Gujrrati Ganit 2nd

Qpgp¡, k„¿ep s¥epf L$fuA¡

fdp A_¡ ei k„¿ep b_phhp_u fds fd¡ R>¡, Ap`Z¡ `Z fduA¡.
hsy®mdp„ L¡$V$gpL$ A„L$ Apàep R>¡. v$f¡L$ rhÛp\}A¡ b¡ A„L$ `k„v$ L$fhp A_¡ k„¿ep
s¥epf L$fhu.

A„L$ 1 ,   3 A„L$ 7 , 8 A„L$ 7 , 5
k„¿ep 13 , 31 k„¿ep , k„¿ep 75 , 57

A„L$ , 1  7  5 A„L$ ,
k„¿ep , 6  3  8 k„¿ep ,
4  9  2
A„L$ , A„L$ ,
k„¿ep , k„¿ep ,

A„L$ ,
k„¿ep ,

fds : ÅX$p L$pNm_u 5-6 QL$suAp¡ s¥epf L$fp¡. v$f¡L$ QL$su `f A¡L$ i|Þe¡sf k„¿ep
gM A_¡ s¡ QL$suAp¡ K^u d|L$.
v$f¡L$ rhÛp\}A¡ L$p¡C`Z b¡ QL$su KQL$u s¡_p `f_p A„L$ Å¡C k„¿ep s¥epf

L$fhu.

41

Ap`¡gp A„L$p¡ hX¡$ kp¥\u dp¡V$u A_¡ kp¥\u _p_u b¡ A„L$u k„¿ep s¥epf L$fhu.
`p„MX$udp„_p Sy>v$p Sy>v$p b¡ A„L$p¡ gB_¡ s¡_p\u \pe s¡V$gu b¡ A„L$u k„¿ep s¥epf L$f.
A_¡ s¡dp„\u kp¥\u dp¡V$u A_¡ kp¥\u _p_u k„¿ep gM.

s¥epf \_pf k„¿ep : 47, 74
4 7 kp¥\u dp¡V$u k„¿ep - 74 kp¥\u _p_u k„¿ep - 47

5 8 s¥epf \_pf k„¿ep : kp¥\u _p_u k„¿ep -
kp¥\u dp¡V$u k„¿ep -

2 s¥epf \_pf k„¿ep : 23, 28, 32, 38, 82, 83
38
kp¥\u dp¡V$u k„¿ep - kp¥\u _p_u k„¿ep -

0 s¥epf \_pf k„¿ep : kp¥\u _p_u k„¿ep -
59

kp¥\u dp¡V$u k„¿ep -

5, 9 Ap k„¿epAp¡ 05, 09 A¡ fus¡ Ap`Z¡ gMsp _\u. s¡_¡ 5,
9 A¡ fus¡ S> gMpe R>¡. s¡ A¡L$ A„L$u k„¿ep R>¡.

rhQpf L$f : A¡L$ S> A„L$ afu afu hp`fu_¡ L¡$V$gu b¡ A„L$u k„¿ep d¡mhu iL$pe ?

