ຄະນິດສາດ

#D dko]q[,u1n,D - 2 3 - 5 5 - 4 2 dD 9q’j 7yfw]jg]d]5,oUD 1 4 4 8 23 - 6 0 - 2 3 5 6 1 4 0D ;ymu]q[g]d,u1n,D 8q;1kj ’!G 23 - 7 = ? sq;ly[ sq;|j;p 2 3 10 10 ສະຫງສ.ວວນ.ລິສຂະສິດ - 7 - 1 6 = 10 ♦ .shgvqksq;|j;pda[sq; 1 6 |j;p]q[daodvj oc8j # ]q[vvd ( [+ wfh8hv’1n, ! ly[ 9kdsq;ly[,kc]h;[;dda[ # wfh !# 9bj’gxao !# { ( = * 0Po * w;hD sq;ly[gfu,gxao @ g,njv 4nd1n,wx ! d=gs^nv ! g,njv[+,u8q;]q[d=-ad]q’,kg]upD 143

8q;1kj ’@G 35 - 18 = ? sq;ly[ sq;|j;p 3 5 10 10 10 - 1 8 1 7 10 10 1 7 ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ .shgvqksq;|;j pda[sq;|;j p ]q[daodvj oc8j & ]q[vvd ) [+wfh 8hv’1n, ! ly[9kdsq;ly[,kc]h;[;dda[ & wfh !& 9b’j gxao !& { ) = ( 0Po ( w;hD sq;ly[gfu,gxao # g,njv4nd1n,wx ! d= gs^nv @ g,jnvgvqk ! ,k]q[vvd9b’j gs^nv !D 7D 9q’j 7yfw]j.lxj B,0PoD - 4 3 - 4 2 9 8 - 6 0 - 3 7 - 5 2 - 3 6 - 2 4 4 5 1 1 3 7 1 8 1 5 - 3 2 - 2 1 - 4 5 1 5 1 9 2 6 144

[qfm u 35 dko7yfw]j !D 9q’j dkj p.ljxB,0Poc]h;7yfw]jD ( 17 + 3 ) - 2 = ... ( 18 + 2 ) - 5 = ... ( 19 + 1 ) +( 3 - 2) = ... ( 18 + 2 ) + ( 18 - 2 ) = ... 25 - 5 + 7 = ... 40 + 20 - 60 = ... 50 - 10 + 6 = ... 47 + 3 - 12 = ... @D 9q’j dkj p.lxj B,0Poc]h;7yfw]Dj {& T!W + 8 4 3 5 7 9 10 10 18 55 50 10 20 ສະຫງສ.ວວນ.ລິສຂະສິດ 20 27 45 ... 30 ... 30 35 ... 20 ... 40 25 ... 50 ... 50 60 15 ... 40 ... #D 9q’j dkj p.lxj B,0Poc]h;7yfw]jzqo[;dD 15 13 25 . . . 16 30 14 . . . 21 17 12 . . . . . . . . . . . . zqo[;dmk’ovo zqo[;dmk’8A’ 145

$D 9qj’djkp.ljxB,0Poc]h;7yfw]Dj + 5 28 + 4 37 + 12 65 + 13 37 + 2 8 1 1 7 - 26 0 - 15 87 - 5 76 - 4 85 - 13 7 5 1 3 9 &D 9qj’djkp.lxj B,0Poc]h;xt8y[af8k,8q;1kj ’D ສະຫງສ.ວວນ.ລິສຂະສິດ 9 19 29 39 49 59 + 2 + 2 11 61 g]d39fD !D ok’ ;P’7e c]oj wxwfh #@ c,fa F pkj ’8+wxvud @) c,fa D 4k,;kj ]k;gfuomk’ma’\\qfwfh9adc,af L @D oadIPoshv’ xD! ,u @& 7qoS shv’ xD@ ,u @W 7qoS shv’ xD# ,u !& 7qoD 4k,;jk oadIPoma’\\qf,u9ad7qo L 146

*D 9q’j djkp.lxj B,0Poc]h;7yfw]Dj 27 + 5 = ... ( 7 + 3 ) - 2 = ... 17 - 5 = ... ( 18 - 5 ) + 3 = ... 37 + 19 = ... 27 - ( 10 + 3 ) = ... 45 - 17 = ... ( 27 + 10 ) - 3 = ... 26 - 17 = ... ( 9 + 2 ) - ( 3 + 1 ) = ... (D 9qj’djkp.ljxB,0Poc]h; xP[mP[9eo;o]5j,oU3fp.-hg7njv’ ສະຫງສ.ວວນ.ລິສຂະສິດ \\kp > ; < ; = D 60 ... 45 51 ... 42 33 ... 33 38 ... 38 57 ... 60 10 ... 10 18 ... 27 49 ... 35 24 ... 16 g]d39fG !D gvNvp0hvp8adoE.ljwsg8a, !* 75F 0hvp c]t ohv’wfhvk[wx c]h; & 75F gvNvp8ad,k.lvj ud $ 754k,;kj 16.j ows,uoEma’\\qf 9ad75 L @D l=0k;da[|’bj ,u $W cm’j F ,Nm|uj ’bj okp76wfh0Po\\qf !W cm’j F ,Nmujlv’0Po\\qf !& cm’j F 4k,;jk l=0k;16j.oda[pa’gs^nv 9adcmj’ L 147

