ຄະນິດສາດ_Math

7D 9q’j 7yfw]jc8]j t[A’]5,j oUD + 2 5 +3 7 + 4 0 + 5 2 + 7 9 1 2 2 1 3 8 4 1 2 0 . . . . . . . . . . +1 2 0 +1 4 6 + 1 0 0 + 1 0 7 +1 5 6 7 9 1 2 1 0 0 3 2 13 . . . . . . . . . . . . ... ’D 9qj’8n,j 9eo;o.lj8k8t]k’]5j,oUD sq;Ihvp sq;ly[ sq;|;j p 30 + 8 = 38 # ) ສະຫງສ.ວວນ.ລິສຂະສິດ 69 + 13 = 82 125 + 5 = 130 108 + 2 = 110 121 + 8 = 129 157 + 12 = 169 182 + 6 = 188 175 + 15 = 190 100 + 37 = 137 100 + 100 = 200 44

9D oadIPolu7j qoc0’j 0aodaoIPog]dS zkj odkod;fdk & 7A’ c8j]t ສະຫງສ.ວວນ.ລິສຂະສິດ 7qowfh7tcoofaj’.o8k8t]k’]5,j oUG mhk; my[rt9ao ok’ ;aoou &S !WS #S (S &S *S $S )S !WS # mhk; cl’8k;ao ok’ vervo )S *S !WS @S & (S #S $S *S _ 9q’j 7yfw]j 7tcoo];,0v’c8]j t7qo c]t 4k,;jk.z wfhmu|b’j D lD mhk; 7e,k -N-v’9qf\\kp |bj’-v’ &W du[F -Nl=fe |bj’dhko $& du[ c]t 1k’]b[ #W du[ 4k,;jkG ]k;8hv’9jkpg’yoma’ \\qf9addu[D -D c,0j v’ mhk; wdcj dh; -N9vdcdh; ) 3s^F r+0v’]k;-N,k8n,j vud # 3s^ 4k,;kj 9vdma’\\qf,u9ad3s^ L X 9vd ! 3s^ gmqjkda[ !@ |j;pF g7y’j 3s^ gmqjkda[ * |j;p ? 45

[qfmu 16 8k8t]k’dko[;dF I6[dko0Po muj[+7q[4h;o !D 8k8t]k’dko[;dD dD 9q’j 0Po8nj,.lj8k8t]k’]5,j oUD 20 30 40 50 60 70 80 90 100 + 10 110 65 60 55 50 40 35 30 25 20 + 20 40 0D 9qj’0Po8n,j .l8j k8t]k’dko[;d]5j,oUD ສະຫງສ.ວວນ.ລິສຂະສິດ + 10 20 30 40 + 15 25 35 45 1 11 31 5 2 22 10 3 20 4 25 + 50 65 70 75 + 55 60 80 90 10 20 15 30 25 40 30 50 46

7D 9q’j 0ufglAo9vj ’.ljzqo[;dmu4j nd8hv’D 120 + 45 145 98 + 60 165 150 + 39 158 68 + 77 151 115 + 36 189 138 + 60 198 @D I6[dko0Pomuj[+7q[4h;oD 12 + . . . + 8 + . . . + 14ສະຫງສ.ວວນ.ລິສຂະສິດ dD 9q’j 0Po9eo;o8n,j .lj[vj o9Eg,afD 8 + 9 + . . . + 13 + 6 . . . . . . . . . . . . 20 28 . . . 48 5 + . . . + 16 + 9 + 1 5 + 6 + . . . + 4 + 7 5 20 . . . 20 . . . 7 5 . . . . . . . . . . . . 37 47

0D 9qj’8n,j 9eo;omugj \\ktlq,.l.j o 1 9 > 1 8 2 0 < 2 1 8 5 = 8 5 4 > 4 8 4 8 < 4 7 = 7 2 3 > 3 8 6 8 < 6 5 = 5 9 6 > 6 8 9 6 < 7 9 3 = 3 7D 9q’j 0Po9eo;o8nj,.lj.o 25 + 10 + 15 ສະຫງສ.ວວນ.ລິສຂະສິດ 72 + 8 + 20 93 + 7 + 12 100 + 15 + 10 48

CD 9qj’xP[mP[9eo;o]5,j oU3fp.-hg7nvj ’\\kp >; <; =. 8 + 4 . . . 8 + 5 18 + 8 . . . 19 + 9 9 + 8 . . . 8 + 9 18 + 9 . . . 19 + 8 9 + 7 . . . 9 + 6 19 + 10 . . . 10 + 18 25 + 6 . . . 25 + 7 46 + 7 . . . 45 + 8 72 + 8 . . . 72 + 9 68 + 4 . . . 68 + 6 9D 9q’j 0Po9eo;o8nj,.lj[jvo9Eg,afD 150 130 120 160 . . . + 100 100 + . . . 100 + . . . 80 + . . .ສະຫງສ.ວວນ.ລິສຂະສິດ 70 + . . . . . . + 80 . . . + 55 . . . + 90 120 + . . . . . . + 90 . . . + 30 . . . + 65 . . . + 90 70 + . . . 75 + . . . 70 + . . . lD 3I’IPoxt4q,csj’|bj’shvC xD! ,uoadIPo $@ 7qoF shv’ xD@ ,uoadIPos^kpdj;kshv’ xD! & 7qo 4k,;jkoadIPo shv’ xD@ ,u9ad7qo L -D mhk; vk16 ,uvkp5 _ xu gvNvp0v’]k;,u vkp5 s^kpdj;k # xu 4k,;jk gvNvp]k;,uvkp59adxu L 49