42

k„¿ephpQL$ (d|ëehpQL$)
¾$dhpQL$ iåv$

h_cp¡S>_

A¡L$ hpf \ey„ kps S>Z_y„ h_cp¡S>_ dS>¡v$pf,
v$f¡L¡$ gphhp_u lsu hp_Nu rgÄS>sv$pf.
L|$v$L$p dpfsp¡ ^p¡mp¡ kkgp¡ Apìep¡ kp¥\u `l¡gp¡,
Dsphmdp„ Of¡ flu Nep¡ Mphp_p¡ X$bp¡ s¡_p¡.
v$p¡X$sy„ v$p¡X$sy„ Apìey„ kp¡_¡fu lfZ buSy>„,
\¡gudp„ s¡ gpìey„ Opk Ly$dmy„ Ly$dmy„.
TpX$ `f\u L|$v$L$p dpfsp¡ ÓuÅ¡ Apìep¡ hp„v$fp¡,
kp\¡ s¡ gpìep¡ fkv$pf amp¡_p¡ V$p¡`gp¡.
`|„R>X$u lgphsu Npe Qp¡\p _„bf¡ Aphu,
b_phu lghp¡ NpS>f_p¡ s¡ sp¡ kp\¡ gphu.
k|„Y$_y„ k„syg_ Åmhsp„ `p„Qdp„ lp\ucpC,
Myi \C NC rdÓd„X$mu k|„Y$dp„ i¡fX$u Å¡C.
QL$u bl¡_ sp¡ R>Ì$p Apìep gC dL$pC v$pZp,
dp¡fcpC sp¡ kpsdp, gpìep dkpgp QZp.
R> S>Zp„ gpìep hõsy, b^p„A¡ gu^u hl¢Qu,
DÅZu dõs L$fu, `¡V$ Nep cfpB.

Al] R>, kps iåv$p¡ k„¿ep R>¡.
`l¡gp¡, buÅ¡, Qp¡\p¡ S>¡hp iåv$p¡
¾$d S>Zph¡ R>¡.

43

Ÿ_ r_rMg iqL$g kp¡ld kp¥fc

• D`f Ap`¡gp rQÓdp„ v$p¡X$hp_u õ`^p®dp„ Ly$g bpmL$p¡ L¡$V$gp„ ? 5

5 A¡ d|ëehpQL$ k„¿ep R>¡.

• v$p¡X$hp_u ifsdp„ kp¥fc_p¡ ¾$dp„L$ L¡$V$gpdp¡ ? `p„Qdp¡

`p„Qdp¡ A¡ ¾$dhpQL$ iåv$ R>¡.

• `l¡gy„ L$p¡Z R>¡ ? • Qp¡\p ¾$dp„L¡$ L$p¡Z R>¡ ?

• dp¡f L¡$V$gpdp„ X$bpdp„ R>¡ ? • `l¡gp X$bpdp„ L$p¡Z R>¡ ?
• kkgy„ L¡$V$gpdp„ X$bpdp„ R>¡ ? • kpsdp X$bpdp„ L$p¡Z R>¡ ?
• tkl_p X$bp_p¡ ¾$dp„L$ L¡$V$gpdp¡ ?
• KV$_p X$bp_u `R>u_p¡ X$bp¡ L¡$V$gpdp¡ ?
• lp\u_p X$bp_u `l¡gp„_p¡ X$bp¡ L¡$V$gpdp¡ ?

1, 2, 3, 4,.... Ap d|ëehpQL$ k„¿ep A_¡ `l¡gp¡, buÅ¡, ÓuÅ¡... A¡ ¾$dhpQL$ iåv$ R>¡, s¡_p
ep¡Áe D`ep¡N D`f cpf Ap`hp¡.

4444

kpr_ep bpNdp„_p R>p¡X$_¡ `pZu Ap`¡ R>¡.

Nygpb bpfdpku NgNp¡V$p¡ dp¡Nfp¡ k|e®dyMu

D`f_p rQÓp¡ Å¡C_¡ Mpgu S>Áepdp„ ep¡Áe iåv$ gM.
• kpr_ep\u `l¡gp ¾$dp„L¡$ .........._p¡ fp¡` R>¡.
• dp¡Nfp_p¡ fp¡` kpr_ep\u ......... ¾$dp„L¡$ R>¡.
• Ly$g ..... fp¡` R>¡.

`yõsL$_p `p_p _„. 33 A_¡ 34 Å¡ A_¡ L$l¡.
• hj®_u iê$Aps\u `p„Qdp¡ A„N°¡Æ drl_p¡ ¼ep¡ ?
• cpfsue hj®_u iê$Aps\u ApW$dp¡ drl_p¡ ¼ep¡ ?

d|ëehpQL$ k„¿ep gM.
• Å„bgu f„N_u dpR>guAp¡

L¡$V$gu R>¡ ?
• gpg f„N_u dpR>guAp¡

L¡$V$gu R>¡ ?
• `ump f„N_u dpR>guAp¡

L¡$V$gu R>¡ ?

