ຄະນິດສາດ

@D m;o7no9eo;oc8j W g4y’ @WD dD 9qj’djkp8k8t]k’.ljxB,0Poc]h;7yfw]Dj 123 45 54321 +12 +14 13 16 19 + 8 6 7 8 9 10 +10 10 9 8 7 6 0D 9qj’xt8y[af8k,8q;1jk’.ljxB,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ 9eo;o 7evkj o I6[c[[dko0Po sq;ly[ sq;|;j p !* ly[sqd !W T * ! * !& ly[shk ly[g9af ly[cxf !W T ) @W -k; 93

7D 9q’j djkp.ljxB,0Poc]h;xP[mP[3fp.-hg7njv’\\kp >; <; =D 12 > 10 20 ... 20 17 ... 11 11 ... 11 6 ... 14 14 ... 16 5 ... 19 18 ... 19 9 ... 12 15 ... 15 19 ... 13 17 ... 17 ’D 9q’j ln[8+0Pog]d]k;]5,j oU.ljxB,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ !!!!!_*$)W @W 9D 9qj’la’gdfc]h;ln[8+0Po8q;g]d8k,]efa[.lxj B,0PoD 1 10 20 94

[qf m u 2 3 m;o7nodjP;da[dko[;d c]t dko]q[0v’s^kp9eo;o !D dko[;d0v’s^kp9eo;oD dD 9q’j la’gdfI6[c]h;8v[7e4k,D ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ ,u]qf9ad\\;fL c8j]t\\;f,u9ad7aoL ]qfma’\\qf,u9ad7aoL 0D 9q’j oa[9eo;ogInv[yo]5,j oUc]h;0Po.lxj B,0PoD !D 7yfw]j8 k,mk ’8ah’D ...+...+... = ... @D 7yfw]j8k,mk’ovoD ...+...+...+... = ... #D g7nvj ’[yoma’\\qf DDDDD ]e 95

ສະຫງສ.ວວນ.ລິສຂະສິດ7D 9qj’0Po9eo;oc8j W g4y’ @W 8k,]efa[.lxj B,0PoD 7 0 16 20 ’D 9qj’djkp.lxj B,0Poc]h;xP[mP[3fp.-hg7nvj ’\\kp > ; < ; = . 2 + 5 . . . 7 + 1 6 + 2 . . . 4 + 5 20 - 15 . . . 10 - 4 12 - 5 . . . 15 + 3 18 + 1 . . . 19 + 1 20 - 8 . . . 13 + 5 5 + 6 . . . 8 + 1 10 + 6 . . . 11 + 4 96

@D dko]q[s^kp9eo;oD ສະຫງສ.ວວນ.ລິສຂະສິດ dD9qj’la’gdfI6[c,’dtg[Nv9kd-hkpsk0;kc]h;8v[7e4k,]5j,oUD ♦ c,’dtg[Nv8v,fvdw,h,u9ad38 L      ♦ c,’dtg[Nv[yowxgmnvj mu|b’j 9ad38 L pa’8v,fvdw,h9ad38 L ♦ c,’dtg[Nv[yowxgmnjvmulv’9ad38 L pa’8v,fvdw,h9ad38 L ♦ c,’dtg[Nv[yowxma’\\qf,u9ad38 L pa’8v,fvdw,h9ad38 L 0D mhk; cdh; ,ux6,gxQk @W |;j pF ]5f,nwx ( |j;pc]tc8d vud # |;j pF x6,gxQk]k;pa’gs^nv9ad|j;p L 97

7D 9qj’0Po9eo;ogxao8q;g]dcmoI6[.ljxB,0Poc]h;7yfw]jD ສະຫງສ.ວວນ.ລິສຂະສິດ ’D 9qj’dkj p.lxj B,0Poc]h;7yfw]jD 7 - 3 = .... 7 - 6 = .... 10 - 6 = .... 10 - 4 = .... 12 - 7 = .... 12 - 6 = .... 18 - 8 = .... 20 - 15 = .... 98

#D dko[;d c]t dko]q[s^kp9eo;oD dD mhk; cdh; gda[svpwfh !& 38S svpw8jvvd9kd75 & 38S ]k;gda[ svpwfh8nj,vud !W 38F 4k,;kj svp16j.o75,u9ad38D ສະຫງສ.ວວນ.ລິສຂະສິດ 0D 9qj’dkj p.ljxB,0Poc]h;7yfw]jD 20 - 9 = 11 15 - 5 = ...... 13 + 5 = ...... 10 + 8 = ...... 18 - 4 = ...... 17 - 5 = ...... 4 + 16 = ...... 18 - 2 = ...... 14 + 5 = ...... 9 - 4 = ...... 99