[qfmu 17 dko0Po c]t dko9af]Po ]efa[9eo;o !D dko0Po9eo;oD dD 9q’j 0Po9eo;og,af gxao8q;g]d c]t 8q;|a’ln X7evjko?D sq; sq; sq; gxao8q;g]d gxao8q;|a’ln Ihvp ly[ |j;p !W# |bj’Ihvplk, D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D ສະຫງສ.ວວນ.ລິສຂະສິດ 0D 9q’j 0Po8n,j .l8j k8t]k’D 9eo;o sq;Ihvp sq;ly[ sq;|;j p 8q;|a’lnX7evjko? !@$ ! @ $ |b’j Ihvp-k;luj &* )_ !W& !#! !_( 50

7D 9qj’0Po9eo;og’yo.lj[vj o9Eg,afD !WW du[ &W du[ &W du[ &W du[ @W du[ !W du[ @W du[ @W du[ ! du[ ! du[ ! du[ ! du[ ! du[ !$$ du[! du[! du[ !)# du[ &W du[ &W du[ &W du[ @W du[ ! du[ ! du[ ! du[ &W du[ ! du[ @W du[ @W du[ !! ddu[u[ ! du[ !! ddu[u[ @W du[ @W du[ D D D D D du[ D D D D D du[ !W du[ ສະຫງສ.ວວນ.ລິສຂະສິດ !WW du[ & du[ ! du[ !WW du[ @W du[ ! du[ !W du[ @W du[ ! du[ !W du[ &W du[ @W du[ ! du[ & du[ @W du[ D DDD D du[ ! du[ D D D D D du[ ! du[ CD 9q’j 0Po9eo;o8n,j .lj[vj o9Eg,afD 40 + . . . . = 45 31 + . . . . = 40 52 + . . . . = 60 67 + . . . . = 70 74 + . . . . = 80 75 + . . . . = 90 83 + . . . . = 90 160 + . . . . = 180 86 + . . . . = 100 195 + . . . . = 200 51

9D 9q’j la’gdf9eo;o]5,j oUD 144; 151; 164; 142; 130 128; 174; 182; 136; 200 ♦ 0Po9eo;omujs^kpd;jk !$*D [[[ ♦ 0Po9eo;omu|j hvpd;jk !&!D [[[ [ s^ lD 9q’j 0Po9eo;omujdq’da[[afc]dxPj oD . . . . . 2[ [[ ສະຫງສ.ວວນ.ລິສຂະສິດ [[ [[ s^ s^ s^ 131 . . . . . 2[ 2[[ 2 s^ s^ [ s^ s^ [ [ s^ s^ s^ s^ s^ s^ s^ s^ s^ s^ s^ s^ s^ . . . . . . . . . . . . . . . -D 9qj’la’gdfc]h;0Po9eo;o8nj,.lj8kmu;j kj ’D 63 59 70 85 31 47 60 95 106 117 65 87 33 62 83 44 100 128 52

@D dko9af]Po]efa[9eo;oD 100 dD 9q’j 0Po9eo;o8nj,.lj8k,]efa[D 94 96 105 111 .sh4nd8hv’D 117 0D 9qj’0Po9eo;o8n,j .lj 110 100 ສະຫງສ.ວວນ.ລິສຂະສິດ 65 70 80 7D 9qj’9af]Po9eo;o]5,j oUD 26 121 34 142 48 156 172 62 200 94 ♦ c8|j hvpsks^kpD ♦ c8js^kpsk|hvpD 53

[qfmu 18 g8adoyddko[;d !D 9q’j [;d9eo;ofh;p]6d7yfD sq;Ihvp sq;ly[ sq;|;j p + = 2 1 4 + 2 3 = . . . . . @ # ( sq;Ihvp sq;ly[ sq;|;j p + = 1 3 6 + 1 2 3 = . . . . . @ & ສະຫງສ.ວວນ.ລິສຂະສິດ_ @D 9qj’[;d9eo;ofh;pg,afD 3 5 1 3 0 + 4 7 + 2 8 . . . . . . . . + 7 5 134 1 0 6 + 36 54

#D 9qj’7yfw]jD 35 + 24 = 59 3 5 8q;8A’[;d + 2 4 8q;[;d 8q;8A’[;d 8q;[;d zqo[;d 5 9 zqo[;d 4 2 + 3 7 = . . . 6 8 + 1 2 = . . . 8 3 + 1 6 =. . . 142 + 2 8 = . . . 160 + 3 8 = . . . 107 + 1 3 =. . . 7 8 8 5 1 5 6 1 6 5 + + + + 3 5 1 7 2 8 3 2 1 2 3 5 6 6 4 8 2 ສະຫງສ.ວວນ.ລິສຂະສິດ + + + + 4 7 1 4 3 1 1 6 1 1 8 $D 9q’j 0Po8n,j .l8j k8t]k’D 8q;8A’[;d &@ (@ )$ !&@ !*) !)W 8q;[;d !$ @* !& !( @$ !& zqo[;d ** 55

&D 9q’j 0Po8n,j .l8j k8t]k’D + 10 20 30 40 50 + 42 51 65 70 84 15 21 16 35 27 63 28 72 39 84 *D 9qj’0Po8n,j .lj8k8t]k’D 5 10 15 20 25 30 +5 10 ສະຫງສ.ວວນ.ລິສຂະສິດ + 10 20 + 20 8 12 15 18 26 34 28 + 30 58 (D 9qj’0Po9 eo;ogru,j 0Bogmnjv]t !W S @W S #W D WF !WF D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D !WW WF @WF D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D !)W WF #WF D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D !)W 56