)D 9q’j djkp.ljxB,0Poc]h;7yfw]Dj ... + 17 = 37 ... - 21 = 31 27 - ..... = 20 ... + 19 = 39 ... - 40 = 20 34 + ..... = 35 ... - 32 = 2 43 - ..... = 30 55 + ..... = 58 60 - ..... = 30 _D 9qj’djkp.ljxB,0Poc]h;xt8y[af8k,8q;1jk’D (35-5)+30 ສະຫງສ.ວວນ.ລິສຂະສິດ 60 50 + 5 18+42 34 + 26 (40-10)+10 (50-10)+20 45 + 15 55 + 5 27 + 13 148

36[qf mu 9eo;o c]t dkoxP[mP[ ສະຫງສ.ວວນ.ລິສຂະສິດ !D [vd9eo;o85ddt8kc]h;8v[7e4k,D 4hkomu|b’j 4hkomulv’ ♦ 4hkomu|bj’ 9eo;o85ddt8k,u G DDDDDD 38 ♦ 4hkomulv’ 9eo;o85ddt8k,uG DDDDDD 38 ♦ 4hko.f ,u9eo;o85ddt8ks^kpd;jk c]t s^kpd;jk9ad38 L @D g]d39fD 136j I’IPoxt4,q cs’j |’jb svh ’ xD! ,9u eo;ooda IPo #W 7oq F .oooA oda IPo-kp,u !) 7oq D svh ’ xD@ c]t svh ’ xD! ,9u eo;ooda IPo gmqjkdaoc8jshv’ xD@ ,u9eo;ooadIPo-kp !@ 7qo 4k,;jkG ♦ 9eo;ooadIPopy’shv’ xD! ,u9ad7qoL ♦ 9eo;ooadIPopy’shv’ xD@ ,u9ad7qoL ♦ oadIPopy’shv’ xD! c]t xD@ shv’.f,u9eo;o|hvpd;jk L 149

#D dkoxP[mP[D 9q’j la’gdf c]t vjkog[y’j ]k7klyo7hk.olv’Ihko7hkc]h; 8v[7e4k,D Ihko ,uw- Ihko cl’7e g9hpgrqk $ .[8+ $W du[D l=ludhko ]t !W du[D l=fedhko g9hpgrqk $ .[ 8+ &W du[D ]t !& du[ l=ludhko]t _ du[D ສະຫງສ.ວວນ.ລິສຂະສິດ l=fedhko]t !& du[ xB,0Posq; xB,0Posq; ]t &W du[D ]t $& du[D ♦ g9hpgrqk.oIhko ,uw- $ .[ ]k7kgmqkj .f L ♦ g9hpgrqk.oIhko cl’7e $ .[ ]k7kgmqjk.f L ♦ 4hk-Nl=luohv’9t-N1j6Ihko.fL fh;pgsfzqospa’ L ♦ ]k7kxB,0Po1j6Ihko.fcr’d;kj L ♦ .olv’Ihko7hk,uvao.f]k7kgmqjkdao L 150

37[qf mu 9eo;o c]t dko0Po9eo;o c8j W g4y’ !WW !D 9eo;oc8j *W g4y’ )WD dD la’gdfI6[c]h;[vdI6[dko[;dD ສະຫງສ.ວວນ.ລິສຂະສິດ 80 = .........+ ......... 76 = . ........ +........ 0D 9qj’xt8y[af8k,8q;1kj ’D 9eo;o sq;ly[ sq;|j;p 9eo;o sq;ly[ sq;|;j p 60 6 0 *@ * @ 6 4 *& 68 *( 70 *_ 7 2 (& 75 () 80 (_ 151

7D 9eo;oc8j *W g4y’ )W ,ufa’j oUD 7evjko g]d]k; g]dvkia[ I6[dko[;d sqdly[ *W *W *W T W sqdly[gvaf *! *! *W T ! sqdly[lv’ *@ *@ *W T @ *# *W T # sqdly[lk, *# *$ *W T $ sqdly[luj *$ *& *W T & ** *W T * sqdly[shk *& *( *W T ( sqdly[sqd ** *) *W T ) sqdly[g9af *( *_ *W T _ sqdly[cxf *) (W (W T W sqdly[gdQk *_ (! (W T ! ສະຫງສ.ວວນ.ລິສຂະສິດ g9afly[ (W (@ (W T @ (# (W T # g9afly[gvaf (! ($ (W T $ g9afly[lv’ (@ (& (W T & (* (W T * g9afly[lk, (# (( (W T ( g9afly[luj ($ () (W T ) g9afly[shk (& (_ (W T _ g9afly[sqd (* )W )W T W g9afly[g9af (( g9afly[cxf () g9afly[gdQk (_ cxfly[ )W 152