7D 9q’j xP[mP[3fp.-hg7njv’\\kp ’D 9qj’]q[vvd @D >; <; = .lxj B,0PoD 15 + 5 = 20 20 - 2 = 18 ສະຫງສ.ວວນ.ລິສຂະສິດ 19 - 5 ... 20 18 - ... = ... 18 - 4 ... 20 16 - ... = ... 17 + 2 ... 20 14 - ... = ... 19 - 4 ... 20 12 - ... = ... 9D 9qj’0Po9eo;orkp.8hI6[dko[;d.ljxB,0PoD ♦ [;d3fp.-hg]d &D 10 = 5 + 5 15 = ... + ... + .... ♦ [;d3fp.-hg]d $D 8 = ... + ... 12 = ... + ... + ... ♦ [;d3fp.-hg]d #D 6 = ... + ... 9 = ... + ... + ... 100

[qfm u 2 4 dko0Po9eo;o !! g4y’ !$ !D dko0Po9eo;o !!D dD 9q’j 8nj,dko[;d]5j,oUD 11= 1 + 10 10 + 1 =11 ສະຫງສ.ວວນ.ລິສຂະສິດ ..........+.........=11 11=.......+......... ..........+.........=11 11=.......+......... ..........+.........=11 11=.......+......... ..........+.........=11 11=.......+......... 11 = 8 + 3 11 = 4 + 7 0D dko0Po9eo;o !!D 11 = 7 + 4 11 = 1 + 10 11 = 5 + 6 11 = 6 + 5 11 = 10 + 1 11 = 2 + 9 11 = 9 + 2 11 = 3 + 8 101

7D 9q’j 7yfw]j.lxj B,0PoD 1 0 9 8 7 6 + + + + + 1 2 3 6 5 1 2 1 5 1 3 1 4 11 + + + + + 3 4 5 1 2 CD 9qj’8n,j 9eo;omujg\\ktlq,.l[j vj o9Eg,afD 10 11 ສະຫງສ.ວວນ.ລິສຂະສິດ ... + 0 9 0 + ... 1 + ... ... + 2 8 ... + 0 ... + 1 3 + ... ... + 4 0 + ... 1 + ... 2 + ... 5 + ... ... + 6 ... + 1 ... + 2 ... + 3 7 + ... ... + 8 2 + ... 3 + ... 4 + ... 9 + ... ... + 10 ... + 3 ... + 4 ... + 5 4 + ... 5 + ... 6 + ... ... + 5 ... + 6 ... + 7 6 + ... 7 + ... 8 + ... ... + 7 ... + 8 ... + 9 8 + ... 9 + ... 10 + ... 102

@D dko0Po9eo;o !@D dD 9qj’8nj,.ldj ko[;d]5j,oUG 12 = 10 + 2 12 = ... + ... 12 = ... + ... 12 = ... + ... ສະຫງສ.ວວນ.ລິສຂະສິດ12 = ... + ... 12 = ... + ... 0D 9qj’xt8y[af8k,8q;1kj ’.lxj B,0PoD 6+5 5+6 8+4 4+8 6+6 11 11 11 12 12 12 7 + 4 4 + ... 6 + ... 9 + ... 3 + ... 103

7D dko0Po9eo;o !@D 12 = 1 + 11 12 = 11 + 1ສະຫງສ.ວວນ.ລິສຂະສິດ 12 = 2 + 10 12 = 10 + 2 12 = 3 + 9 12 = 9 + 3 12 = 4 + 8 12 = 8 + 4 12 = 5 + 7 12 = 7 + 5 12 = 6 + 6 12 = 6 + 6 CD 9qj’djkp.ljxB,0Poc]h;7yfw]jD 10 + 3 = . . . 5 +8 =... 8 + 1 = . . . 9+2=... 6+9=... 5 + 6 = . . . 7 + 4 = . . . 104 9 + 4 = . . . 7+8=...

#D dko0Po9eo;o !#D dD 9qj’8nj,.ldj ko[;d]5j,oUD 13+0 13 12+..... ....+..... ສະຫງສ.ວວນ.ລິສຂະສິດ ....+..... ....+..... ....+..... ....+..... 0D dko0Po9eo;o !#D 7 + 6 = 13 8 + 5 = 13 0 + 13 = 13 9 + 4 = 13 10 + 3 = 13 1 + 12 = 13 11 + 2 = 13 2 + 11 = 13 12 + 1 = 13 3 + 10 = 13 13 + 0 = 13 4 + 9 = 13 5 + 8 = 13 6 + 7 = 13 105

7D 9qj’djkp.ljxB,0Poc]h;ln[8+xt8y[af8k,8q;1kj ’D 0 + 13 13 + 0 ສະຫງສ.ວວນ.ລິສຂະສິດ 1 + 12 12 + 1 2 + ... 11 + ... 3 + ... 10 + ... 4 + ... 9 + ... 5 + ... 8 + ... 6 + ... 7 + ... 7 + ... 6 + ... 8 + ... 5 + ... 9 + ... 4 + ... 10 + ... 3 + ... 11 + ... 2 + ... 12 + ... 1 + ... ’D 9q’j xt8y[af8k,8q;1kj ’.ljxB,0PoD 6+5 6 + 7 2 + 11 11 5 + 7 12 9+3 13 8 + 3 9 + 4 10 + 3 106