)D 9q’j la’gdfc]h;0Po8n,j .lj[jvo9Eg,afc]t8k8t]k’D sq;Ihvp sq;ly[ sq;|j;p 100 + 10 + 10 + 10 + 10 + 6 1 4 6 . . . + . . .+ . . .+ . . .+ . . .+ . . .+ . . .+ . . .+. . . 1 7 1 ...+...+...+... 100 + 1 0 + 10 + 10 + 4 . . . + . . .+ . . .+ . . .+ . . .+ . . .+ . . .+ . . . 7 5 . . . + . . .+ . . .+ . . .+ . . .+ . . .+ . . .+ . . . 1 6 5 _D 9q’j 8n,j 8q;g]dmugj \\ktlq,.l.j o + 7 4 +8 6 + 8 7 + 9 2 ສະຫງສ.ວວນ.ລິສຂະສິດ+ 5 0 1 3 4 54 15 4 9 8 99 9 0 18 6 +1 2 0 + 1 0 0 + 8 0 + 5 +1 5 2 0 9 8 4 5 1 1 7 0 1 9 9 1 4 8 1 4 0 35 3 !WD 7v[7q;]5’l5d]hP’cdjz6h @& 38F wdjc,j && 38F wdoj hvp !WW 38 4k,;jk7v[7q;]5’l5d]hP’wdj ma’\\qf9ad38 L !!D l;o0v’]5’lk]u ,u8Qo\\kd,;j ’ &@ 8QoF 8Qo\\kd,U !W 8QoF 8Qo \\kd]ewp !) 8Qo 4k,;jk l;o0v’]k;,u8Qo\\kdw,hma’\\qf 9ad8Qo L 57

[qfmu 19 dko-vdsk9eo;o|bj’0v’ dko[;d !D 9qj’la’gdfc]h;7yfw]jD 8q;8A’[;d T 8q;[;d = zqo[;d -vdsk8q;8A’[;d = zqo[;d { 8q;[;d !W 8q;1jk’G d T $ = !W d = !W {$ d = * X d c,jo8q;8A’[;d? d $ -vdsk8q;[;d = zqo[;d { 8q;8A’[;d !W ສະຫງສ.ວວນ.ລິສຂະສິດ 8q;1kj ’G * T 0 = !W 0 = !W { * 0 = $ X 0 c,jo8q;[;d? * 0 . . . + 5 = 11 8 + . . . = 17 . . . + 10 = 37 91 + . . . = 99 . . . + 100 = 160 100 + . . . = 189 . . . + 36 = 136 70 + . . . = 130 . . . + 13 = 28 72 + . . . = 185 58

@D 9qj’0Po8n,j .lj8k8t]k’D 8q;8A’[;d 8q;[;d zqo[;d 8q;8A’[;d 8q;[;d zqo[;d ( !# @W !W @& #& !@ #@ @! $) @W &W &W $& *# )@ !@W !&# (! @_ !#W &@ ສະຫງສ.ວວນ.ລິສຂະສິດ #D 9q’j 8n,j 8q;g]dmujg\\ktlq,.l.j o + 9 4 + + 5 5 + + 1 0 5 180 5 9 31 1 3 2 1 3 5 1 2 3 8 6 + +1 2 3 + + 1 7 5 + 2 2 58 16 7 6 2 1 8 8 199 1 6 9 1 8 9 $D ok’[q;;aogs^qkw,h46jlv’7A’F 7A’mu|b’j gs^qkwfh &) fY; w,h46jmu]k; gs^qkwfhma’\\qf,u !&W fY;D 4k,;kj 7A’mulv’]k;gs^qkwfh9adfY;D 59

[qfmu 20 dko]q[ !D 9qj’7yfw]jD 18 - 12 = 6 3 5 8q;8A’]q[ - 8q;]q[ 8q;8A’]q[ 8q;]q[ zqo]q[ 24 5 9 zqo]q[ 2 8 - 1 5 = . . . ; 4 7 - 3 1 = . . . ; 5 3 - 2 1 =. . . ; 124 - 2 3 = . . . ; 156 - 3 5 = . . . ; 189 - 7 2 =. . . . 5 9 7 4 8 3 9 6 - - - - ສະຫງສ.ວວນ.ລິສຂະສິດ 3 5 5 1 7 2 5 6 1 4 2 1 5 7 1 7 6 1 9 4 - - - - 2 1 4 5 1 5 0 1 0 2 @D 9q’j 0Po8nj,.lj[jvo 53 -13 -20 75 -15 -30 150 -20 -15 60

#D 9q’j 0Po8n,j .l8j k8t]k’D 8q;8A’]q[ 8q;]q[ zqo]q[ 8q;8A’]q[ 8q;]q[ zqo]q[ 54 24 146 25 78 62 152 131 85 15 175 145 87 27 184 140 98 48 191 181 $D 9q’j 0Po8q;g]d8nj,.lj - 5 4 - 6 - 7 3 - 8 ສະຫງສ.ວວນ.ລິສຂະສິດ- 9 5 3 1 4 2 4 24 4 2 2 2 5 3 2 6 0 5 4 &D djvo[+maos^Yo ok’ [5o,u ,ucdjo\\kd0k,faj’.oI6[]5j,oUS rkps^a’ sY^oc]h; ]k;glpcdjo\\kd0k, @) cdjoD 4k,;jk cdjo \\kd0k,0v’]k;pa’gs^nvgmqjk.f L X9qj’8A’gxao[A’g]d c]h;7yfw]j?D 61

[qfmu 21 g8adoyddko]q[ !D 0hvp,ug’yo !@& du[F wfh9kj pwxc]h; (# du[ 9qj’la’gdf;ymu muj0hvp xt8y[afc]t0Po.lj 100 10 100 10 10 10 10 10 10 1 10 1 10 10 10 10 1 1 10 10 10 1 1 1 1 10 10 1 10 10 10 10 1 1 125 -3 122 . . . -70 . . . . ສະຫງສ.ວວນ.ລິສຂະສິດ -73 125 - 73 = . . . . . @D 9q’j la’gdfg[y’j dko7yfw]j !)$ { !@&D 7 10 + 4 ♦ $ sq;|j;p]q[ & sq;|j;p[+wfh 1n, ! 1 8 4 sq;ly[ 9kd ) sq;ly[,k 8nj,.ljgxao 1 2 5 !$ sq;|j;pD!$ sq; |j;p]q[vvd & 0 5 9 sq;|j;p gmqjk _ sq;|;j p ♦ ) sq;ly[1n,wx ! sq;ly[gs^nv ( sq;ly[D ( sq;ly[]q[vvd @ sq; ly[gmqjk& sq;ly[D ♦ ! sq;Ihvp]q[ ! sq;Ihvpgmqjk WD 62

