDDDDDD DDDDDDDDDD &D 9q’j [vdI6[c[mujlk,kfxtdv[.shgxaoI6[dhvolkdwfhD #D !D @D $D &D *D ສະຫງສ.ວວນ.ລິສຂະສິດ *D 9q’j 8afI6[lk,c9ltg\\umu,j u0hk’pk; dD !W cm grnjvlhk’gxaoI6[ Xd?D 4k,;kj 9t.-hI6[lk,c9ltg\\u9advao9bj’9tr= L 118

II. .97;k, D I6[dhvos^kp|hk c,oj I6[dhvomujxtdv[fh;pI6[|hkrP’s^kpI6[g-aoj G I6[dhvolkdlhk’fh;pI6[9t85]af * I6[gmqkj daoD I6[dhvo ) |hklhk’fh;p I6[ lk,c9ltg\\u ) I6[gmqkj dao I6[da[lkdlhk’fh;pI6[lucj 9lkd * I6[g-yj’c8j ]tI6[16gj -yj’|hk daogmqkj daoD III. [qfg/udsafD !D 9q’j c8h,I6[]5,j oU.lxj nh,0PoD I6[da[lkd I6[mkf]Pj , ສະຫງສ.ວວນ.ລິສຂະສິດI6[m+dq, @D 9q’j ]vdc[[I6[]5,j oUc]h;8af c]t xtdv[gxaoI6[dhvos^kp|hkF dD 0D 7D 119

[qfmu 44 9eo;omqfltoypq, c]t dko;afcmd I. dyf9tdeD !D 9q’j 76og]d8+Mdaowxgrnvj -vdskoE|ad0v’lafc8j]t-toyf]j5,oUG V #F& dtx6 dq[ V !& V @WF@ d5h’ 2 g xkwoສະຫງສ.ວວນ.ລິສຂະສິດ V &F) g8qkj mtg] @D ]5’ 7e ,uoE|adgmqjk\\kdvb @W |j;pF \\kdsj5’ #W |j;p c]t \\kd dhP’ohvp !@ |j;pF I6h;jk\\kddhP’ohvp|j;p|bj’|adxt,ko WF!@& kgF glAozkj o.9dk’cmdwfh WFW( mD \\kds5j’|;j p|b’j |adgmqjk\\kddhP’ohvp !W |j;pF \\kdvb|j;p|b’j |adgmqjk\\kddhP’ohvp !& |j;pD 4k,;jk ]5’ 7e ,uoE|adgmqjk\\kddhP’ohvp9ad|j;p L gxao9addy3]dik, L 4hkgvqk\\kddhP’ohvpma’\\qf mujgmqjkda[oE|ad ]5’ 7e ,k]Po8+dao9tpk; 9adc,af L 120

II. .97;k,D 8k8t]k’dkoxjPosq;|;j p;afcmdmugj Iqkg7up.-h sq;rao s;q Ivh p sq;ly[ sq;|j;p l;j oly[ lj;oIhvp lj;orao 1000 100 10 1 1 s^n 0,1 1 s^n 0,01 1 s^n 0,001 10 100 1000 8k8t]k’;afcmd];’pk; 8k8t]k’;afcmd,;olko d, I, fd, , f, -, ,, dd Id fdd d fd -d ,d km hm dam m dm cm mm kg hg dag g dg cg mg 1 km = 1000 m 1 1 kg = 1000 g 1 g 1000 1 mg = 0,001 g = 1000 1 mm = 0,001 m = m ສະຫງສ.ວວນ.ລິສຂະສິດ II. [qfg/udsafD !D 9qj’xjPosq;|j;p;afcmd]5j,ouhS 4,641 kg = ............. g 6,53 kg = .............. g 3,582 km = ............ m 325 g = .............. mg 675 g = ............... hg 1,25 m = ............. dm 5246 g = .............. kg 2 m 51 cm = ............. cm 20 m = ............. cm 215 cm = ............. mm @D 7v[7;q 0v’ mkh ; l;5 oa mv’ rkdoa wxcmd];’l’6 c]t -’aj oE|da 1l6j d5 lk]k[kh oF c8j]t7qo,uoE|ad c]t ];’l6’faj’oUG r+l6’ !F*$ m c]t |ad (WF& kg S c,j 8ej d;jkr+ WFW) m c]t |ads^5fr+ !F) kg S mhk; l5;aomv’ 8jed;kj r+ WF@_ m c]t |ads^5fr+ @_F_ kg S ok’ 8yd 8jed;kj r+ WF$$ m c]t |ads^5fr+ #$ kg 4k,;jkc,j c]t ]6dc8]j t7qo,uoE|ad c]t ];’l6’gmqkj .f L 121

45[qfmu 9eo;omqfltoypq, c]t dko;afcmd];’pk; I. dyf9tdeD !D 9qj’cmd];’pk;0v’38 c]t sk’|6F c]h;[vd-nj |6c8j]t383fpvu’.lj 8k8t]k’D ສະຫງສ.ວວນ.ລິສຂະສິດ -nj ];’pk;0v’38 ];’pk;0v’sk’ |6-y’ # cm &mm sk $ cm $mm # cm (mm sk # cm _mm |6gInvo # cm !mm sk # cm $mm $ cm sk $ cm $ |60u !W @ cm @mm sk @ cm *mm |6ok $ cm &mm sk $ cm ) & cm !mm sk & cm $mm !W & cm sk &cm #mm @S 9q’j la’gdfc]h;0Po8nj,.l.j o dD 3,1 cm 6,2 cm 9,3cm 0D 4,3 cm 12,9 cm 17,2 cm 122