$D dko0Po9eo;o !$ 14 = ... .+ .... 14 = .... + .... dD 9q’j 8nj,.ldj ko[;d]5,j oUD 14 = 8 + 6 14 = ... + ... 14 = .....+ ... 14 = ..... + .... 14 = .... + ... 14 = ..... + .... 0D dko0Po9eo;o !$D ສະຫງສ.ວວນ.ລິສຂະສິດ !$ W T !$ ( T ( 0 + 14 7 + 7 ! T !# ) T * 1 + 13 8 + 6 @ T !@ _ T & 2 + 12 9 + 5 # T !! !W T $ 3 + 11 10 + 4 $ T !W !! T # 4 + 10 11 + 3 5 + 9 12 + 2 & T _ !@ T @ 6 + 8 13 + 1 * T ) !# T ! 107

7D 9qj’ln[8+xt8y[af8k,8q;1kj ’.lxj B,0PoD 14 + 0 7 +... 12 + 2 9+2 14 +... 14 +... 8+6 14 6 + 4 11 +... 14 2 +... 5+7 9+5 8+6 5 +... 13 +... 7+7 ສະຫງສ.ວວນ.ລິສຂະສິດ ’D 9qj’djkp8k8t]k’.lxj B,0Poc]h;\\kp X ?.l8j kmu,j uzqo [;d4nd8hv’D 13 14 13 14 7+6 3 + 11 9+5 7+7 6+8 13 + 0 14 + 0 12 + 2 5+8 8+6 108

[qf mu 2 5 dko7yfw]jskzqo[;d c]t zqo]q[ !D dko7yfw]jskzqo[;dD c]h;7yfw]8j k,0Ao8voD dD 9q’j 0Po9eo;oI6[.l.j o ++ ++ສະຫງສ.ວວນ.ລິສຂະສິດ + + 0D 9q’j 7yfw]8j k,0Ao8vomujwfhdeoqf.shD 3 +5 + 5 +1 3 + 5 + 5 +1 ... + ... ... + ... ... ... 109

7D 9qj’0PoI6[dko[;d.lxj B,0PoD 46 5 ... ... ... + ... + ... ... + ... CD 9qj’.-hg7njv’\\kp >; <; = grnjvxP[mP[9eo;o\\kd[uj 0v’ ok’ ,tou c]t mhk; l5[ao .ljxB,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ 5+5+5+3 5+5+5+4 9D 9qj’0uf;q’vhv,gvqkI6[dko[;d]5,j oU.lxj B,0PoD ♦ I6[dko[;d.f|hvpd;jkD 3+3+3+2 3+3+3+3+2 ♦ I6[dko[;d.fs^kpd;kj D 3+3+3+2 3+3+3+3 110

@D dko7yfw]jskzqo]q[D dD ok’ my[rtrvo wx-Ng7njv’mujIhko7hkcs’j |b’j F gxaog’yoma’ \\qf !W du[F ]k;wfhgvqk.[ @W du[.shr+7hk 4k,;kj r+7hkmvo g’yo.sh ok’ my[rtrvo gmqjk.f L ສະຫງສ.ວວນ.ລິສຂະສິດ 0D 9qj’djkp.ljxB,0Poc]h;8n,j 9eo;o.sh4ndD +3 -5 +9 -3 7 ... ... ... ... 7D 9qj’dkj p8k8t]k’.lxj B,0Poc]h;7yfw]jD 3 8 12 5 11 7 9 10 4 +2 111

CD 9qj’djkp.lxj B,0Poc]h;xP[mP[3fp.-h g7nvj ’\\kp > ; < ; = D 3 + 4 + 9 ..... 15 - 2 - 1 16 + 2 +1 ..... 20 - 1 - 2 17 + 3 +2 ..... 18 - 2 - 4 18 - 2 - 0 ..... 15 + 3 + 2 20 - 5 - 4 ..... 16 + 4 + 1 9D 9q’j 8nj,9eo;o c]t g7nvj ’\\kp T S { .lj 8 14 13 10 19 ສະຫງສ.ວວນ.ລິສຂະສິດ {! lD 9q’j djkp.ljxB,0Poc]h;7yfw]jD 1 8 1 4 2 0 8 1 6 + - - + - 1 1 0 1 0 7 1 2 1 5 1 8 1 6 1 4 1 7 - - + - + 1 1 1 3 4 7 4 112

[qf mu 2 6 dko0Po9eo;o !& g4y’ !* !D dko0Po9eo;o !&D dD 9qj’-U[vdI6[dko[;dmuj,uzqo[;dgmqkj da[ !&D 13+2 4+11 12+0 10+5 ສະຫງສ.ວວນ.ລິສຂະສິດ 9+5 0D dko0Po9eo;o !&D = 8 + 2 + 5 15 = 8 + 7 = 4 + 5 + 6 = 7 + 3 + 5 15 = 9 + 6 = 6 + 5 + 4 = 8 + 4 + 3 15 = 10 + 5 = 10 + 3 + 2 = 9 + 5 + 1 15 = 11 + 4 15 = 12 + 3 15 = 13 + 2 15 = 14 + 1 113