#D 9qj’7yfw]Dj - 91 51 - 8 1 1 1 5 . . . . . . 7 6 - 7 5 - 6 15 2 6 2 6 . . . . . . . . . . . . - 48 43 - 7 13 4 4 ສະຫງສ.ວວນ.ລິສຂະສິດ . . . . . . ... ... - 97 34 - 8 13 7 4 . . . . . . ... ... $D 9qj’7yfw]jD - 5 7 - 7 6 - 7 3 - 8 5 - 9 4 2 8 3 7 3 7 4 9 2 8 - 1 5 4 - 1 3 2 -1 6 3 - 1 8 6 - 1 9 1 1 2 5 1 2 1 4 5 6 7 8 3 63

&D 9qj’xt8y[af8k,0Ao8vo.oI6[grnvj ]q[g]d8+wxoUD d !$& { !WW !$& ]q[ !WW 0 !@$ { !W& { !WW {& DDDDD @$ !@$ 145 - 100 = ..................... 124 - 105 = ..................... 7 !&( { !#$ !&( { !#$ C !_$ { )& 8 14 13 1 9 4 + 8 5 .. .. ... ..... ..... 157 ສະຫງສ.ວວນ.ລິສຂະສິດ 157 - 134 = ..................... 194 - 85 = ..................... 9 @WW { )* l !#$ { *) + 4 . . . + . . . + . . . 2 14 86 200 1 3 4 6 5 ... ..... ..... 200 - 86 = ..................... 134 - 68 = ..................... 64

*D 9qj’8A’[A’g]dc]h;7yfw]Dj 183 - 119 = . . . 149 - 128 = . . . 184 - 151 = . . . 192 - 154 = . . . 147 - 129 = . . . 165 - 136 = . . . 194 - 182 = . . . 178 - 127 = . . . 179 - 128 = . . . 146 - 132 = . . . (D 9qj’7yfw]Dj ສະຫງສ.ວວນ.ລິສຂະສິດ - 1 6 4 - . . . - 1 9 8 - 1 7 3 - ... . . . 1 2 3 . . . . . . 135 0 7 1 1 2 9 1 1 9 051 1 0 9 )D ok’ ok]u ,u\\kddhP’ !&) |j;pF ]k;0kpwxc]h; *_ |;j p 4k,;jk \\kddhP’pa’gs^nv9ad|;j p L _D ;aomu ! gfnvo ,u45ok xudkpoU 3I’IPoxt4q,cs’j |bj’x6d8Qow,h !(@ 8QoF l;j oxuoUx6d !_W 8QoD 4k,;kj xuoUx6ds^kpd;jkxudkp 9ad8Qo L 65

[qfmu 22 mtot[af X g’yodu[ ? !D mtot[af X g’yodu[ ?F ສະຫງສ.ວວນ.ລິສຂະສິດ 66

@D 9qj’la’gdf9eo;og’yo0v’c8]j t7qoc]h;8v[7e4k,D ok’ ,uok mhk; lk]u T ok’ ,uok ,ug’yo9addu[ L T mhk; lk]u ,ug’yo9addu[ L T .z,ug’yo s^kpd;jk c]t s^kpd;j kgmqjk.f L ສະຫງສ.ວວນ.ລິສຂະສິດ #D 9qj’7yfw]9j eo;og’yo8+wxoUG dD + + + = 165 0 D + + =. . . . . . 7 D + + =. . . . . . C D + + =. . . . . . 9D + + =. . . . . . 67

ສະຫງສ.ວວນ.ລິສຂະສິດ$D 9qj’[vd]k7k\\kdw,hc8]j t-toyfD 7k]kGD D D D D 7k]kGD D D D D 7k]kGD D D D D 7k]kGD D D D D 7k]kGD D D D D 68

&D 9qj’la’gdfI6[c]h;8v[7e4k,D dh;p9no ! 4q’ &W du[ 0a[]qf7A’]t !@W du[ /kd]qf4u[ #W du[ ]qf9ad &W du[ 0P[ czoj ]t !W du[ -kg1ao4q’]t @W du[ 0a[pqo7A’]t !&W du[ \\kdx6,gxQk|j;p]t !& du[ \\6o7A’]t !WW du[ ♦ ]k7kdh;p9nocr’d;jk]k7kg0Qk0P[gmqjk.f L ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ ]k7k2kd]qf4u[ 4ndd;kj ]k7k2kd]qf9adgmqkj .f L ♦ x6,gxQk # |j;p]k7kgmqkj .f L ♦ ]k7klyo7hkc8j]txtgrfvao.f4ndd;jk\\6j c]t vao.fcr’ d;kj \\6j L *D 9qj’-j;pc]dxjPog’yo]5j,oUG ♦ g’yo.[ !WW du[ c]dxPj ogvqk.[ &W du[ 9twfh9ad.[ L ♦ g’yo.[ !WW du[ c]dxjPogvqk.[ @W du[ 9twfh9ad.[ L ♦ g’yo.[ &W du[ c]dxPj ogvqk.[ !W du[ 9twfh9ad.[ L ♦ g’yo.[ @W du[ c]dxjPogvqk.[ !Wdu[ 9twfh9ad.[ L ♦ g’yo.[ @W du[ c]dxjPogvqk.[ & du[ 9twfh9ad.[ L ♦ g’yo.[ !W du[ c]dxjPogvqk.[ ! du[ 9twfh9ad.[ L 69