#D 9q’j 0Po9eo;o.o8k8t]k’]5j,oU sq;Ihvp sq;ly[ sq;|;j p 1 11 10 100 1000 56 2 3 1 = 56, 231 135 4 764 8 =....... 831 2 1 =....... 596 4 5 5 =....... 678 3 7 2 =....... 4 =....... $D 9qj’0Po9eo;o]5j,oUgxao9eo;omqfltoypq,Xgvqk m gxaosq;|j;p? 3m 5 dm ; 1m 138 mm ; 7 cm 6 mm ; 6m 8 dm ; 3 m 15 cm ; 9dm 8 mm ; 4m 67 cm ; 5m 5 mm ; ສະຫງສ.ວວນ.ລິສຂະສິດ 6m 42 cm ; 7 dm 4 cm . &D 9qj’xP[mP[9eo;omqfltoypq,c8]j t76j]5,j oU 3fp.-hg7nvj ’\\kp X < ; > ; = ? 1,9 kg . . . . . . . . 1,90 kg 15,6 kg . . . . . . . . . 16,5 kg 6,4 m . . . . . . . . 5,8 m 20,10 m . . . . . . . . . 20,1 m 90,9 * . . . . . . . . 90,1 L 0,75 L . . . . . . . . . 7,5 L 5,3 L . . . . . . . . 8,3 L 28,4 m . . . . . . . . . 28,1 m 6,50m . . . . . . . . 6,7 m 0,01 kg . . . . . . . . . 0,010 kg II. .97;k, D 9eo;omqfltoypq,];,,u @ rkdlj;o7n rkdl;j o4h;o c]t rkdl;j o mqfltoypq,D 4hkoa[c8-j hkpsk0;kF 9eo;omu1j 6jmk’|hk\\kp95fc,jo rkdl;j o4h;oF 9eo;omuj16mj k’s^a’\\kp95fc,oj rkdlj;omqfltoypq,D 123

8q;1kj ’ G 3, 105 rkdlj;o4h;o rkdl;j omqfltoypq, 1mm= 1 cm = 0, 1cm 10 l=fepk; !! cm & mm s^n s^n !! cm 5 10 !!F & cm II. [qfg/udsafD ສະຫງສ.ວວນ.ລິສຂະສິດ !D 9q’j 7yfw]j c]h;0Po8n,j .l[j vj o9Eg,af dD 4 cm + 3 mm = ................................................cm 0D 5 cm 6 = ................................................cm 10 7D (3 # 1 cm) + 5cm = ................................................cm 10 CD (5 # 2 cm) = ..... cm = ................................................cm 10 10 @D dko0tspkp8q;0v’I;dD vkmyfmu # vkmyfmu * vkmyfmu ) vkmyfmu !$ vkmyfmu !@ 124

g;]k ];’pk;0v’38 ];’pk;0v’sk’ # vkmyf WF( cm !F! cm * vkmyf !F$ cm @F! cm ) vkmyf !F& cm @F! cm !@ vkmyf !F* cm !F_ cm !$ vkmyf !F( cm WF@ cm dD 38I;dpk;vvdgmqjk.f9kdvkmyfmu # skvkmyfmu ) L 9kdvkmyfmu * skvkmyfmu !$ L 0D sk’0v’I;dpk;vvdgmqjk.f 9kdvkmyfmu # skvkmyfmu ) L 7D c,jow]pt9kdvkmyfmugmqjk.f skvkmyfmugmqjk.f muIj ;d0tspkp8q;w; L #D 9q’j la’gdfc]h;0Po8n,j .lj.o ສະຫງສ.ວວນ.ລິສຂະສິດ dD 1,2 cm 1,2 cm 3,6 cm 0D 3,5 cm 10,5 cm 14 cm $D 9qj’xPj osq;|j;p]5,j oU.shgxao9eo;omqfltoypq,D 5 mm = cm 12 hm = km hm 81cm = dm 1,45 km = dam cm 107 dm = m 28,56 hm = cm 526 m = dam 5,74 dm = 6499 dam = hm 82,1 mm = &D 9qj’0Po9eo;omqfltoypq,.shwfh !W 9eo;oD *D gsa^d];fglAo|b’j pk; !#(&W cm. 4k,;jkgs^ad];fglAooAopk;9adc,af(m ) L 125