Ýep_dp„ fpMp¡ : hõsy NZhp dpV¡$ S>¡ k„¿ep hp`fhpdp„ Aph¡ R>¡ s¡ d|ëehpQL$ k„¿ep
R>¡. hõsy_p¡ lpfdp„_p¡ ¾$d L$l¡hp dpV¡$ S>¡ iåv$ h`fpe R>¡ s¡ ¾$dhpQL$ L$l¡hpe R>¡.

45

rQÓ `f\u dprlsu d¡mhuA¡.

hN}L$fZ

D`f_p kpàsprlL$ bÅf_y„ r_funZ L$fu_¡ _uQ¡_p Qp¡fk cf.

1) ipL$cpÆ_u lp\NpX$u_u k„¿ep -

2) am h¡Q_pfp dpZkp¡_u k„¿ep -

3) bÅfdp„ h¡QpC fl¡gp Qpf am -

4) bÅfdp„ h¡QpC fl¡gp `p„Q ipL$ -

5) bÅfdp„ v¡$Mpsp Ly$g R>p¡L$fpAp¡ -

6) bÅfdp„ v¡$Mpsu Ly$g R>p¡L$fuAp¡ -

7) bÅfdp„ L$`X$p_u \¡gu gC_¡ Aph¡gu Ly$g ìe[¼s -

4466

rQÓp¡_y„ r_funZ L$fu_¡ _uQ¡ Ap`¡gp¡ ãgp¡ QpV®$ `|Z® L$f.

rQÓdp„_p hpl_p¡ NZu_¡ gM.

rQÓ `f\u âñp¡_p DÑf gM.
1) gpg gpCV$ \ep `R>u L$ep„ ¼ep„ hpl_p¡ \p¡cu Nep R>¡ ?
2) gugu gpBV$ \ep `R>u ¼ep„ ¼ep„ hpl_p¡ S>C füp R>¡ ?
3) rQÓdp„ lhp_y„ âv|$jZ r_dp®Z L$f_pfp hpl_p¡ ¼ep„ ?
4) kpeL$g, dp¡V$f kpeL$g, L$pf, bk A_¡ qfnp `¥L$u ¼ep„ hpl_p¡_u k„¿ep kp¥\u

h^y R>¡?
r_funZ L$f :
• A¡L$ fplv$pfu fõsp_p qL$_pf¡ hpgu kp\¡ Ecp„ flu 15 rdr_V$dp„ Sy>v$p Sy>v$p f„N_u

L¡$V$gu NpX$uAp¡ v¡$Mpe R>¡ s¡ Å¡. s¡_p `f\u gp¡L$p¡_¡ L$ep f„N_u NpX$u h^y Nd¡ R>¡
s¡ _½$u L$f.
• QL$gu A\hp L$b|sf_¡ v$pZp Ap`u L¡$V$gp `nu v$pZp QZhp Aph¡ R>¡ s¡ NZ.
A¡L$ S> `nu afu afu v$pZp QZhp Aph¡, sp¡ Ap¡mMu iL$pe L¡$ ?

47

Mpk kfhpmp, hØuhpmp

8 A_¡ 4 v$uhpkmu dmu_¡ 12 v$uhpkmu 7 A_¡ 8 A¡L$d dmu_¡ 15 A¡L$d \ep.
\B. s¡dp„\u 10_y„ S|>\ s¥epf L$fu v$iL$ s¡dp„\u 10_y„ S|>\ bp„^u_¡ v$iL$ b_phuA¡.
b_phuA¡.
v$iL$ A¡L$d v$iL$ A¡L$d
v$iL$ A¡L$d v$iL$ A¡L$d

Ýep_dp„ fpMp¡ : A¡L$d_p Ofdp„ 9 L$fsp„ dp¡V$u k„¿ep fMpe _l], dpV¡$ Ap`Z¡
10_y„ A¡L$ S|>\ s¥epf L$fu_¡ s¡_¡ v$iL$_p Ofdp„ d|L$uA¡ R>uA¡.