[qfmu 23 I6[c[[dko0Po9eo;o !D 9q’j 0Po9eo;omujdq’da[[afc]dxjPo.l[j vj o9Eg,af X 2 = !WW S [ = !W S s^ = ! ? [[ 2 [ [ [[ [[ [ [[ s^ s^ 2 s^ s^ [ [ [ s^ s^ s^ [ [ s^ D D D D D D D D D D D D D D D D D D D D 2[ 2 sss[^^^ 2 [[ [ 2 [[ [ s^ sssD^^^ [ [ [ [ s^ s^ [[ [[ s^ s^ D D D D D DDDDD D D D D D D D D D ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9qj’la’gdfc]h;xt8y[af8k,8q;1jk’D 9eo;ogxao 9eo;ogxao I6[c[[dko0Po sq;Ihvp sq;ly[ sq;|j;p 8q;g]d 8q;|a’ln X7evjko? !W_ |bj’IhvpgdQk !WW T _ ! W _ !)$ @WW #D 9q’j 0Po9eo;o8n,j .l[j vj o9Eg,af.sh4nd8hv’D 100 + 20 + . . . = 122 100 + . . . + 5 = 185 . . . + 1 + 8 = 16 100 + 80 + . . . = 190 20 + 8 + . . . = 48 100 + 90 + . . . = 196 . . . + 60 + 3 = 163 100 + 20 + . . . = 127 50 + 10 + . . . = 69 60 + 40 + . . . = 146 70

$D dko0Po9eo;o|bj’.oI6[c[[8jk’MD . . . . . . . . . . . 1 2 5 !WW T!W T!W T & |nj’Ihvp-k;shk &D 9q’j 7yfw]cj ]h;8n,j .l8j kmu;j jk’.o8k8t]k’D ສະຫງສ.ວວນ.ລິສຂະສິດ + 5 6 7 8 9 + 50 51 52 53 54 5 11 12 14 50 6 11 13 14 51 7 12 14 16 52 53 8 14 16 17 54 9 14 16 17 *D 9q’j 0Po9eo;ogxao8q;\\a’lnD ** = . . . !&@ = | bj’Ihv pshk ly[l v’ !# = . . . @* = . . . _! = . . . $( = . . . 71

[qfmu 24 dko7yfw]7j ;k,]5f]njo !D 9qj’la’gdfI6[F 7yfw]j c]h;0Po7e8v[.lj[vj o9Eg,afD 0hvpl6’!#& -a’8uc,af ,hk0hvpl6’ !$W -a’8uc,af 0hvpl6’ !$& -a’8uc,af ok’ g9ap]u mhk; ]=g1u ສະຫງສ.ວວນ.ລິສຂະສິດ ,hkl6’ DDDDDDDDDDDDDD -a’8uc,afD mhk; ]=g1u l6’ DDDDDDDDDDD -a’8uc,af ok’ g9ap]u l6’ DDDDDD -a’8uc,afD mhk; ]=g1u l6’]njo ok’ g9ap]uDDDD -a’8uc,af @ D 9qj’la’gdf8k8t]k’F 7yfw]cj ]h;0Po7e8v[.l[j vj o9Eg,afD ]efa[ -n j 7tcoo @_ ! ok’ 95]u @ mhk; lvow- ## # ok’ ]ugra’ #& $ mhk; 9aofu @( & mhk; -q’dk; #W mhk; -q’dk; wfh7tcoo]5f ok’ ]ugra’ DDDDDDDDDDDDDDDDDDDDD 7tcoo mhk; lvow- wfh7tcoo]njo ok’ 9aofu DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD7tcoo 72

#D 9q’j la’gdfdkos^uho c]h;0Po.lj[jvo9Eg,afD 2 gxQk\\kp f 0 42 43 44 45 46 47 48 49 50 51 52 53 54 ♦ 7;k,]f5 ]ojn doa ]ts;kj ’8km,ju /u kvfa cd;h lcu f’ c]tgxkQ \\kp c,oj G $_ T DDDDDD = &$D ♦ 7;k,]f5 ]ojn doa ]ts;kj ’8km,ju /u kvfa cd;h l0u P; c]t gxkQ \\kp c,joG $_ { DDDDDD = $&D $D 9q’j oe.-hczoj 9eo;ogrnjv0Po.l8j k8t]k’D ສະຫງສ.ວວນ.ລິສຂະສິດ gxQk\\kp /kvafcdh; 7;k,]5f gxQk\\kp /kvafcdh; 7;k,]5f 8qd.l8j k ]njodao 8qd.l8j k ]noj dao !# *@ # #@ *@ !@ !( !W $# @& !& #& _ #@ $* $* ( ## $& #* @W $) $! #_ !$ 73

&D .odkoc]oj mqoF 7;k,]5f]noj daofhkog;]k]ts;kj’z6hwfhmu|b’j c]t z6hmulv’c,jo # okmuS ]ts;kj ’z6hmulv’ c]t mulk,c,oj @ okmuF I6h;jkz6hwfhmulv’.-hg;]kc]jo $@ okmuD 9qj’-vdskg;]k 0v’z6hmu|b’j c]t z6hmulk, L oadc]jo g;]k oadc]joz6hwfhmu|bj’ oadc]oj z6hwfhmulv’ $@ okmu oadc]joz6hwfhmulk, *D 9qj’la’gdfI6[c]h;8v[7e4k,D ສະຫງສ.ວວນ.ລິສຂະສິດ 0hvp,uoE|ad 0hvp,uoE|ad 0hvp,uoE|ad $& dy3]dik, #@ dy3]dik, $W dy3]dik, $& dy3]dik, #@ dy3]dik, $W dy3]dik, mhk; lk]u ok’ [5o,u ok’ 8kfe ♦ mhk; lk]u |ad]njo ok’ [5o,u $& - #@ = DDDDDDDDD dy3]dik,D ♦ ok’ [5o,u |ad]5f ok’ 8kfe $W - #@ = DDDDDDDDD dy3]dik,D ♦ mhk; lk]u |ad]noj ok’ 8kfe $W + DDDDD = $& dy3]dik,D 74