46[qfmu I6[c[[8kj ’M.odko0Po9eo;omqfltoypq, I. dyf9tdeD !D 9q’j la’gdfc]h;0uf8=jI6[c[[dko0Pomulj tcf’g4y’9eo;ofP;dao.ldj ao cxfraog9afIhvpshkly[95fl6oshksqd 0,105 l6o95f|bj’l6oshk ( 4 x 10 ) + 1 + ( 9 x 0,1 ) + ( 3x 0,01 ) + ( 7x 0,001 ) 56 93 7 8 000 + 700 + 50 + + 40 + 1 + + + 10 100 1 000 100 1000 9000 + 300 + 10 + 6 + 75 + lulj y[gvaf95fgdQklk,g9af 10 1000 ສະຫງສ.ວວນ.ລິສຂະສິດ 41,937 gdQkraolk,Ihvply[sqd95fg9afl6oshk ( 10 x 0,01 ) + ( 5 x 0,001 ) (9 x 1000) + (3 x 100) + (1x 10) + 6 + (7 x 0,1) + (5 x 0,001) 15 8750,056 + 10 1 000 ( 8 x 1 000 ) + ( 7 x 100 ) + ( 5 x 10 ) + ( 5 x 0,01 ) + ( 6 x 0,001 ) @D 9q’j 0Po9eo;o]5j,ouh.oI6[c[[dt9kp0v’dko[;d 8q;1jk’ G 95,153 = 90 + 5 + 0,1 + 0,05 + 0,003 86,3 = .............. 27,56 = ............... 5,92 =.................... 5,78 = .............. 43,24 =................ 70,9 = ................... 8,01 = .............. 6,15 = ................ 64,21 = ................. 126

#D 9q’j 0Po9eo;o]5j,oU.oI6[c[[dt9kp0v’dko76oD 8q;1jk’ G 8750,056 = (8 x 1000) + (7 x 100) + (5 x10) +( 5 x 0,01 )+ ( 6 x 0, 001) 0,105 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95,06 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27,216 =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311,01 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52,07 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $D 9q’j 0Po9eo;omqfltoypq,]5,j oUgxao7evjkoD 8q;1kj ’G $!F_#( = lujly[gvaf95fgdqhklk,g9af 801,05 = ....................................... 92,281 =........................................ 101,21 = ....................................... ສະຫງສ.ວວນ.ລິສຂະສິດ 30,01 = ...................................... 341,002 = ...................................... &D 9q’j 0Po9eo;o]5j,oUgxao8q;g]dD 8q;1kj ’ G shkIhvpg9afly[lv’95f|bj’l6ogdQk &(@F!W_ sqdIhvp-k;shk95flk,g9af S gdQkly[lv’95fsqdcxf S lujIhvply[g9af95f|b’j l6ocxf S shkly[sqd95flv’gdqhkluj S cxfly[shk95flk,IhvpsqdgdQk S gdQkly[lk,95fcxfIhvpsqdg9afD *D 9qj’0Po9eo;omqfltoypq,8=wj xoUgxaog]dlj;oD 8q;1jk’ G 7, 12 = 712 100 0,3 ; 3,5 ; 8,4 ; 9,5 ; 1,6 ; 25,1 ; 50,2 ; 72,3 ; 2,39 ; 0,002 . 127

II. .97;k,D gIqklk,kf0Po9eo;omqfltoypq,rkp.8hs^kpI6[c[[D 8q;1jk’G sq;Ihvp sq;ly[ sq;|j;p l;j oly[ l;j oIhvp lj;orao 2 17 45 3 217 + 0,453 = 217 + 4 + 5 + 3 10 100 1000 = ( 2 x 100 ) + ( 1 x 10 ) + 7 + ( 4 x 0,1 ) + ( 5 x 0,01 ) + ( 3 x 0,001 ) = 217 + ( 4 x 1 ) + ( 5 x 1 ) + ( 3 x 1 ) 10 100 1000 = 217,453 ສະຫງສ.ວວນ.ລິສຂະສິດ = lv’Ihvply[g9af95flusj hklk, III. [qfg/udsafD 41 + 0, 3 + 0, 07=................. !D 9q’j 0Po9eo;o8nj,.lj[jvo9Eg,afD 8q;1jk’G 3 + 0, 2 + 0, 03 = 3, 23 8 + 3 + 2 =...................... 10 100 8 + 0, 03 + 0, 007 =........ 451 + 0, 4 + 0, 07=.............. 51 + 0, 1 + 0, 07 =........... 315 + ^4 # 0, 5h =............. 39 + 0, 1 + 0, 09 =............... 98 + 0, 4 + 0, 08 =........... 12 + 3 + 2 =..................... 112 + 0, 1 + 0, 01 =......... 10 100 128

@D 9q’j 0uf8+I6[c[[dko0Pomulj tcf’g4y’9eo;ofP;daoD 5 x 1000 + 4 x 100 + (1 x 10 ) + 5 + ( 7 x 0,01 ) + ( 6 x 0,001 ) shkraoljuIhvply[shk95fl6og9afsqd 61 3 7000 + 300 + 60 + 4 + + + 0,542 10 100 1 000 5415,076 g9afraolk,Ihvpsqdly[lu9j 5fsqd|bj’lk, l6o95fshklulj v’ 76 5000 + 400 + 10 + 5 + + 100 1000 7 x 1000 + 3 x 100 + 6 x 10 + 4 + ( 6x 0,1 ) + ( 1 x 0,01 ) + ( 3 x 0,001 ) 7364,613 54 2 ++ 10 100 1000 ສະຫງສ.ວວນ.ລິສຂະສິດ #D 9qj’0Po9eo;o]5,j oUgxao8q;g]dD lk,95fl6oshk DDDDDDDDDDDDDDDDDDDDDDDDD S shkly[95flk,ly[gdqhk DDDDDDDDDDDDDDDDDDDS cxfly[luj95fg9afly[lv’ DDDDDDDDDD S sqd95f-k;cxf DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDS lujIhvpsqdly[lv’95f|bj’Ihvp-k;gvaf DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD D $D 9q’j 0Po9eo;o]5j,oUgxao7evkj oD 48,214 = ....................... S 2,38 = .................... S 67,432 = ....................... S 6,29 = .................... S 34,57 = ................... S 125,50 = ...................... . &D 9qj’0Po9eo;o]5,j oU.oI6[c[[dt9kp0v’dko[;dD 8q;1kj ’ G 3,25 = 3 + 0,2 + 0,05 6,18 = ................... S 8,37 = ...................... S 12,34 =.....................S 27,46 = ................. S 51,27 = .................... . 129