7D 9qj’oe.-h[af9eo;o]5,j oUgmnjv]t # [af grnjv0PoI6[c[[dko[;d .shwfhzqo[;dgmqkj da[ !& .lxj B,0Po Xc8]j t[af.-hwfhgmnvj fP;?D 8q;1jk’G 15 = 7 + 2 + 6 5 5 7 4 3 5 4 6 2 4 ’D 9q’j xt8y[af8k,8q;1jk’.lxj B,0PoD !& X ly[shk ? ສະຫງສ.ວວນ.ລິສຂະສິດ 15 + 0 0 + 15 14 + ... ....+ .... 13 + ... ....+ .... 12 + ... ....+ .... 11 + ... ....+ .... 10 + ... ....+ .... 9 + ... ....+ .... 8 + ... ....+ .... 114

@D dko0Po9eo;o !*D dD 9qj’0Po9eo;ocmog,affe16cj 8]j tI6[.lj[jvo9ED 1 2 3 16 = 10 + 6 16 = ...... + ...... 16 = ....... + ...... 16 = 6 + ..... 16 = ...... + ...... 16 = ...... + ...... 456 ສະຫງສ.ວວນ.ລິສຂະສິດ 16 = 6 + 5 + 5 16 = ... + ...+...+... 16 = ...+..+..+..+... 16 = ... + ... + ... 16 = ... + ...+...+... 16 = ...+..+..+..+... 0D dko0Po9eo;o !*D 16 = 8 + 8 16 = 12 + 4 16 = 9 + 7 16 = 13 + 3 16 = 10 + 6 16 = 14 + 2 16 = 11 + 5 16 = 15 + 1 115

7D 9q’j 0Po9eo;ocmog,affe.lj.o .ljxB,0Poc]h;[vd I6[mu,j u9eo;ogmqjk!*D 3 12 456 ສະຫງສ.ວວນ.ລິສຂະສິດ ’D 9q’j 0Po8q;g]d]5,j oU.l[j jvo9E.sh4nd8hv’D 4 9 13 0 16 8 14 11 2 6 0 < ... < ... < ... < ... < ... < ... < ... < ... < 16 116

#D m;o7nodko0Po9eo;o !& c]t !*D dD 9qj’[vd9eo;omuj0kfskpwxD 6 84 0 2 16 10 14 12 0D 9qj’xt8y[af8k,8q;1kj ’.ljxB,0PoD ສະຫງສ.ວວນ.ລິສຂະສິດ l !y[ &shk !* ly[sqd .......1.............5........ + .......0............. . .......0............. ....... . ++++++++ 15 16 + 0 0 + 16 + .... ....+ .... + .... .... + ... ....+ .... + .... ....+ .... + .... .... + ... ....+ .... + .... ....+ .... + .... .... + ... ....+ .... + .... ....+ .... .... + ... .... + ... .. ...... + ...... + 117

7D 9q’j dkj p.ljxB,0Poc]h;xt8y[af8k,8q;1kj ’D ສະຫງສ.ວວນ.ລິສຂະສິດ 7 + 5 + 3 = 10 + 5 = 15 8 + 2 + 6 = ... ... ... ... ... 9 + 4 + 1 = ... ... ... ... ... 6 + 5 + 5 = ... ... ... ... ... 1 + 5 + 9 = ... ... ... ... ... ’D 9q’j djkp.ljxB,0Poc]h;xt8y[af8k,8q;1jk’D 9 + 7 = 9 + 1 + 6 = 10 + 6 = 16 8 + 4 = . . . + . . . + . . .= . . . + . . . = . . . 7 + 9 = . . . + . . . + . . .= . . . + . . . = . . . 8 + 8 = . . . + . . . + . . .= . . . + . . . = . . . 9 + 5 = . . . + . . . + . . .= . . . + . . . = . . . 6 + 7 = . . . + . . . + . . .= . . . + . . . = . . . 9D 9qj’djkp.lxj B,0Poc]h;xP[mP[3fp.-hg7nvj ’ \\kp > ; < ; = . 8 + 6 . . . 9 + 6 8 + 8 . . . 9 + 7 7 + 4 . . . 8 + 3 10 + 5 . . . 11 + 2 9 + 7 . . . 10 + 5 11 + 3 . . . 11 + 2 118

[qf mu 2 7 m;o7nodko0Po9eo;o !D 9q’j la’gdfI6[c]h;8v[7e4k,D ♦ pqolucf’,u9ad]e L ♦ pqolu0P;,u9ad]e L ♦ pqoma’\\qf,u9ad]e L ສະຫງສ.ວວນ.ລິສຂະສິດ @D g]d39fD mhk; lk]u,u\\kd[u _ |;j pF ok’ ok]u ,us^kpd;j k mhk; lk]u & |j;p c]t ok’ w, ,u|hvpd;jk ok’ ok]u $ |;j pF 4k,;jk c8]j t7qo,u\\kd[u9ad|;j pL 9q’j 7yfw]j c]t c8h,I6[9eo;o\\kd [u0v’c8j]t7qo.ljxB,0PoD mhk; lk]uD ok’ ok]uD ok’ w,D _ |;j pD DDDDD |j;pD DDDDD |;j pD 119