(D 9qj’la’gdfI6[ c]h;8v[7e4k,D ♦ 9eo;owdj]noj 9eo;ogxaf 12 + … = 18 38D ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ 9eo;osjko]5f9eo;owdj 18 - 10 = …. 38. ♦ 9eo;ogxaf]noj 9eo;osjko 10 + … = 12 38D )D 9q’j 8nj,g7njv’\\kp > S < .l[j vj o9Eg,afD 7 + 6 … 6 + 8 8 + 8 . . . 7 + 8 6 + 9 - 5 … 11 24 + 2 … 13 – 2 8 + 6 - 10 . . . 3 98 + 32 … 98 + 40 80 + 20 … 96 50 + 6 . . . 60 + 6 60 + 48 . . . 48 +70 75 – 25 . . . 49 75

25[qfm u dko0Po9eo;ofh;pI6[c[[dko76o !D 9qj’-vdsk9eo;olyj’0v’c8]j t-toyfD  8Qow,h # c4;F c4;]t & 8QoD  8Qow,h & 4aoF 4ao]t # 8QoD  8Qow,h,uma’\\qf # & s^n & # ສະຫງສ.ວວນ.ລິສຂະສິດ 8kg9ap,u !W !W 8k gsa^d8kx6 ! c4; ,u _ * fvd dtf5, ! c4;,u ) * vao s^n D D D D D D s^n D D D D D D s^n D D D D D D @D 9q’j c8h,I6[lujc9lkdF 9t85]afF lk,c9.l8j kdk3i8k,9eo;o ]5j,oUD 76

#D 9qj’g]nvdI6[c[[dko76o.sh4ndda[zqo76o]5j,oUD 13 x 3 9 x 5 3 x 4 14 x 2 12 x 2 7 x 5 9 x 3 10 x 3 6 x 6 8 x 9 1 2 = 3 x 4 3 6 = . . . . . . . . . 2 8 = . . . . . . . . 3 5 = . . . . . . . . . . 2 4 = . . . . . . . . 4 5 = . . . . . . . . . . 2 7 = . . . . . . . . 3 0 = . . . . . . . . . . 7 2 = . . . . . . . . 3 9 = . . . . . . . . . . ສະຫງສ.ວວນ.ລິສຂະສິດ $D 9qj’7yfw]Dj 9 1 2 2 1 3 4 6 3 x x x x x 4 5 2 3 3 D D D D D D D D D D D D D D D &D oadIPoshv’ xD@ x6dzaddkfwfh _ c4;M]t ) 8QoD 4k,;kj g0qk g9Qkx6dzaddkfwfhma’\\qf9ad8Qo L *D .ldkolv[gla’rkdIPomu ! ,uoadIPofugfaoj 9eo;o !@ 7qoF c8]j t7qowfhIa[0v’0a;oxB,0Poz6h]t # sq;D 4k,;jk 9eo;oxB, 0PomujoadIPowfh Ia[ma’\\qf,u9adsq; L 77

26[qfmu I6[c[[dko76o c]t I6[c[[dko[;d ສະຫງສ.ວວນ.ລິສຂະສິດ !D 9q’j la’gdfI6[c]h;0PoI6[c[[dko76oD oEs;ko ! ]a’ ,u $ c4; c8]j tc4;,u * cdh; oEs;kom a’\\qf,u $ x * cdh; s^n * x $ cdh;D \\kdoaf ! c4; ,u DDDDDDD c4; c8 j]tc4;,u DDDDDDDDDD |j;p \\kdoafma’\\qf,u DDDDDDxDDDDD |j;p s^n DDDDDDxDDDDD |j;pD @D 9eo;o @$ lk,kfltcf’fh;p;af45lyj’0v’ rkp.8hs^kp I6[c[[dko76oF $ x * s^n * x $D @ x !@ s^n !@ x @ # x ) s^n ) x #D ! x @$ s^n @$ x !D 78

#D 9q’j ltcf’9eo;o]5,j oUrkp.8hs^kpI6[c[[ dko76oF !@ #@ $) #* $ V ) ) V $ @ V !* !* V @ ! V #@ $D 9q’j 0Po9eo;oI6[oqd.oI6[c[[dko[;d c]t dko76oD ສະຫງສ.ວວນ.ລິສຂະສິດ 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 5 V 9 . . . . . . . .. . . . . . . . . . . . . . . . . . .= . . . . . . . 79

&D 9q’j 9afI6[c[[dko0Pomujltcf’g4y’ 9eo;ofP;daow;h[jvo fP;daoD 24 36 32 20 30 12 + 12 3 x 10 8 x 4 10 + 10 + 10 6 + 6 + 6 + 6 2 x 18 3 x 12 4 x 8 8 + 8 + 8 12 + 12 + 12 7 x 4 7+7+7+7 16 + 8 6 x 5 16 + 16 5 + 5 + 5 + 5 + 5 *D 9qj’7yfw]Dj ສະຫງສ.ວວນ.ລິສຂະສິດ 4 + 4 + 4 + 4 = 4 x 4 = 16 7 + 7 + 7 + 7 + 7 = . . . x . . . = . . . 5 + 5 + 5 + 5 = . . . x . . . = . . . 8 + 8 + 8 = . . . x . . . = . . . 10 + 10 + 10 + 10 =. . . x . . . = . . . (D .oshv’ xD@ ,u38t c]t 8a’j ma’\\qf !W -5f c8]j t-5foa’j wfh @ 7qo 4k,;jk oadIPoma’\\qf,u9ad7qo L 80