[qfmu 47 dko[;d9eo;omqfltoypq, I. dyf9tdeD !D 9q’j la’gdf8q;1kj ’c]h;0Po9eo;omqfltoypq,]5j,oU.oI6[c[[dt9kpD 74,319 ( 16j.os^ad $ 16.j o # 16j.os^ad ! 16j.os^ad _ 16j.os^ad ly[,u s^ad|;j p l;j oly[ lj;oIhvp l;j orao 7jk (W ,u7kj $ ,u7kj WF# ,u7kj WFW! ,u7jk WFWW_ { fa’j oAo 0Po ($F #!_ .oI6[dt9kpwfhfaj’oU G ສະຫງສ.ວວນ.ລິສຂະສິດ95,153 S 74,319 = 70 + 4 + 0,3 + 0,01 + 0,009 81,701 . 86,3 S 65,19 S 7,532 S 3,256 S 487,381 S 54,21 S 78,351 S 96,765 S @D 9q’j [;dg]d]5,j oU G 6,3 13,2 61,75 52,35 78,14 + + + + + 3,7 6,4 6,21 7,83 6,95 57 + 33,09 = .................. 381 + 71, 68 = ................... 48,11 + 35,89 = ................. 105,2 + 55,84 = ................... 132,60 + 28 = ................. 774 + 0,07 = ................... 130

II. .97;k,D dko[;d9eo;omqfltoypq,8hv’xt8y[affaj’oU G i 8ah’g]d.shg7njv’\\kp95fg-yj’g7nvj ’\\kp95f c]t 8q;g]ds^ad.f.shg-y’j 8q;g]ds^adoAoD i dko[;d.shxt8y[af7ndaoda[dko[;d9eo;o4h;oD  i .l\\j kp95f.ozqo[;d.sh-ndj ao]q’,kD III. [qfg/udsafD !D 9qj’[;dg]d]5j,oU G 27,3 35,05 42,45 79,43 38,54 + + + + + 4,1 4,31 38,24 6,12 21,3 DDDD DDDD DDDD DDDD DDDD ສະຫງສ.ວວນ.ລິສຂະສິດ @D .odkoc0’j 0aocd;’j oE|ad mhk; 7eI5j’ cd;’j wfhwd !#F$& c,afF mhk; 9aomu cd;’j wfhwdd;jk mhk; 7eIj5’ @F#* c,afD 4k,;jk mhk; 7eI5j’ cd;’j wfh9ad c,af L #D 4hkgvqkl=lk,glAomju,u];’pk;gmqjkdao,k;k’8+dao9tpk;];,daowfhgmqjk.fL I6h;jkl=glAo|b’j pk; !_FW@ -a’8uc,afD $D 38t|;j p|yb’j l6’ WF(& c,afF oadIPo7qo|b’j l6’!F#& c,afD g,njvoadIPo7qooU1no gmy’38t sq;0v’oadIPo7qooUl6’9kdrnho9adc,af L &D .odkogfuomk’wx3I’IPo mhk; cdh; 8hv’pjk’vvd9kd[hkowx0Bo]qfgxao w]ptmk’ WF$& dy3]c,afF 0u]j qfxt9emk’gxaow]ptmk’ !@F& dy3]c,afc]h; pkj ’8+9oq g4’y 3I’IPovdu WF#& d3y ]c,fa ];,w]ptmk’9kd[kh o0v’mkh ; cd;h g4y’3I’IPo,u9addy3]c,af L 131

[qfmu 48 dko]q[9eo;omqfltoypq, I. dyf9tdeD !D 9qj’lhk’mvj o-nmj u,j u];’pk;8k,deoqf.sh c]h;8afvvd8k,mudj eoqf 8q;1jk’ G mjvo-njpk; #F( 8afvvd @F$ 3,7 6 4 4 4 4 4 44 7 4 4 4 4 4 44 8 1 4 4 4 4 44 2 4 4 4 4 44 31 4 4 4 4 44 2 4 4 4 4 44 3 144444424444443 8afvvd @ pa’gs^nv !F # 8afvvd WF$ 3, 7 _ 2,4 = 1,3 dD mvj o-npj k; !WF& 8afvvd $F@ ສະຫງສ.ວວນ.ລິສຂະສິດ 0D mvj o-njpk; (F( 8afvvd #F# 7D mjvo-npj k; &F) 8afvvd @F* @D 9qj’]q[g]d8=jwxoU G _ 481,3 _ 134,27 _ 123,46 _ 354,68 _ 24,212 150,1 46,95 31,23 34,25 6,8 .... ..... ..... ..... ..... II. .97;k,D dko]q[9eo;omqfltoypq,8hv’xt8y[affaj’oU G !D 8A’g]d.shg7njv’\\kp95fg-yj’g7njv’\\kp95f c]t 8q;g]ds^ad.f.shg-yj’8q;g]d s^adoAoD @D dko]q[.shxt8y[af7nda[dko]q[9eo;o4h;oD #D .l9j 5f.ozqo]q[.sh-njdao]q’,kD 132