#D 9qj’0Po9eo;o8k,I6[ c]h;xP[mP[3fp.-hg7njv’\\kp >; < .ljxB,0PoD DDDDDD I6[ DDDDDD DDDDD I6[ ສະຫງສ.ວວນ.ລິສຂະສິດ $D 9qj’djkp8k8t]k’.ljxB,0Poc]h;0Po8n,j .lj.sh4nd8hv’D 7evjko g]d]k; g]dvkia[ !& |b’j ! ! 0 + 15 8 + 7 $ & 1 + ... 9 + ... g9af ( 2 + ... 10 + ... ly[lv’ !@ 3 + ... 11 + ... ly[lk, !# 4 + ... 12 + ... ly[sqd !* !* 5 + ... 13 + ... -k; @W 6 + ... 14 + ... 7 + ... 15 + ... 120

[qf mu 2 8 9eo;oc8j @W g4y’ #W !D 9’jq [vd9eo;og,fa fe c]t zoq [;dm’a \\fq rvh ,m’a cpd s;q |;j pF sq;ly[D 10 + 10 + 8 = .... ........ + ........ = ...... sq;ly[ sq;|j;p sq;ly[ sq;|j;p ສະຫງສ.ວວນ.ລິສຂະສິດ @D 9eo;oc8j @W g4y’ #W ,ufaj’oUD 7evjko g]d]k; g]dvkia[ 7evkj o g]d]k; g]dvkia[ -k; @W @W -k;sqd @* @* -k;gvaf @! @! -k;g9af @( @( -k;lv’ @@ @@ -k;cxf @) @) -k;lk, @# @# -k;gdQk @_ @_ -k;luj @$ @$ lk,ly[ #W #W -k;shk @& @& 121

#D 9qj’xt8y[af8k,8q;1kj ’.lxj B,0PoD I6[ltcf’ I6[dko0Po sq;ly[ sq;|j;p 23 = 20 + 3 2 3 .... = .... + .... .... .... .... = .... + .... .... .... .... = .... + .... .... ....ສະຫງສ.ວວນ.ລິສຂະສິດ .... = .... + .... .... .... .... = .... + .... .... .... $D 9q’j 7yfw].j ljxB,0PoD 1 3 2 0 1 3 1 1 20 + + + + + 1 0 5 1 2 1 1 10 2 2 1 1 12 1 5 2 0 + + + + + 5 1 0 12 1 4 8 122

[qf mu 29 dkodeoqfg;]k !D g;]k.o|b’j ;aoD dD 9qj’[vdg;]k0v’I6[ ! c]t @D 12 0D .o|b’j ;ao,udk’g;ao c]t dk’7noD ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ dk’g;ao,uG 8vog-QkF 8vol;kpXmPj ’? c]t 8voc]’D 12 3 ♦ dk’7no,uG sq;7ej F mPj ’7noF 0hvoc9h’D 45 6 123

7D 9q’j 8v[7e4k,]5,j oU3fp.-h7e;jkG dk’g;ao s^n dk’7noD ♦ r;dgIqkgsaogfnvo c]t fk;g;]k.f L ♦ 8kg;aoljv’cl’g;]k.f L ♦ oadIPowx3I’IPog;]k.f L ♦ oadIPoovog;]k.f L ’D 9qj’la’gdfI6[c]h;9af]efa[dkog7nvj ows;0v’mhk; cdh; .o|bj’;ao.ljxB,0PoD 11 12 12 !W 3,’ 11 12 1 * 3,’ 11 12 1 !*3,’X$3,’c]C? 10 cdh;vvds^Uo 10 2 cdh;8bjoovo 10 6 2 cdh;g]udIPo 9 3 9 3 9 3 8 7 6 5 4 8 7 4 8 7 6 5 4 5 o [ ສະຫງສ.ວວນ.ລິສຂະສິດx 11 12 12 ( 3,’ #W 11 12 12 @W3,’X)3,’c]’? 11 12 12 !@3,’ X8vomjP’? 10 cdh;wx3I’IPo 10 10 9 3 9 3 9 3 cdh;g0Qkovo 8 7 54 cdh;dyog0Qkl;kp 8 7 6 54 8 7 6 5 4 6 f8p ♦ oe.-h8q;vadlvo16cj 9I6[grnvj 9af]Po]efa[dkog7nvj ows; 0v’mhk;cdh;.o|b’j ;aoD [ ♦ .sh0Pogxaoxt3spddPj ;da[ @ gsfdkos^a’9kd8vomjP’ X s^a’ !@ 3,’ ? .ljxB,0PoD 124