@D 9eo;oc8j )W g4y’ !WWD ສະຫງສ.ວວນ.ລິສຂະສິດ dD 9qj’[vd9eo;o8+wx8k,8q;1jk’.o0=h ! S @ S # S $ D ! @ # $ 0D 9q’j djkp8k8t]k’.ljxB,0Po c]h;0Po8nj,.l.j sh4nd8hv’D 1 2 3 10 11 15 18 23 26 29 31 34 38 40 42 45 48 50 58 63 65 69 72 76 80 81 84 86 89 93 97 100 153

7D 9eo;oc8j )W g4y’ !WWD 7evkj o g]d]k; g]dvkia[ I6[dko[;d cxfly[ )W cxfly[gvaf ) ! )W )W T W )W T ! cxfly[lv’ ) @ )! )W T @ )W T # )@ )W T $ )W T & cxfly[lk, ) # )# )W T * )W T ( cxfly[lu j ) $ )$ )W T ) )W T _ cxfly[shk ) & )& _W T W _W T ! cxfly[sqd ) * )* _W T @ _W T # cxfly[g9af ) ( )( _W T $ cxfly[cxf ) ) _W T & )) _W T * ສະຫງສ.ວວນ.ລິສຂະສິດ _W T ( cxfly[gdQk ) _ )_ _W T ) _W T _ gdQkly[ _ W _W !WW T W gdQkly[gvaf _ ! _! gdQkly[lv’ _ @ gdQkly[lk, _ # _@ gdQkly[lu j _ $ _# _$ gdQkly[shk _ & _& gdQkly[sqd _ * gdQkly[g9af _ ( _* gdQkly[cxf _ ) _( gdQkly[gdQk _ _ _) __ |bj’Ihvp ! WW !WW 154

#D dko0Po9eo;oc8j ! g4y’ !WWD dD 9qj’dkj p.ljxB,0Poc]h;xt8y[af8k,8q;1jk’D 40+20+30 50+50+0 10+40+50 14+26+30 100 5+15+10 41+49+10 60+10+30 22+58+15 0D 9qj’djkp.ljxB,0Poc]h;xt8y[af8k,8q;1kj ’D ສະຫງສ.ວວນ.ລິສຂະສິດ 9e dko[;d dkodt9kp sq; sq; sq; o;o 0v’dko[;d Ihvp ly[ |j;p 26 20 + 6 10 + 10 + 6 2 6 37 40 + 8 10+10+10+10+9 72 84 80 + 4 100 90 + 10 10+10+10+10+10 1 0 0 10+10+10+10+10 155

7D 9qj’djkp.ljxB,0Poc]h;7yfw]j.lxj B,0PoD !D 10 10 10 10 10 10 10 10 10 10 20 20 20 20 10 + 10=.... ... + ... + ... + ... + 10 + 10 =.... @D 10 10 10 10 10 10 10 10 10 10 ສະຫງສ.ວວນ.ລິສຂະສິດ ... + ... + ... + ... + ... = .... ’D 9qj’xP[mP[9eo;o]5j,oUD ♦ c8j|hvpsks^kpD 1 75; 70; 35; 90; 40; 65; 50; 100; 39; 28. ... > ... > ... > ... > ... > ... > ... > ... >... > ... ♦ c8sj ^kpsk\\hvpD 2 40; 90; 65; 70; 50; 100; 28; 35; 39; 85. ... < ... < ...< ... < ...< ... < ...< ... < ...< .... 156

38[qfm u m;o7nodko0Po9eo;o c]t dko7eo;o !D dko0Po9eo;oD dD 9qj’0Po9eo;o]5j,oUrkp.8hI6[dko[;dD .-h8q;g]d ! 2 = 1 + 1 3 = ... + ... + ... 4 = ... + ... + ... + ... 5 = ... + ... + ... + ... +... .-h8q;g]d @ ສະຫງສ.ວວນ.ລິສຂະສິດ 4 = ... + ... 6 = ... + ... + ... 8 = ... + ... + ... + ... 10 = ... + ... + ... + ... + ... .-h8q;g]d # 6 = ... + ... 9 = ... + ... + ... 12 = ... + ... + ... + ... 15 = ... + ... + ... + ... +... 0D 9q’j 0Pog]dvkia[8k,7evkj o]5j,oUD ly[shk = !& sqdly[ =. . . sqdly[sqd =. . . -k;gvaf = @! g9afly[cxf =. . . lk,ly[gdQk =. . . lk,ly[lv’ =. . . cxfly[g9af =. . . g9afly[lk, =. . . shklu[lu j =. . . lujly[cxf =. . . lk,ly[gdQk =. . . 157

7D 9q’j 0Po8q;g]d]k;.shdq’da[9eo;ow,hfY;]5j,oUG ! ..... ...... ...... ...... ...... ...... ...... ...... ສະຫງສ.ວວນ.ລິສຂະສິດ ’D 9q’j 0Po8n,j .l8j k8t]k’]5,j oUG 9eo;o sq;ly[ sq;|;j p I6[c[[dko[;d 7evjko ! # ! # !W T # ly[lk, @ ( !) # & @$ ( * 158