sq;Ihvp sq;ly[ sq;|;j p |b’j lj;oly[ |bj’lj;oIhvp _5 6 7, 2 5 4 1 5, 3 2 1 5 1, 9 3 III. [qfg/udsafD !D 9q’j lhk’mjvo-nmj u,j u];’pk;8k,deoqf.sh c]h;8afvvd8k,mudj eoqfD dD mvj o-njpk; )F* 8afvvd &F! 0D mvj o-njpk; !WF# 8afvvd *F@ 7D mvj o-njpk; !@F& 8afvvd !WF$ @D 9qj’]q[g]d8=jwxoUD _ 6, 34 _ 7, 71 _ 5, 94 _ 3, 61 _ 42, 64 2, 16 2, 46 3, 47 2, 47 24, 35 #D 9q’j 8A’[ha’g]dc]h;7yfw]jD ສະຫງສ.ວວນ.ລິສຂະສິດ 4,37 - 2,58 = 8,25 - 9,36 = 7,64 - 5,24 = 34,56 - 32,18 = 75,7 - 24,9 = 68,7 - 21,9 = $D 9q’j 0Po8q;g]d8nj,.lj.o ]5j,oUD _ 4, 7 _ 3, 7 _ 8, 6 _ 9, 4 5, 3 8 3, 6 2, 8 2, 6 22 1, 2 5 3, 9 ,28 &D g,njvmhk;7elvovkp5wfh * xu ]k;,uoE|ad @$F( kg c]t ,u];’l6’ !F!( mF g,nvj vkp50v’]k;wfh !W xu ]k;-aj’wfh #)F@ kg c]t cmd];’l6’wfh !F$@ m i 9q’j 7yfw]vj af8kgruj,0Bo0v’oE|ad c]t ];’l6’0v’]k; .o]ts;j k’ * xusk !W xu 133

49[qfmu dko76o9eo;omqfltoypq,da[9eo;o4h;o I. dyf9tdeD !D 9q’j la’gdfg[yj’8q;1kj ’c]h;7yfw]j0=h8+wx D 8q;1kj ’G 4 x 3,8 = 3,8 + 3,8 + 3,8 + 3,8 = 15,2 6 x 2,7 = 3 x 4,25 = 7 x 5,5 = 4 x 8,5 = 5 x 7,8 = 8 x 6,4 = @D 9qj’7yfw]jc]h;0Po8n,j .l8j k8t]k’]5,j oU D x 10 100 1000 x 10 100 1000 1,5 150 2,31 3,45 3450 4,6 ສະຫງສ.ວວນ.ລິສຂະສິດ 5,12 8,42 63,4 85,3 70,2 93,81 II. .97;k,D dko76o9eo;omqfltoypq,da[9eo;o4h;od=xt8y[af7ndaoda[ dko76o9eo;o 4h;oda[9eo;o4h;o c]h;9yj’\\kp95f.ljzqo76o3fp.sh9eo;o8q;g]d16js^a’95f0v’ zqo76ogmqkj da[9eo;o8q;g]d16js^a’95f0v’9eo;omqfltoypq,mujgvqk,k76oD 8q;1kj ’ G 1,5 x 7 = 1,5 + 1,5 + 1,5 + 1,5 + 1,5 + 1,5 + 1,5 = 10,5 s^n 1, 5 x7 10, 5 134

III. [qfg/udsafD lD 2,121 x 3 = ............... !D 9q’j 7yfw]gj ]d8=jwxoUG -D 4,053 x 4 = ............... pD 5,215 x 5 = .............. dD 2,64 x 3 = .......... 9D 7,502 x 6 = .............. 0D 3,42 x 5 = ............ 8D 8,476 x 7 = ............... 7D 5,25 x 6 = ........... CD 6,51 x 7 = ........... 9D 9,73 x 8 = ............ @D 9qj’7yfw]cj ]h;0Po8nj,.lj8k8t]k’]5j,oUD x 10 23 x 10 102 3 2,76 10 10 6,14 10 31,4 15,3 8,25 9,125 ສະຫງສ.ວວນ.ລິສຂະສິດ 91,6 27,42 6,232 84,37 X @ = !W V !W = !WW c]t # = !W V !W V!W = !WWW ? !W !W #D ]5’ 7e,u -nhoEfjn,[=]yl5f grnvj ,k1kp.shc0dfn,j .o’koz6dc0oxu.\\jmugj Invo 0v’]k; 9eo;o @ cdaf Xcdaf|bj’,u #W cdh;? I6h;jkoEfn,j cdh;|b’j [ao95oE WF& ]yfD 4k,;kj oEfn,j ma’\\qf,u9ad]yf L $D xhk 7e9ao -nhxk @F$ kg, dy3]dik,]t !& WWW du[D 4k,;jk]k;8hv’ 9jkpg’yo7kj xkma’\\qfgmqjk.f L 135