@D ;ao.o|bj’vkmyfD ສະຫງສ.ວວນ.ລິສຂະສິດ dD 9q’j 8v[7e4k,]5,j oUG ♦ vkmyf|b’j ,u9ad;aoL ;ao.fcfj L ♦ ;aomevyf0v’vkmyfc,jo;aospa’ L ♦ ;aol5fmhkp0v’vkmyfc,oj ;aospa’ L ♦ vkmyf|bj’oadIPo,k3I’IPo9ad;ao L ♦ ;aomevyf0v’dko,k3I’IPoc,oj ;aospa’ L ♦ ;aol5fmhkp0v’dko,k3I’IPoc,oj ;aospa’ L ♦ .ovkmyf|bj’,u;aorad3I’IPo9ad;aoL ;ao.fcfj L 0D -nj c]t 9eo;o;ao.o|b’j vkmyfD ♦ vkmyf|bj’,u ( ;ao 7nG ;aovkmyfF ;ao9aoF ;aova’7koF;aor5fF ;aortsafF ;aol5d c]t ;aoglqkD ♦ ;aomevyf0v’vkmyfc,jo ;aovkmyfD ♦ ;aol5fmhkp0v’vkmyfc,jo ;aoglqkD 7D 9q’j 8n,j ;ao c]t ;aomu.l8j k8t]k’]5j,oU.ljxB,0PoD ,N;kooU ,NoU ,Nvnjo ,N;kooU ,NoU ,Nvnoj ;aor5f ;aovkmyf _ !# 125

’D 9q’j dkj pxt8ymyo]5,j oU.lxj B,0Poc]h;8n,j 8q;g]d.lj.sh4ndD ,uok glqk & myf 9ao va’7ko r5f rtsaf l5d !@ !_ ! @ # @* * ( _ !# !& !( @W @! @# @$ @& @) @_ #! ສະຫງສ.ວວນ.ລິສຂະສິດ 9D 9qj’la’gdfxt8ymyoc]h;ln[8+0Po;ao8k,]efa[.lxj B,0PoD ♦ ;aovkmyf ♦ ;aortsaf ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 126

[qfm u 3 0 9eo;o c]t dko0Po 9eo;oc8j #W g4y’ $W !D 9eo;oc8j #W g4y’ $WD dD 9qj’[vd9eo;omuj0kfskpwx.o8k8t]k’D 1 4 8 20 ສະຫງສ.ວວນ.ລິສຂະສິດ40 29 0D 9eo;o #W g4y’ $W ,ufaj’oUD 7evkj o g]d]k; g]dvkia[ 7evkj o g]d]k; g]dvkia[ lk,ly[ #W #W lk,ly[sqd # * #* lk,ly[g9af # ( lk,ly[gvaf #! #! lk,ly[cxf #) #( lk,ly[lv’ #@ #@ #) lk,ly[lk, ## ## lk,ly[gdQk #_ #_ lk,ly[luj #$ #$ lulj y[ $W $W lk,ly[shk #& #& 127

7D 9q’j djkp.lxj B,0Poc]h;xt8y[af8k,8q;1jk’]5,j oUD 9eo;o 7evkj o I6[dko0Po s^adsq;ly[ s^adsq;|;j p 3 1 l k,l y[gvaf 30 + 1 3 1 32 33 ສະຫງສ.ວວນ.ລິສຂະສິດ 34 35 36 37 38 39 40 ’D 9q’j djkp.ljxB,0Poc]h;xP[mP[9eo;o]5j,oU 3fp.-h g7njv’\\kp >; <; = D 38 .............. 35 28 .............. 38 26 .............. 26 35 .............. 35 29 .............. 39 21 .............. 34 40 .............. 30 40 .............. 40 10 .............. 30 39 .............. 37 128

@D dko0Po9eo;oc8j #W g4y’ $WD dD 9q’j [vd9eo;ow,hfY;ma’\\qfc]h;cpdsq;|j;pF sq;ly[D I6[ltcf’9eo;o 9eo;o sq;ly[ sq;|j;p 10 10 23 2 3 10 10 10 10 10 10 10 ສະຫງສ.ວວນ.ລິສຂະສິດ 0D 9q’j xt8y[af8k,8q;1jk’.ljxB,0PoD 40 Xx 32 26 xX 37 18 20+6 30+7 10+8 30+2 12+6 33+7 21+5 31+9 129

7D 9q’j 7yfw].j lxj B,0PoD 30 + ..... = 31 30 + ..... = 40 30 + ..... = 35 34 + ..... = 38 30 + ..... = 36 38 + ..... = 39 30 + ..... = 39 40 + ..... = 40 30 + ..... = 38 20 + ..... = 40 ’D 9q’j xt8y[af8k,8q;1kj ’.lxj B,0PoD ly[shk ສະຫງສ.ວວນ.ລິສຂະສິດ lujly[ 15 22 -k;lv’ lk,ly[g9af 40 38 lk,ly[cxf 37 34 lk,ly[luj 130

[qfm u 31 dkoc]dxjPo ສະຫງສ.ວວນ.ລິສຂະສິດ !D dt8ydkdkoc]dxPj o !W 8+ !D g,af0k; !W g,af xjPogvqkg,affewfh ! g,afD dvj odkoc]dxPj oD s^a’dkoc]dxjPoD 46 ♦ s^a’dkoc]dxPj owfhg,affe $ g,af c]t g,af0k; * g,afD @D 9q’j dkj p8k8t]k’.lxj B,0Poc]h;8n,j 8q;g]d.sh4ndD dt8ydkdkoc]dxjPoG ♦ g,af0k; !W g,af xjPogvqkg,affewfh ! g,afD ♦ g,affe !W g,af xPj ogvqkg,afcf'’wfh ! g,afD 131