@D dko7eo;oD ສະຫງສ.ວວນ.ລິສຂະສິດ dD g]d39fD mhk; [5o,u 1no1j60Aomu *& c]t ok’ok]u 0oB Ivf0oA mu &$ 0v’ mk’0Bomkfcs’j |b’j D 4k, ;kj ok’ok]9u t8vh ’0oB vdu 9da 0Ao9’bj mao mhk; [5o,uD 9kdoAo r;dg0kq 0oB Ivf0oA mu ($ c]t p’a !) 0oA 9tg4’y [vj og0kq 1kd 0BoD 4k,;kj [vj og0qk1kd0Bo ,uma’\\qf9ad0AoD 0D 9qj’djkp.lxj B,0Poc]h;xt8y[af8k,8q;1kj ’D 50 + 9 = 59 27 = 20 + 7 60 + 3 = . . . 76 = ... + ... 70 + 2 = . . . 58 = ... + ... 30 + 4 = . . . 36 = ... + ... 80 + 5 = . . . 54 = ... + ... 90 + 10 = . . . 96 = ... + ... 159

7D 9q’j 9af]Po9eo;ofaj’oUD 1 9af]Po9kds^kpsk|hvpD 85 70 30 90 40 65 80 100. 2 9af]Po9kd|hvpsks^kpD 6 5 45 30 75 95 80 20 55. ’D 9qj’0Po8nj,.l8j k8t]k’.sh4nd8hv’D ສະຫງສ.ວວນ.ລິສຂະສິດ I6[dko[;d 7evkj o sq;ly[ sq;|j;p 9eo;o * T # sqdly[lk, * # *# ( @ gdQkly[sqd *& 70 + 8 _ $ 160

39[qf mu ]efa[9eo;oc8j W g4y’ !WW !D ]efa[9eo;oD dD 9q’j 7yfw]cj ]h;0Po8n,j .lj;q’,qo]5,j oUD 6 +2 8 +4 +3 15+ 10+ 8+ -5 ສະຫງສ.ວວນ.ລິສຂະສິດ 43 +9 +6 10 58 -10 -4 +16 60 33 13+ 20+ 7+ 87 0D 9q’j la’gdfc]h;0Po8nj,.lDj 88 98 76 78 80 88 80 83 86 30 100 98 96 35 60 55 50 53 50 47 161

7D 9q’j djkp.lxj B,0Poc]h;xP[mP[3fp.-h g7nvj ’\\kp >; <; = D 42 ... 81 52 + 8 ... 60 80 ... 40 60 + 12 ... 74 40 ... 40 60 + 19 ... 79 25 ... 15 70 + 5 ... 70 + 9 ’D oda IPo & 7oq c0’j 0oa doa IPog]dS zkj odkod;fdk $ 7’A c8]j t 7oq wfh7tcoofaj’8k8t]k’]5,j oUG X9qj’7yfw]cj ]h;9afmu? .lxj B,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ -noj adIPo 7tcood;fdk 7tcoo];, ]efa[mu ok’ ,tou;ao & T ) T # T ( ok’ l5fltfk ) T * T & T @ ok’ ;aolu $ T * T ( T _ mhk; lq,rvo * T & T ) T * mhk; dycdh; & T * T ( T $ 162

@D m;o7noD dD 9q’j djkp.ljxB,0Poc]h;0Po8q;g]d8nj,.l.j sh4nd8hv’D I6[ltcf’9eo;o 9eo;o sq;Ihvp sq;ly[ sq;|;j p 10 10 10 10 10 10 10 10 10 10 10 10 10 ສະຫງສ.ວວນ.ລິສຂະສິດ 10 10 10 10 10 0D 9qj’djkp.ljxB,0Poc]h;7yfw]Dj 80 + 10 = ... 50 + 20 + 10 = ... 30 + 20 + 40 = ... 60 + 30 = ... 60 + 10 + 20 = ... 40 + 20 + 20 = ... 40 + 40 = ... 40 + 50 + 10 = ... 40 + 60 = ... 20 + 60 = ... 163

7D 9qj’9af]Po9eo;o]5j,oUD 1 c8|j hvpsks^kpD & *S ( _S $ WS _ !S #&S (& S &@ S !WWD 2 c8sj ^kpsk|hvpD &*S (_S $WS _!S #&S (&S &@S !WWD ’D 9qj’0ufglAomk’wx0v’ mhk; lao8y c]t ok’ 7elu .odkog0Qk -q,’ko;k’ltcf’D ສະຫງສ.ວວນ.ລິສຂະສິດ Cko;k’ltcfC 50 glAomk’gfuo0v’mhk;lao8y 93 75 73 90 53 90 + 3 70 + 6 80 + 8 60 + 10 81 77 69 l-6okdlke’rx7aot0 71 80 + 1 50 + 8 68 56 glAomk’gfuo0v’ok’7elu 88 87 89 61 59 90 + 9 60 + 1 70 76 79 90 + 2 50 + 9 58 80 + 9 50 + 6 80 + 7 50 + 3 74 80 82 92 60 + 8 50 58 99 164