[qfmu 50 m;o7nodjP;da[9eo;omqfltoypq, I. dyf9tdeD !D 9q’j la’gdfI6[dko0Poltg\\uzqo]5,j oUc]h;7yfw][j A’8+wxD 8q;1jk’G 342 = 34 + 2 = 34, 2 10 10 625 = 6 + 2 + 5 = 6, 25 100 10 100 82648 = 82 + 6 + 4 + 8 = 82, 648 1000 10 100 1000 54 =................; 642 =......................; 758 =...................; 10 10 10 1251 =................; 9872 =......................; 6544 =...................; 100 100 100 82643 =................; 96482 =......................; 75637ສະຫງສ.ວວນ.ລິສຂະສິດ=...................; 1000 1000 1000 @D 9q’j 0Po.l[j vj o9Eg,afD 100 10 1 1 11 10 100 1000 sq;Ihvp sq;ly[ sq;|;j p |b’j lj;oly[ |’bj l;j oIhvp |b’j l;j orao 42 3 = 42,3 52 6 =....... 46 5 7 8 =....... 9 0 5 3 =....... 136

#D 9qj’0Po9eo;o]5,j oUgxao8q;g]dD 8q;1kj ’ G g9afly[lv’95fcxf = 72,8 gdQkly[lk,95fg9afly[luj = ...... ...... gdQkIhvpsqdly[lu9j 5flk,ly[g9af = ...... ...... sqdIhvplk,ly[lv’95fsqdIhvplk,ly[gvaf= ...... g9afIhvp-k;cxf95fgdQkly[sqd = lv’raosqdIhvpluj95fg9afIhvpshkly[luj = $D 9qj’0Po9eo;o]5,j oUgxao7evkj oD ສະຫງສ.ວວນ.ລິສຂະສິດ 41,74 = . . . . . . 5 53,92 = . . . . . . 541,36 = . . . . . . 375,743 = . . . . . . 604,856 = . . . . . . &D 9q’j 0Po9eo;o8n,j .lj.o 4 4,2 6,20 6,30 6,22 II. [qfg/ydsafD !D 9qj’9af]Po9eo;o8+wxoUc8|j hvpsks^kp D 4,5 ; 3,2 ; 11 ; 5 ; 7,3 ; 1,2 ; 8,4 ; 6,9 ; 10,4 ; 9 ; 2 . 137

@D 9qj’[vd9eo;omuj|hvpd;j k\\6.j oc8j]t0=h8+wxoUD dD 5,8 ; 7,2 ; 6,2 ; 5,2 ; 4,1 7D 5,4 ; 6,2 ; 7,5 ; 5,5 ; 6,3 0D 9,3 ; 9,1 ; 9,6 ; 9,5 ; 9,9 CD 8,2 ; 7,9 ; 8,1 ; 7,9 ; 8,7 #D 9qj’0Po9eo;o.lj.o .sh4nd8hv’D 3 4 4,2 5 ... ... ... ... ... $D 9qj’0Po.lj[jvo9Eg,afD sq;Ihvp sq;ly[ sq;|;j p |b’j lj;o |bj’lj;o |bj’lj;o = 76,38ສະຫງສ.ວວນ.ລິສຂະສິດ rao =....... ly[ Ihvp =....... 1 =....... 76 3 8 7 =....... 38 2 5 5 10 5 6 62 4 1 3 59 1 2 0 &D 9qj’0Po9eo;o.l8j k8t]k’D sq;ly[ sq;|;j p |bj’lj;o |bj’lj;o |bj’lj;o 12,735 ly[ Ihvp rao 0,304 (3 x 10)+(5 x 0,01)+( 6x 0,001) 12 7 3 5 sqdIhvplk,l;j orao g9af95fl6oshk|b’j 138

*D 9q’j la’gdf];’l6’0v’c8]j t7qo c]h;8v[7e4k,D 1m 25 m 8m 10 100 1m 24 cm 100 1m 18 m 9 c]t 100 1m 4 c]t 5 m 10 100 ok’ 7efuD mhk; cdh;D mhk; 7eD ok’ lq,luD ok’ \\voD dD 9q’j [vd];’l6’0v’c8]j t7qogxao cm. 0D 9qj’[vd7qomujl6’d;kj \\6j c]t 7qomuj8+kd;jk\\6Dj 7D 9qj’7yfw]j7;k,]5f]njo]ts;jk’7qomu8j +kl5fda[7qomujl6’l5fD (D 9qj’0Po9eo;o8nj,.lj[jvo9Eg,afD 10 x 0,01 = . . . . . . 10 x 0,001 = . . . . . . 0,001 x 100 = . . . . . 1217 x 10 = . . . . . . 1217 ' 100 = . . . . . . 0,017 x 10 = . . . . . . 0,017 x 1000 = . . . . . . 1217 ' 1000 = . . . . . 12,17 x 10 = . . . . . . 17 ' 10 = . . . . . . 17 ' 100 = . . . . . 0,1 ' 10 = . . . . . ສະຫງສ.ວວນ.ລິສຂະສິດ )D 9qj’]vdc[[8k8t]k’oU7noc]h;8n,j .lj8k,8q;1kj ’D sq;Ihvp sq;ly[ sq;|j;p 1 1 1 9eo;o g]dlj;o 10 3 100 1000 mqfltoypq, mqfltoypq, 5 8 3,5 3 + 5 12 2 10 4 7 0 5 8 0 0 3 56 0 0 0 0 6 18 2 32 2 05 5 08 0 00 139