#D 9q’j djkp8k8t]k’.lxj B,0Po c]h;8nj,8q;g]d.sh4ndD s;q ly[ sq;|j;p 14 = 10 + 4 s;q ly[ sq;|j;p 17 = 10 + 7 $D 9qj’c]dxjPo8k,dt8ydkfaj’]5,j oUG \\kd[u !W |;j p xPj odt8=hwfh ! |;j p dt8=h !W |j;p xjPo\\kd[kowfh ! |j;p ສະຫງສ.ວວນ.ລິສຂະສິດ ♦ dt8=h # |;j p9twfh\\kd[u9ad|j;pL ♦ [ko @ |j;p9twfhdt8=h9ad|;j pL ♦ dt8=h #W |j;p9twfh\\kd[ko9ad|;j pL 132

32[qf mu m;o7nodkoc]dxjPo !D 9q’j [;d7tcoo0v’c8]j t7qoc]h;9af]efa[mu.o8k8t]k’D dt8ydk0v’dkoc]dxjPo < !W 8+ ! < 8+ 8+ -nj zqowfhIa[ 7t]c;o,o 9afmu ສະຫງສ.ວວນ.ລິສຂະສິດ mD lq,gff W @ ! @! oD ohvp oD graf mD gdfcdh; mD lk]u oD oq’ 133

ສະຫງສ.ວວນ.ລິສຂະສິດ@D ok’ ,k]u ,ug’yo $W du[ 4hk]k;c]dgvqkg’yo.[ @W du[F .[ !W du[F .[ & du[ c]t .[ ! du[ 9twfhfa’j oUG ♦ 4hkc]dgvqkg’yo.[ @W du[ wfh @ .[D ♦ 4hkc]dgvqkg’yo.[ !W du[ wfh $ .[D ♦ 4hkc]dgvqkg’yo.[ & du[ wfh ) .[D ♦ 4hkc]dgvqkg’yo.[ ! du[ wfh $W .[D #D 9qj’xt8y[af8k,8q;1jk’.ljxB,0Po 3fpvu’.ljdt8ydk0v’dko c]dxPj o < & 8+ !<D 10 3 15 2 20 6 25 5 30 4 35 8 40 7 134

[qf mu 3 3 9eo;oc8j $W g4y’ *W !D 9eo;oc8j $W g4y’ &WD dD 9qj’[vd9eo;og,af0k; c]t zqo[;dma’\\qfrhv,cpdsq;|j;pF sq;ly[ D ....+....+....+....+.... =..... ....+....+....+....+....ສະຫງສ.ວວນ.ລິສຂະສິດ sq;ly[ sq;|j;p sq;ly[ sq;|;j p 0D 9eo;oc8j $W g4y’ &W ,ufaj’oUG 7evkj o g]d]k; g]dvkia[ 7evkj o g]d]k; g]dvkia[ lulj y[ $W $W lulj y[sqd $* $* lujly[gvaf $! $! lulj y[g9af $( $( lujly[cxf $) lujly[lv’ $@ $@ lujly[gdQk $_ $) shk ly[ &W lulj y[lk, $# $# $_ lujly[lu j $$ $$ lujly[shk $& $& &W 135

7D 9q’j dkj p.ljxB,0Poc]h;7yfw]Dj 40 - 20 = ... 49 - 10 = ... 10 + 20 = ... 37 - 8 = ... 31 + 11 = ... 47 - 7 = ... 22 + 13 = ... 25 - 5 = ... 30 + 14 = ... 40 + 5 = ... ’D 9qj’dkj p.lxj B,0Poc]h;8n,j 9eo;o.sh4ndD 42 44 38 41 ສະຫງສ.ວວນ.ລິສຂະສິດ 30 35 10 20 9D 9q’j dkj p.ljxB,0Poc]h;xP[mP[3fp.-h g7nvj ’\\kp > ; < ; = D 10 ..... 20 15 + 25 ..... 23 + 17 40 ..... 30 36 + 11 ..... 19 + 16 40 ..... 50 20 + 18 ..... 15 + 13 45 ..... 35 19 + 27 ..... 30 + 16 136

@D 9eo;oc8j &W g4y’ *WD dD 9qj’[vd9eo;og,affe c]t zqo[;dma’\\qfc]h;cpdsq;|j;pF sq;ly[D 60 sq;ly[ sq;|;j p ສະຫງສ.ວວນ.ລິສຂະສິດsq;ly[ sq;|;j p 0D 9eo;oc8j &W g4y’ *W ,ufaj’oUG 7evjko g]d]k; g]dvkia[ 7evjko g]d]k; g]dvkia[ shkly[ &W &W shkly[sqd &* &* shkly[gvaf &! &! shkly[g9af &( &( shkly[lv’ &@ shkly[cxf &) &@ shkly[gdQk &_ &) shkly[lk, &# Iqdly[ *W &# &_ shkly[luj &$ &$ shkly[shk && && *W 137