40[qf mu mtot[af Xg’yodu[? ສະຫງສ.ວວນ.ລິສຂະສິດ !D 9qj’la’gdfxtgrf0v’g’yo]5,j oUD dD g’yo16j0hk’gmy’oU,u.[spa’cfj L 0D 4hkgvqk.[ !WW du[xPj ogvqk.[ @W du[9twfh9ad.[ L 7D 4hk,u.[ &W du[ @ .[wxxPj ogvqk.[ !WW du[9twfh9ad.[ L ’D 4hk,u.[ !W du[ $ .[S .[ @W du[ @ .[ c]t .[ & du[ $ .[ ];,g0Qkdaoma’\\qf9tgxao9addu[ L 165

@D 9q’j c]dxPj og’yo]5,j oUc]h;0Po.ljxB,0PoD 1 c]dxPj ogvqk.[ ! du[ 2 c]dxjPogvqk.[ & du[ & du[ = .[ & du[ = .[ !W du[ = .[ !W du[ = .[ @W du[ = .[ @W du[ = .[ &W du[ = .[ &W du[ = .[ !WW du[ = .[ !WW du[ = .[ #D 9qj’7yfw]j.lxj B,0PoD 2 ສະຫງສ.ວວນ.ລິສຂະສິດ 1 #du[ T &du[ T DDD T @Wdu[ TDDDD=.... @Wdu[T!Wdu[T&Wdu[T&du[T!du[= DDDD 166

$D g]d39fD 1 ok’w, mhvog’yowfh #W du[F vhkp0v’]k;gvqk.sh8nj,vud &W du[D 4k,;kj ]k;,ug’yoma’\\qf9addu[ L ok’ w, ,ug’yogmqkj oUdu[D #W du[ T &W du[ = DDDDDDDDDD du[ 8v[G DDDDDDDDDD du[ 2 mhk; 7elu -N\\kd[ko1k’\\j;p|bj’ _& du[F g;]k9jkp g’yogsao;jkc,7j hkmvog’yo,k.sh & du[D 4k,;kj 7elugvqk gCyo.shc,7j hkgmqkj .f L ສະຫງສ.ວວນ.ລິສຂະສິດ _ & du[ 7elu9kj pg’yo.shc,7j hkgmqjkoUdu[D + & du[ _& du[ T & du[ = DDDDDDDDDD du[ DDDDDDD du[ 8v[G DDDDDDDDDD du[ 3 ok’ lq,lu,ug’yo !WW du[ ]k;gvqkwx-N\\kddh;p|b’j s;u ]k7k )W du[D 4k,;jk r+7hkmvog’yo.sh ok’lq,lu gmqjk.f L r+7hkmvog’yo.shok’lq,lugmqjkoUdu[D !WW du[ { )W du[ = DDDDDDDDDD du[ 8v[G DDDDDDDDDD du[ 167

4 ­­mhk; 7efu ,ug’yo _( du[ ]k;-NxB, ! sq;F ]k7k &W du[ c]t -Nl=fe ! dhkoF ]k7k @W du[D 4k,;kj mhk; 7efu -N g7nvj ’\\qfg’yogmqjk.f L mhk; 7efu -Ng7nvj ’\\qfg’yogmqjkoUdu[D &W du[ T @W du[ = DDDDDDDDDDDDDdu[ 8v[ = DDDDDDDDDDDDDdu[ ]k7k &W du[ ]k7k @W du[ ສະຫງສ.ວວນ.ລິສຂະສິດ &D 9jq’djkp.lxj B,0Poc]h;xP[mP[3fp.-h g7njv’\\kp >; <; = D &du[ T & du[ > !Wdu[ { &du[ _Wdu[ T !Wdu[ !WWdu[ { &Wdu[ D D D !WWdu[ { @Wdu[ $Wdu[ T @Wdu[ D D D )Wdu[ { (Wdu[ #W du[ { @Wdu[ D D D (Wdu[ T @Wdu[ *W du[ T #Wdu[ D D D 168