v$uhpkmu, dZL$p A\hp V$`L$p„ hp`fu_¡ _uQ¡_p kfhpmp L$f A_¡ S>hpb gM.
v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡
+ 9+ 6+ 7+ 6+ 4
65469

+  = ApS> kfhpmp¡ Ap fus¡ gMu
10 + 1 4 =
24 iL$pe. v$iL$ A¡L$d

v$ A¡ + 1 0
13 1 4
+4 0
_uQ¡_p kfhpmp L$f. 24

v$ A¡ v$ A¡ v$ A¡
10 1 7 15
+1 6 +3 +5 0
0

4488

v$iL$ A¡L$d • â\d AL¡ $d_p¡ kfhpmp¡ L$fu_¡ AL¡ $d_p Ofdp„ gM.
hØu 1
5 A¡ + 9 A¡ = 14 A¡
15 Ap 14 A¡L$ddp„\u 10 dZL$p_u 1 dpmp L$fu_¡ 4 R|>V$p dZL$p
+9 A¡L$d_p Ofdp„ fpMuiy„.

2 14

14 A¡ = 1 v$ 4 A¡

• 10 A¡L$d_p¡ _hp¡ v$iL$ L$ep£, s¡_¡ "hØu' L$l¡hpe R>¡.
• lh¡ 1 v$ + 1 v$ = 2 v$, A¡V$g¡ L¡$ kfhpmpdp„ b¡ v$iL$ \ep. s¡_¡ v$iL$_p Ofdp„

gMuA¡.

v$iL$ A¡L$d • 3 A¡ + 7 A¡ = 10 A¡
10 A¡ = 1 v 0 A¡
hØu 1
• S>¡dp„ 1 v$ A¡V$g¡ hØu. s¡_¡ v$iL$_p Ofdp„ gMuiy„. A¡L$d_p
+2 3 Ofdp„ i|Þe gMuiy„.
27
40 • lh¡ b^p dmu_¡ Qpf v$iL$ \ep. s¡_¡ v$iL$_p Ofdp„ gMuiy„.

kfhpmp¡ 4 v$ + 0 A¡, A¡V$g¡ L¡$ 40
23 + 17 = 40

v$iL$ A¡L$d • 4 A¡ + 9 A¡ = 13 A¡ v$iL$ A¡L$d
13 A¡ = 1 v$ + 3 A¡
hØu 1
• 2 + 1 + 1 A¡d Qpf v$iL$
+ 1 4 Qpf v$iL$ A_¡ ÓZ A¡L$d + 1 4
2 9 2 9
A¡V$g¡ L¡$ 4 v$ + 3 A¡ = 43
3 13 4 13
14 + 29 = 43

Ýep_dp„ fpMp¡ : kfhpmp¡ L$fsu hMs¡ `lg¡ p„ AL¡ $d_p Of_p¡ kfhpmp¡ L$fhpdp„ Aph¡ R>.¡

49

• rQÓ Å¡C_¡ kfhpmp_p Dv$plfZ s¥epf L$f A_¡ NZ. v$iL$ A¡L$d
v$iL$ A¡L$d

• kfhpmp¡ L$f.
v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡
36 32 47 68 44 38

+2 5 +2 8 + 5 +2 2 +4 8 +1 4

v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡
71 2 5 3 5 4 2 2 7 4 4
+1 9 +3 7 +2 9 +1 9 +3 4 +2 7

v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡
4 9 55 69 63 65
+ 3 + 8 + 9 +2 8 +2 6

Ap Dv$plfZp¡ dpV¡$ rinL¡$ 10-10 v$uhpkmu_p S|>\ A_¡ R|>V$u
v$uhpkmu, v$k-v$k dZL$p_u dpmp A_¡ R|>V$p dZL$p, v$k_u _p¡V$p¡ A_¡
A¡L$ ê$r`ep_p rk½$p hN¡f¡ kprlÐe D`gå^ L$fphu âpÐernL$ L$fphhy„.