[qfmu 27 dkorq;rao]ts;kj ’|hk8jk’MI6[dhvo !D 9q’j la’gdfI6[0hk’]5j,oUD 2 3 1 4 5 6 ສະຫງສ.ວວນ.ລິສຂະສິດ  I6[dhvo0hk’gmy’oUwfhltcf’.shgsaoc8j]tmjk0v’I6[|hk 0v’r;d,aoD 9qj’[vdI6[dhvooEg[u.f ltcf’.shgsaoI6[|hk fa’j 8+wxoU X ,us^kp7e8v[ ?D 81

@D 9qj’0uf9vj ’I6[mu7j hkp7ndao.ldj aoD 1 2 3 4 5 d 0 97 C #D 9qj’-U[vdI6[mujdq’da[I6[c[0v’,aoD ສະຫງສ.ວວນ.ລິສຂະສິດ 82

$D .sh\\kddt]avd 8yfda[ $ |hkvnjoMD 9qj’[vd|hk  |hkmuj,u # c8h, muj8yfda[,aoD  9q’j [vd;jk|hk 8yfda[|hk.f L  .oc8j]td=]tou9qj’[;dc8h,0v’|hkmuj[+8yfda[,aoda[c8h,ສະຫງສ.ວວນ.ລິສຂະສິດ 0v’|hkmuj.sh,kD &D 9q’j 0ufglAo9vj ’I6[.lIj vprNo0v’,aoD d   0 7 C ! @ # $ 83

*D 9q’j -U[vdI6[c8]j tvao.lIj vprNo mujdq’da[,ao g-ajoI6[ X ! ? dq’da[ I6[ X d ?D ສະຫງສ.ວວນ.ລິສຂະສິດ (D 9qj’la’gdfc]h;8v[7e4k,]5j,oUG  dtfkofe.spj16.j oshv’ gxaoI6[spa’ L  |hk38t76gxaoI6[spa’ L  rNo0v’shv’IPogxaoI6[spa’ L  xt86shv’IPogxaoI6[spa’ L  xB,c[[IPo7toyflkf xD@ gxaoI6[spa’ L 84

[qfm u 2 8 dkolhk’ c]t dkooe.-h 8k8t]k’ dko76o !D dkolhk’8k8t]k’dko76oD dD 9q’j la’gdf4q’dhvosuo0v’lv’7qoD ok’ [5,uD mhk; [5og8a,D ( dhvo & dhvo ♦ ok’ [5o,u ,udhvosuo 7 x 5 = . . . .dhvoD ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ mhk; [5og8a, ,udhvosuo 5 x 7 = . . . .dhvoD ♦ la’gdf9eo;odhvosuo0v’lv’7qogxaoco;.f L 0D 9qj’ln[8+0Po8n,j .l8j kmu;j jk’D x 1 2 3 4 5 6 7 8 9 10 1 2 5 8 2 6 12 18 3 3 12 21 30 4 8 20 32 5 15 30 45 6 24 42 60 7 7 35 56 8 16 48 72 9 27 63 90 10 40 80 100 85

@D dkooe.-h8k8t]k’dko76oD dD 9q’j ln[8+0Po9eo;og’yo.l8j kmuj;kj ’D xtgrf 9eo;o.[g’yo g’yo ! @ # $ & * ( ) _ ! du[ ! du[ $ du[ (du[ & du[ !Wdu[ @&du[ $Wdu[ !W du[ #Wdu[ *Wdu[ _Wdu[ 0D 9q’j 0Po8n,j .l8j k8t]k’D x 1 2 3 4 5 6 7 x 3 4 5 6 7 8 9ສະຫງສ.ວວນ.ລິສຂະສິດ 1 6 2 7 3 8 4 9 5 10 7D 9qj’7yfw]jD 10 9 9 8 7 x x x x x 2 6 4 3 5 . . . . . . . . . . . . . . . 6 x . . . = 30 24 = 3 x . . . 42 = 6 x . . . 8 x . . . = 64 9 x . . . = 54 60 = 10 x . . . 86

[qfm u 29 dko7eo;o8k,]efa[ c]t dko0Po.oI6[c[[xtlq, !D dko7eo;o8k,]efa[D dD 9qj’7yfw]8j k,[kfdhk;mujdeoqf.shD 9 x 3 + 5 x 5 + 7 x 8 + 4 x 6 + + + 0D 9q’j 7yfw]j8k,[kfdhk;mujdeoqf.shD 5 + 8 + 6 + 4 + 7 ສະຫງສ.ວວນ.ລິສຂະສິດ . . . . . . 5 + 8 + 6 + 4 + 7 5 + 8 + 6 + 4 + 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7D 9qj’7yfw]j8k,[kfdhk;mudj eoqf.shD 4 + ( 5 x 3 ) + 7 ( 4 + 5 ) x ( 3 + 7 ) 4 + 5 x ( 3 + 7 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

@D dko0Po.oI6[c[[xtlq,D dD 9qj’0PoI6[c[[xtlq,]5,j oU.l8j k8t]k’D ( 4 x 2 ) + 4; ( 10 x 2 ) + 5; 2 ( 2 x 10 ) + 10; ( 2 x 5 ) + 5 9eo;o !@ @& #W !& I6[c[[xtlq, X $ x @ ? T $ D D D D D D D D D D D D D D D 0D 9q’j cdh39f]5,j oUD ( 2 x 15 ) + 5 !D ok’ 9aofu ,u\\kd,;j ’ @ 4q’M]t . . . . . . !& |j;p c]t [+wfh.lj4q’vud & ສະຫງສ.ວວນ.ລິສຂະສິດ |j;p 4k,;jk]k;,u\\kd,j;’ ma’\\qf9ad|;j p L @D mhk; [5o,u -Nl= # dhkoM]t &W du[F ( 3 x 50 ) + ( 2 x 60 ) -N[yd @ dkh oM ]t *W du[D 4k,;kj . . . . . . ]k;\\qfg’yo ma’\\qfgmqkj .f L . . . 7D 9qj’7yfw]jsk7e8v[.oc8]j t0=h]5j,oU c]h;gvqk8q;|a’lnmu,j u7e8v[ c8|j hvpsks^kp .lj8k8t]k’9twfh7;k,\\kpspa’ L (5 x 3)+ 4=... P (5 + 3) - (8-4)= . . . 3 (3 x 2) + (2 + 4) = . . . C 3 x (10-5)=... I (4 + 8) + (2 x 7) = . . . o (2 x 7) - 9 = . . . I 88