41[qf mu dko7yfw]7j ;k,s5^f]jno !D dko7yfw]jD dD 9q’j la’gdfdkos^Yo]5j,oUD 1 mhk; 7efu 3po/kvafcdh;oEs;ko g-y’j ,ulucf’F lu0P; c]t lu2hk 3po.lcj 4[g9hpglAo9eo;oD 2 gxqhk\\kp f0 42 43 44 45 46 47 48 49 50 51 52 ♦ 7;k,s^5f]noj dao]ts;jk’8kmuj,u/kvafcdh;lu0P; c]t gxQk ສະຫງສ.ວວນ.ລິສຂະສິດ \\kpc,oj G DDDDDDDDDDDDDDDDD grkt $_ T DDDDDDDDDD = &@ ♦ 7;k,s5^f]noj dao]ts;kj ’8kmuj,u/kvafcdh;lucf’ c]t gxQk \\kpc,oj G DDDDDDDDDDDDDDDDD grkt $_ { DDDDDDDDDD = $& 2 9q’j djkp8k8t]k’.lxj B,0Poc]h; gxQk 8kmu/j k 7;k, ln[8+0Po.l[j vj os;kj ’.o8k8t]k’ \\kp vafcdh;16 j s^5f]noj 3fp.-hc4[g9hpglAo9eo;o]5,j oUD !* !# # 10 11 12 13 14 15 16 17 18 19 20 21 22 23 @& DDD ) 24 $* DDD ( 38 37 36 35 34 33 32 31 30 29 28 27 26 25 DDD #* @W 39 #_ DDD !$ 40 41 42 43 44 45 46 47 48 49 50 51 52 53 $) $& DDD 54 68 67 66 65 64 63 62 61 60 59 58 57 56 55 &) DDD ! 169

0D g]d39fD ສະຫງສ.ວວນ.ລິສຂະສິດ 1 mhk; 7ely’ s^qdsphkvvd9kdl;owfh _@ 8QoF lj;o ok’ ;P’ s^qdwfh )( 8QoD 4k,;kj c,jo.zs^qdwfhs^kp d;jk c]t s^kpd;jkgmqkj .f L mhk; 7ely’s^qdsphkwfhs^kpd;jk ok’ ;P’D DDDDD 8Qogrkt )( T DDDD = _@ 8QoD 8v[G DDDDD 8QoD 2 mhk; dycdh; gda[\\kddtmaowfh *& |j;pF ok’ vervo gda[wfh *! |j;pD 4k,;kj c,oj .zgda[\\kddtmaowfh |hvpd;kj c]t |hvpd;kj gmqkj .f L ok’ vervogda[\\kddtmaowfh|hvpd;kj mhk;dycdh;D DDDDD |j;pgrkt *& _ DDDDD = $ |j;pD 8v[G DDDDD |j;pD 7D 9qj’8nj,.sh7q[9eo;o !WW .lj[jvo9Eg,afD 8 0 +... 90 + ... 100 _ ... 30 + ... 100 78 + ... 48 + ... 64 + ... 55 + ... 170

@D dkoxP[mP[D dD dko-a’j D 1 9qj’la’gdfzk’-y’c]h;dkj p7noxt3spd]5,j oU.ljxB, 0Po c]t 8n,j .ljxt3spd.sh4nd8hv’G ♦ dkoE|ad gmqkj da[ \\kdIj5’D ♦ \\kdI5j’ DDDDDDDDDDDDDDD dkoED 2 9q’j dkj pxt3spd]5,j oU.ljxB,0Po c]h;0Po8n,j .lj3fp.-hG < |add;kj < c]t <g[qkd;kj < rhv,ma’vu’.lIj 6[dko-aj’D ♦ \\kd,U DDDDDDD dkoED ♦ dkoE DDDDDDD \\kd,UD ສະຫງສ.ວວນ.ລິສຂະສິດ 3 9qj’djkp8k8t]k’]5j,oU.ljxB,0Po c]t \\kpX?.lj.sh 4nd8hv’vu’8k,I6[0v’dko-aj’D I6[ g[qkd;j k |adgmqjkda[ |add;kj dkoE dkoE dkoE d 0 d 0 7 C 7C 171

0D 9qj’8n,j 8q;g]d.l.j sh7q[D 52 50 51 56 60 65 ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ 9eo;ol5fmhkpc,jo = DDDDDDDDDD ♦ ]njo9eo;omevyf = DDDDDDDDDDD 7D 9qj’xP[mP[3fp.-hg7nvj ’\\kp >; <; = .lxj B,0PoD 1 100 .... 99 2 _W .... _! 89 .... 80 (_ .... ( @ 98 .... 98 47 .... 64 @* .... # & 56 .... 39 $) .... $ ) !W W .... _ W 172

#D g]d39fD 1 mhk; cdh; -a’j 85ddt8kc,;0v’]k;G 85ddt8kc,;ohvp c]t 85ddt8kc,;.spjF 3fp.-h\\kd[uj -aj’grnjvxP[mP[F .shla’gdfI6[]5,j oUG c,;.spj c,;ohvp !) |;j p @( |j;p ♦ .sh7yfw]j9eo;o\\kd[ujma’\\qfmuj mhk; cdh; oe.-hgrnjv-a’jສະຫງສ.ວວນ.ລິສຂະສິດ xP[mP[da[ 85ddt8kc,;0v’]k;.ljxB,0PoD 2 grnjvc8h,czoza’shv’IPoF ok’ rvograf c]t ok’ ,uok wfhpkj ’vhv,shv’IPofaj’ltcf’.oI6[0hk’]5,j oUD ok’ rvograf pjk’wfh *W [kfdhk;D ok’ ,uok pkj ’wfh $W [kfdhk;D 4k,;jk9eo;o [kfdhk;0v’.zs^kpd;jk L c]t sk^ pd;kj 9eo;ogmkjq .f L 173