[qfmu 51 ];’Iv[ I. dyf9tdeD gxaosq;|;j pgrnvj ;afcmd];’Iv[0v’I6[]5,j oUc]h;8v[ ! 9q’j oe.-h0hk’0v’ 7e4k,D I6[ d I6[ 0 I6[ 7 ສະຫງສ.ວວນ.ລິສຂະສິດ I6[ 9 I6[ C { c8j]t0hk’0v’c8]j tI6[,u9ad8k X sq;|;j p ? L { zqo[;dma’\\qfm5d0hk’0v’c8]j tI6[,u9ad8k X sq;|;j p ? L @D 9qj’-vdsk];’Iv[0v’c8j]tI6[]5j,oU g,nvj I6h;jk c8j]t0hk’0v’sq;|j;p cmdwfh ! cm I6[ 0 I6[ 7 I6[ d I6[ 9 I6[ C I6[ l { c8j]t0hk’0v’c8j]tI6[,u9ad-a’8uc,af X cm ? L { zqo[;dma’\\qfm5d0hk’0v’c8j]tI6[,u9ad-a’8uc,af X cm ? L 140

II. .97;k,D { dvj o9t;afcmd];’Iv[0v’I6[|bj’ s^n s^kpI6[8hv’lhk’sq;|;j p;afcmd ];’Iv[glpdvj oD { sq;|;j p;afcmd];’Iv[c,oj c,af X m ?F v5xt76o c]t mt;u76o0v’c,afD { ];’Iv[0v’c8]j tI6[c,jo];’pk;ma’\\qf0v’0hk’ s^n gmqjkdaoda[zqo[;d ];’pk;0v’[aofk0hk’0v’I6[oAoD III. [qfg/udsafD !D 9qj’7yfw]j];’Iv[0v’c8j]tI6[]5j,oU3fpoe.-hsq;|;j pc,jo0hk’0v’ D I6[ d I6[ 0 I6[ 7 I6[ C I6[ 9 I6[ l I6[ - ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9qj’7yfw]]j ;’Iv[0v’c8j]tI6[]5,j oUgxao cm g,njvI6h;kj gmqjkda[ ! cm I6[ 0D I6[ 7D I6[ dD 36 m #D l;o8vo|b’j gxaoI6[lucj 9lkdg-yj’,u ];’pk;cmdwfh #* m c]t ];’ 12 m d;hk’cmd wfh !@ m D 4k,;jk l;o 8vofa’j dk;,u];’Iv[gmqkj .f L 141

[qfmu 52 goNvmuj I. dyf9tdeD !D rNoshv’oEgxaoI6[ * c9ltg\\uD gryoj .-hfyo]kpgxaoI6[ # c9ltg\\ux6shv’oEoUD i9qj’oa[g[yj’;jkgryoj .-hfyo]kp9adczoj 9b’j r=fu L i9qj’c[j’rNoshv’oEoUgxao * l;j oltg\\udaoc]h;mkluc8]j tlj;o X c[j’9kd.9dk’ ? i9qj’0tspkpI6[rNoshv’oEoU.sh.spdj ;kj gdqkj c]h;8afgxao * l;j olt g\\udao3fpg]u,j 9kd.9dk’0v’I6[ * c9D ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9q’j oe.-hsq;|;j p grnvj ;afcmdgoNvmuj0v’I6[]5,j oUc]h;8v[7e4k,D d0 { c8]j t0hk’,u9ad8k L { c8j]t0hk’,u9ad8k L { goNvmumj a’\\qf,u9ad8k L { goNvmumj a’\\qf,u9ad8k L 142

#D lt4komucj s’j oUgxaome,t-kfmujl;p’k,csj’|b’j 9q’j -vd;ymugrnjvxP[mP[ goNvmuj0v’|v’lv’cs’j oUD $D I6[/kgInvogrD 9qj’-vdskgoNvmu0j v’/kgroAo9tgmqkj da[fyo9u9j addhvoDສະຫງສ.ວວນ.ລິສຂະສິດ g0fmjugr &D 9q’j gvqkI6[9t85]afmu,j u0hk’ ! cm gxaosq;|j;pgrnjv;afcmdgoNvmuj I, II, III 0v’I6[ dF 0F 7D ! cm III II IIII III d 07 143