[qfmu 30 9eo;oc8j !WW g4y’ ___ !D 9qj’la’gdfc]h;0Po8n,j .l8j kmu;j kj ’D 22 22 2 2 *WW T @W *@W sqdIhvp-k; 2 = 100 [ [ [ = 10 $WW T ( s^ = 1 2 22 #$@ [[ s[^ [s^ 2 2 2 2 g9afIhvplk,ly[ 22 2[ s^ s^ s^ ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9q’j 0Po9eo;o.ljg7njv’oa[]5,j oUD 5 6 3 5 4 8 3 8 9 +1 +10 +100 #D 9qj’xP[mP[ 9eo;o]5j,oU3fp.-hg7nvj ’\\kp >; <; = 708 > 307 421 = 421 895 < 598 352 . . . . 532 906 . . . . 609 109 . . . . 109 515 . . . . 515 658 . . . . 865 698 . . . . 869 909 . . . . 990 889 . . . . 989 999 . . . . 999 89

$D 9q’j 0Po9eo;ogxao8q;g]dc8j|hvpsks^kp.lj8k8t]k’D |b’j Ihvp sq;Ihvp sq;ly[ sq;|;j p ! W W lk,Ihvp gdQkIhvply[lk, cxfIhvplv’ sqdIhvpg9aflly[shk &D 9qj’-vdsk9eo;o7tcoo .odkosU^o-af]6dlvo.lgj xQk\\kp 0v’ mhk; mv’cf’ c]t ok’ le]ufaj’oUD 9 9 ok’ le]u mhk; mv’cf’ 15000 15000 500 500 ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ mhk; mv’cf’-af]6dlvodvj oc]h; ! ]6d 4nd95f !WW c]t pa’ gs^nv]6dlvo @ ]6dF ]k;9t8hv’-af]6dlvomugj s^nv.sh4nd[vj o.f grnjv.sh]k;wfh7tcoo *W_ L ♦ ok’le]u ,u]6dlvo $ ]6dF ]k;8hv’-af.sh4nd[jvo.f grnjv. sh]k; wfh7tcoo *W_ 7ndao L *D 9qj’9af]Po9eo;o]5j,oUG ♦ c8|j hvpsks^kp &WS !WWS #$&S &)WS @&WD ♦ c8sj ^kpsk|hvpD $&WS *#WS )#WS @@WS &)WD 90

[qfmu 31 9eo;orao !D 9qj’\\6og7njv’oa[gruj,0Bogmnvj ]t ! sq;|j;pD 0 9 8 9 0 9 9 0 0 9 9 1 0 9 9 2 @D 9qj’8n,j [aflu c]t c]dxPj o.lj8k8t]k’D ສະຫງສ.ວວນ.ລິສຂະສິດ 0 cmo.sh9eo;o !WWW = |b’j rao 2 cmo.sh9eo;o !WW = |bj’Ihvp [ cmo.sh9eo;o !W = ly[ s ^ cmo.sh9eo;o ! = |bj’ 222 [ [ [ s^ 22222 [ [ [ s^ [ [[ 8n,j .lj 2 8n,j [ .lj 8n,j s^ .lj 91

#D 9qj’la’gdfc]h;0Po8nj,.l8j kmu;j kj ’D 9eo;o 9eo;ogxao8q; sq;rao sq;Ihvp sq;ly[ sq;|j;p gxao8q;g]d |a’ln X7evjko? ! WWW |bj’rao ! W W W |bj’raoluj ! $ # * |b’j raoluIj hvp ສະຫງສ.ວວນ.ລິສຂະສິດ !W@& lk,ly[sqd |b’j raoshkIhvp g9afly[gvaf !_)( $D 9qj’0Po9eo;o7tcoo mujwfhIa[9kddko-af]6dlvo0v’ c8j]t7qoD mhk; 7elu ok’ ok]u 1 1 10 10 100 100 500 500 mhk;7elu D D D D D7tcoo ok’ ok]u D D D D D7tcoo 92

[qfmu 32 ;aoF gfnvoF xu !D 9qj’ln[8+0Po;ao8jk’M.o|b’j vkmyfD ;aovkmyf ;aor5f @D 9qj’oe.-hxt8ymyogrnvj 8v[7e4k,]5,j oU X8q;g]d lucf’ c,oj ;aorad?D gfnvo g,lk ;ao vkmyf ;ao 9ao ;ao va’7ko ;ao r5f ;ao rtsaf ;ao l5d ;ao glqk ! @ # $ & * ( ) _ !W !! !@ !# !$ !& !* !( !) !_ @W @! @@ ສະຫງສ.ວວນ.ລິສຂະສິດ @# 30 @$ @& @* @( @) @_ gfnvo rbfltrk ;ao vkmyf ;ao 9ao ;ao va’7ko ;ao r5f ;ao rtsaf ;ao l5d ;ao glqk ! @ # $ & * ( ) _ !W !! !@ !# !$ !& !* !( !) !_ @W @! @@ @# @$ @& @* @( @) @_ #W #! ♦ oadIPoshv’ xD@ IPo7toyflkf.o;aova’7koF ;aortsaf c]t ;aol5d 4k,;jk G ♦ .ogfnvog,lk r;dg0qkg9Qk wfhIPo 7toyflkf9ad;ao L ♦ .ogfnvornfltrk r;dg0qkg9Qk wfhIPo 7toyflkf9ad;ao L 93