ສະຫງສ.ວວນ.ລິສຂະສິດ3 ok’7erPo ,uvkp5 * xuF vhkp 0v’]k;,uvkp5 !_ xuD 4k,;jk vhkp0v’]k;,uvkp5]noj ]k;9adxu L 4 8Qorhk;l6’ !@ c,afF 8Qo\\kdl6’s^5f8Qorhk; $ c,afD 4k,;jkG ♦ 8Qorhk;l6’]njo8Qo\\kd9adc,af L ♦ 8Qo\\kdl6’9adc,af L 5 9q’j oa[0Bogmnvj ]t @ F # F $ F * gxQk\\kp @$ c]h; 0Po.lxj B,0PoD dD @F $F DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @$ 0D #F *F DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @$ 7D $F )F DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @$ CD *F !@F DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD @$ 174

42[qfm u m;o7nodjP;da[dkoxP[mP[ 1 9qj’la’gdfc]h;[vd;jkvao.fl6’ L 2 9qj’la’gdfI6[ dF 0F 7 c]h;[vd;jkG ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ c8]j tI6[,uI6[dhvo9addhvoL ♦ I6[.f8jed;jk\\6jL 9qj’.shgsfzqoD ♦ I6[dhvoma’\\qf,u9addvho L d 0 7 3 9qj’xP[mP[I6[ d c]t 0F 7 c]t ’F 9 c]t lD d 0 7 C 9 l 175

4 9qj’xP[mP[];’l6’ 0v’gfadohvp]5,j oUG ♦ mD cdh; DDDDDDDDDDDDDDDDDDDDDDDDD oD ok]u mhk; cdoh;k’ ♦ mD cdh; DDDDDDDDDDDDDDDDDDDDDDDDD mD gff ok]u gff mhk; ♦ mD cdh; DDDDDDDDDDDDDDDDDDDDDDDDD oD lufk ok’ lufk ♦ oD ok]u DDDDDDDDDDDDDDDDDDDDDDDDD mD gff ♦ oD ok]u DDDDDDDDDDDDDDDDDDDDDDDDD oD lufk ♦ mD gff DDDDDDDDDDDDDDDDDDDDDDDDD oD lufk ♦ .sh[vd7qomujl6’d;kj \\6j c]t 7qomu8j jed;jk\\6jD 5 9qj’.-hv5xtdvo8k,.9grnjvcmdmjvo-nj dF 0 c]t 7 d c]h;8v[7e4k,]5,j oUG ສະຫງສ.ວວນ.ລິສຂະສິດ 0 7 ♦ mjvo-n.j fpk;d;kj \\6jL ♦ mjvo-nj.flAod;jk\\6j L 6 9qj’.-h[aomafcmd];’pk; 0v’mjvo-nj]5j,oUc]h;0Po .lj[jvo9Eg,afD d d = DDDDDDDDDDDDDDDDDD -, 0 0 = DDDDDDDDDDDDDDDDDD -, 7 7 = DDDDDDDDDDDDDDDDDD -, 176

7 9q’j -vd;ymugrnjv[vd;jkI6[ d s^n I6[ 0 c,oj I6[.f pk;d;kj daoL c]t I6hwfhco;.f L d 0 8 9q’j la’gdf7aos^k;D 09 dD 0D ສະຫງສ.ວວນ.ລິສຂະສິດ 7D CD 9D C d7 .shcmdw,h7aos^k;fh;pv5xtdvo8k,.9c]h;c8h,glAomu,j u];’ pk;gmqkj da[w,h7aos^k; c8]j tvao.lj8kdk3ioAo fa’j 8q;1kj ’D .sh xP[mP[];’pk; 0v’w,h7aos^k;c8j]tvaoc]h; [vdw,h7ao s^k;mujpk;d;jk\\6j c]t w,h7aos^k;mulj Aod;jk\\6jD 9 mk’;P’9aosk[hkomjk[qd,u _W dy3]c,afD c]t mk’;P’9ao sk [hko lq,lts;kf,u *$ dy3]c,afD 4k,;jkmk’wxsk[hko .flAod;kj L c]t lAod;kj gmqjk.f L 177

10 .sh\\kpg]dmu3fpdkola’gdfg[y’j ;kj ]6dlvog]u,j vvd9kd dtgxqkmujg[qkd;jkskdtgxqkmu|j add;jkc]h;9af]Po8k,]e fa[c8gj [qksk|adD !# 11 @ ສະຫງສ.ວວນ.ລິສຂະສິດ ! .shla’gdfg7njv’-a’j ma’ # I6[16j]5,j oUG # ♦ I6[g]qkj oUvao.f|adgmqkj dao.sh\\kpfh;pg]d ♦ I6[muj,udtxJv’oq,|add;kj .sh\\kpg]d ♦ I6[mujgs^nv.sh\\kpg]d 12 38t76da[gdQkvuhvao.f9t|add;kj 4hkgIaffh;pw,h-toyffP;daoL 178