II. .97;k,D { djvo9txP[mP[goNvmuj0v’ @ I6[ s^n s^kpI6[8hv’lhk’sq; |j;p;afcmdgoNvmujdjvoD { sq;|;j p;afcmdgoNvmuj c,oj goNvmuj0v’I6[9t85]afmuj,u0hk’ G ! cm 8+ ! cm ! cm2 ! dm 8+ ! dm !WW gmnvj ! dm2 ! m 8+ ! m !W WWW gmnjv ! m2 { I6[c8d8jk’daolk,kf,ugoNvmujgmqjkdaoD 8q;1jk’ G I6[c[8kj ’Mgs^qkj oUxtdv[fh;pI6[9t85]afmujgmqkj daoD ສະຫງສ.ວວນ.ລິສຂະສິດ III. [qfg/udsafD !D .oI6[ * vaooU,u & I6[ mu,j ugoNvmujgmqjkdaoF ,u ! I6[ mu,j ugoNvmuj 8jk’\\6Dj 9q’j -vdsk I6[mu,j ugoNvmu8j kj ’\\6j 3fp.-hI6[lk,c9 gxaog7nvj ’,n Xsq;|;j p;afcmd? .odko;afcmdD 144

0 7 d C l 9 @D ]5’ [q;lu vvdc[[shv’oEgxaoI6[ $ c9lkd c]t I6[9t85]af 7nI6[]5,j oUD 9kd oAo gryoj .-hfyo]kpgxaoI6[9t85]af x6shv’oEfaj’djk;D { 9q’j oa[g[y’j ;jk gryjo.-hfyo]kp9adczjo.oc8]j tI6[ L { ma’lv’I6[.-hfyo]kpma’\\qf9adczoj L ສະຫງສ.ວວນ.ລິສຂະສິດ X I6[ d ? X I6[ 0 ? #D I6[/kgInvomujd+[+maoc]h;D 9q’j -vdskgoNvmuj0v’/kmujd+[+maoc]h;oAo9tgmqkj da[ fyo9uj9addhvo L g0fmujd+[+c]h; $D 9qj’c8h,I6[lujc9lkdmu,j u];’pk;gmqjk ( 8kdk3i c]t ,u];’dh;k’ * 8kdk 3iD 4k,;jk g9hpmujc8h,,uma’\\qf9ad8kdk3iD 145

[qfmu 53 sq;|;j p;afcmdgoNvmuj I. dyf9tdeD !D 9q’j g]nvdgvqksq;|;j p;afcmdgoNvmuj ! cm2S ! m2 ; 1 km2 mujg\\ktlq,le ]a[;afcmdgoNvmuj8+wxoU G goNvmujshv’IPo goNvmuxj tgmf l x x ]k; goNvmu|j hkxqd0v’xB,0Po goNvmujfyogInvoD @D 9qj’0Po9eo;o.l.j o8k8t]k’]5,j oU G kdm,@2 hIm,@2 dfadm,@2 m,@2 dfm,@2 c-m,@2 m,m,@2 95676 dm2 95676 127,54 dam2 12754 7,49 km2 ສະຫງສ.ວວນ.ລິສຂະສິດ 32765 m2 50 000 cm2 II. .97;k,D sq;|;j p;afcmdgoNvmujmuj.-hs^kpc,oj G km2 ; m2 ; cm2 8k8t]k’sq;|j;p;afcmdgoNvmuj G d,@ I,@ fd,@ ,@ f,@ -,@ ,,@ km2 hm2 dam2 m2 dm2 cm2 mm2 50000 00 1 3500000 2900 5 m2 = 50 000 cm2 ; 1 dm2 = 0,01 m2 ; 3,5 km2 = 3500 000 m2 ; 29 cm2 = 2 900 mm2 . 146

III. [qfg/udsafD !D 9q’j oe.-h8k8t]k’grnjvxjPosq;|;j p;afcmd]5j,oUD m2 dm2 cm2 42 m2 7 dm2= . . . . . . . . . . cm2 3285 cm2 = . . . . . . . . . . . dm2 42 07 85 180 cm2 32 80 = . . . . . . . . . . . dm2 6 1 52 dm2 = . . . . . . . . . . . m2 52 80 6 m2 80 dm2 = . . . . . . . . . . . cm2 @D 9q’j xPj osq;|j;p;afcmdgoNvmu]j 5j,oUD 60 km2 = . . . . . . . . . . . . hm2 1,4 dm2 = . . . . . . . . . . . . . . mm2 300 mm2 = . . . . . . . . . . . dm2 5 cm2 ສະຫງສ.ວວນ.ລິສຂະສິດ= . . . . . . . . . . . . . . dm2 18 hm2 = . . . . . . . . . . . . dam2 120 m2 = . . . . . . . . . . . . . . cm2 36,4 m2 = . . . . . . . . . . .. hm2 9 dam2 = . . . . . . . . . . . . . . m2 650000 cm2 = . . . . . . . . . . . m2 48000 dm2 = . . . . . . . . . . . . . . m2 #D 9qj’la’gdf8q;1jk’c]h;oe.-h.o0=h8+wxD 115 dm2 25 cm2 = 1 m2 15 dm2 25 cm2 340 m2 50 dm2 = 3 dam2 40 m2 50 dm2 247 dam2 40 m2 = 2 hm2 47 dam2 40 m2 242 dm2 42 m2 = 546 dm2 60 cm2 = ...................... 5379 hm2 38 dam2 = 1345 dam2 60 m2 = ...................... ...................... ...................... 147