7D 9qj’djkp.lxj B,0Poc]h;xt8y[af8k,8q;1jk’D 9eo;o 7evjko I6[c[[dko0Po sq;ly[ sq;|;j p &$ shkly[luj 54 = 50 + 4 5 4 &! shkly[gvaf 51 = 50 + 1 5 1 4 6 lujly[sqd . . . = . . . + 6 6 0 3 8 sqdly[ . . . = . . . + 0 5 7 lk,ly[cxf . . . = 30 + . . . ສະຫງສ.ວວນ.ລິສຂະສິດ shkly[g9af . . . = . . . + 7 ’D 9qj’0ufglAo8+.l9j eo;omujgmqkj da[ &W c]t *W .ljxB,0PoD 50 +10 40 + 10 60 - 0 50 60 30 + 20 5 +30 40 + 20 30 + 25 45 + 15 55 - 5 58 - 8 138

[qfm u 3 4 dko[;d c]t dko]q[9eo;o muj,u @ sa^d !D dko[;d[+,u9nDj dD 9q’j [;d9eo;oI6[9t85]af]5j,oUD sq;ly[ sq;|;j p + 0D dko[;dg]dmuj,u @ s^ad,ufaj’oUD ສະຫງສ.ວວນ.ລິສຂະສິດ 1 ♦ [;d8k,mk’ovo8hv’ [;dc8-j hkpsk0;k Xsq; 2 ♦ [;d8k,mk’8A’8hv’ |;j p[;dsq;|;j pF sq; [;dc8j0;ksk-hkpXsq; ly[[;dsq;ly[?D 8q;1jk’G |j;p [;dsq;|;j pF sq; ly[[;dsq;ly[?D 8q;1jk’G 10 + 22 + 24= 56 1 5 2 5 + 2 1 + 3 3 3 6 5 8 139

7D dko[;d8k,0Ao8voD ♦ [;d8k,0Ao8voc,joxt8y[affaj’]5,j oUD 1 2 23 + 16 35 + 21 (20 + 3) + (10 + 6) (..... + ...... ) + ( ..... + .....) 30 + 9 ..... + ..... 39 ..... CD 9q’j dkj p.ljxB,0Poc]h;7yfw]jD ສະຫງສ.ວວນ.ລິສຂະສິດ 21 + 13 = ............... 11 + 12 + 13 = ............. 10 + 24 + 15 = ............. 33 + 25 = ............... 21 + 22 + 16 = ............. 13 + 20 + 25 = ............. 15 + 14 = ............... 18 + 21 + 10 = ............. 25 + 14 + 20 = ............. 24 + 15 = ............... 32 + 6 + 21 = ............. 48 + 11 = ............... 35 + 13 + 11 = ............. 50 + 9 = ............... 29 + 10 + 20 = ............. 56 + 3 = ............... 19 + 20 = ............... 31 + 28 = ............... 140

@D dko[;d,u9njD 26 + 15 (...... +...... ) + ( ..... + ...... ) dD 9qj’7yfw]gj ]d8+wxoUD 46 + 14 = 38 + 22 = 42 + 18 = 3 6 2 2 ....... + ....... +2 4 + 1 8 ...... +10 0D dko[;dg]d,u9nj8hv’xt8y[affa’j oUD ♦ gvqksq;|;j p[;dsq;|j;p 4hkzqo[;d0v’sq;|j;pg4y’ !W ສະຫງສ.ວວນ.ລິສຂະສິດ 0Bowx.sh0Posq;|j;pc]h;9njsq;ly[9kdoAogvqk9eo;omu9j njwx [;d.lsj q;ly[ faj’8q;1jk’G 8q;9nj sq; sq; ly[ |;j p 1 + 2 0 + 6 2 6 1 0 + 5 1 5 30+11 = 30 + 10 + 1 4 11 = 40 + 1 = 41 141

7D 9qj’7yfw]8j k,8q;1jk’.ljxB,0PoD 1 44 + 17 33 + 18 39 + 21 sq;ly[ sq;|j;p sq;ly[ sq;|;j p sq;ly[ sq;|;j p 4 4 .......... ......... ......... .......... + + + .......... 1 7 .......... ......... ......... 6 1 .......... ......... .......... ......... 44 + 17 = 61 38 + 18= ......... 39 + 21 = .......... 2 35 + 27 46 + 17 42 + 18 30 + 5 + 20 + 7 ...+.... + ....+... ...+.... + ....+...ສະຫງສ.ວວນ.ລິສຂະສິດ 50 + 12 ... + ... ... + ... 62 ....... ....... 3 + 2 4 + 1 9 + 4 6 + 3 5 + 2 9 + 2 6 2 8 2 2 1 4 1 7 3 1 2 5 5 2 ..... ..... ...... ...... ...... CD g]d39fD !D mhk; ohvp ,u0t|q, !* dhvoF vhkp]k;gvqk.shvud #* dhvoD 4k,;kj ]k;,u0t|q,ma’\\qf9addhvo L @D oadIPoshv’ x!Dd ,u #W 7qo c]t shv’ x!D0 ,u @( 7qoD 4k,;jkma’lv’shv’,uoadIPo9ad7qo L 142