13 9qj’la’gdfI6[ dS 0S 7 c]h;[vd;jkc8j]tI6[c,oj vao.f|adL d 0 7 14 9q’j la’gdfI6[ d c]t I6[ 0 ]ts;jk’\\kdvbF I6[dhvo c]t \\kdoaf c,jovao.f|add;jk\\6j L vao.fg[qkd;jk\\6j L d0 ສະຫງສ.ວວນ.ລິສຂະສິດ 15 mhk; mv’cf’ -a’j 85ddt8k\\k0v’]k;G 8Jv[F cf’ c]t djko3fp.-hdhvosuomuj,u0t|kfgmqjkdao,k-a’j mP[D ♦ 9qj’7yfw]9j eo;odhvosuoma’\\qfmuj mhk; mv’cf’ .-h-aj’ xP[mP[\\k0v’]k;D 8Jv[ cf’ $# dhvo djko !) dhvo !$ dhvo 179

ສະຫງສ.ວວນ.ລິສຂະສິດ16 7qo,u9eo;o7q[da[9eo;o8a’j oa’j [=L .sh[vd;jkvao.f|hvp d;jkL .sh0Po9eo;oc,jpy’D z6h-kp.l.j o c,jpy’ z6h-kp 17 9eo;oxkf5dda[9eo;oxk7+-toyf.fs^kpd;kj L 18 9eo;o9vdcdh;gmqkj da[9eo;o9koc,jo s^n [+ L 19 9eo;ooadIPopy’ c]t 9eo;ooadIPo-kp.oshv’IPo 0v’g9Qkgrf.fs^kpd;kj L grf.f|hvpd;kj L 180

20 ,u9eo;owdjs^kpd;kj 9e 21 ,u9eo;oI6[lk,c9s^kp o;ogxafc,jos^n[+c,oj L d;j k9eo;oI6[9t85]afc,jo s^n[+c,joL 22 .zl6’d;kj L 23 38.f8ej d;jk Lສະຫງສ.ວວນ.ລິສຂະສິດ mhk; cdh; c,j,hk ]6d,hk ok’ ok]u 24 9q’j [vd-nlj afmuj.splj 5f c]t ohvpl5fmujg9QkI6h-toyf]t ! 38D 25 -hk’ c]t 7;kp 38.f.spdj ;jk L 38.fohvpd;jk L 181

26 9qj’la’gdfI6[c]h;8v[7e4k,]5,j oUD dD 9qj’xP[mP[9eo;o\\kdw,hma’lv’8QoD ສະຫງສ.ວວນ.ລິສຂະສິດ 0D 0t|kf0v’8Qo\\kdw,hgxaoco;.f L 7D 7;k,l6’0v’8Qo\\kdw,hgxaoco;.f L CD c,pj y’7qooAo4ndt8kj 9advaoL grnvj spa’ L 27 9qj’c8h,g,affe.lj # s^admujgs^nv.sh4nd8hv’ c]t .shgmqkj da[ 0t|kf0v’g,affemu,j uc]h;D 9kdoAoF 8nj,9eo;o.lj[jvo 9eg,af.sh4nd8hv’D 5 > ....... > 3 > ......... > 1 ♦ .shvkj ozqo0v’dkoxP[mP[s^a’9kd8n,j c]h;D 182

43[qfmu m;o7nodko[;d c]t dko]q[ 1 9q’j l? a’gdfc]h;8nj,.l.j o X I 6[dkola[xjPo[jv o ? ... + ... X ... + ... ... + ... ... + ... ........ ........ ........ ........ 2 9q’j 7yfw].j ljxB,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ 3 + 2 + 2 =. . . 15 + 4 - 3 =. . . 3 + 3 + 3 =. . . 8 _ 4 + 2 =. . . 7 + 2 _ 1 =. . . 20 + 2 + 4=. . . 9 _ 3 + 1 =. . . 18 _ 4 + 1 =. . . 10 + 2 _ 3 =. . . 3 9q’j 8nj,.lj8k8t]k’ D T 0 1 2 3 4 _ 0 1 2 3 4 0 0 1 1 2 2 3 3 4 4 5 5 183

gr’-kf -kf]k;8A’c8.j f,k ]k;m5dmq;j |hkg-uf-6l5f.9 Ij;,cI’Ij;,9yfI;j ,.9 lk,ad7udaogxaode]a’fP; gfaffjP;rhv,daodhk;|hk [6-k-6dPf0v’]k; lq’j glu,.-hlyfgxaog9Qk ]k;m5d-qogzqkj ltg\\urk[dao [+.sh/6’9addtraf c]tr;d0kp-kf g0Qk,k]q[d;o ]k;ma’,;o-6gvdt]kf vyflt]trk[ 0v’-kf]k;w;h 8aflyo.9 l6h-u’gvqkw- rk-kfdhk;wxlj67;k,;afmtokD ສະຫງສ.ວວນ.ລິສຂະສິດ