50

hpspd® p„ kfhpmp - 2

• Np¥fu `pk¡ 15 ê$r`ep lsp. dçduA¡ s¡_¡ buÅ 26 ê$r`ep Apàep. lh¡ s¡_u `pk¡

L¡$V$gp ê$r`ep \ep ?

iy„ Apàey„ R>¡ ? Np¥fu `pk¡ 15 ê$r`ep, dçduA¡ 26 ê$r`ep Apàep

iy `|Rey„ R>¡ ? Np¥fu `pk¡ Ly$g L¡$V$gp ê$r`ep

iy„ L$fuiy„?
v$ A¡

1

+1 5 Np¥fu `pk¡ ê$r`ep lsp
2 6 dçduA¡ ê$r`ep Apàep

4 1 Ly$g ê$r`ep

Dv$plfZ hp„Q. `pV$u `f `¡_ hX¡$ v$iL$-A¡L$d_p Mp_p v$p¡fu ep¡Áe õ\m¡ A„L$ gMu.
kfhpmp¡ L$f.

• A¡L$ d¡v$p_dp„ 24 Npe A_¡ 28 c¢k Qfsu lsu. sp¡ d¡v$p_dp„ Ly$g L¡$V$gp Y$p¡f Qfsp„
lsp„ ?

• kgdpA¡ NC L$pg¡ 34 ê$dpg kuìep lsp. ApS>¡ s¡Z¡ buÅ 38 ê$dpg kuìep. sp¡ b¡
qv$hkdp„ kgdpA¡ Ly$g L¡$V$gp ê$dpg kuìep ?

• hrkd `pk¡ 25 Np¡V$uAp¡ lsu. ApS>¡ fdsdp„ s¡ 13 Np¡V$uAp¡ ÆÐep¡, sp¡ lh¡ hrkd
`pk¡ L¡$V$gu Np¡V$uAp¡ \C ?

• NC L$pg¡ vy$L$p_v$pf `pk¡ 35 `s„N lsp, ApS>¡ s¡ buÅ 19 `s„N gpìep¡, sp¡ lh¡
vy$L$p_v$pf `pk¡ Ly$g L¡$V$gp `s„N \ep ?

_uQ¡_p kfhpmp dpV¡$ ip[åv$L$ Dv$plfZp¡ s¥epf L$f A_¡ NZ.

• 22 + 37 • 34 + 28 • 30 + 19

• 26 + 34 • 59 + 29 • 49 + 17

51

kfm kfhpmp A_¡ bpv$bpL$u, v$iL$ Dd¡fu_¡ A\hp Ap¡R>p¡ L$fu_¡

41 + 10 = +=

 4 v$iL$ 1 A¡L$d + 1 v$iL$ =  5 v$iL$ 1 A¡L$d

  41  +  10  =   51

41 - 10 = -=

 4 v$iL$ 1 A¡L$d - 1 v$iL$ =  3 v$iL$ 1 A¡L$d

  41  -  10  =   31

Al] Ap`Z¡ 10_p V$à`¡ kfhpmp¡ A_¡ bpv$bpL$u L$fsp„ iu¿ep.

kfhpmp¡ (20 D„d¡fu_¡) bpv$bpL$u (20 Ap¡R>p L$fu_¡)

37 + 20 = +=

 3 v$iL$ 7 A¡L$d + 2 v$iL$ =  5 v$iL$ 7 A¡L$d

  37  +  20 =   57

37 - 20 = -=

 3 v$iL$ 7 A¡L$d - 2 v$iL$ =  1 v$iL$ 7 A¡L$d

  37  -  20 =   17

• kfhpmp¡ L$f. • bpv$bpL$u L$f. 26 − 10 =
6 + 10 = 18 + 20 = 17 − 10 = 53 − 10 =
29 + 30 = 62 + 10 = 34 − 20 = 92 − 30 =
77 + 20 = 84 + 10 = 67 − 20 =

rhQpf L$f : Ap`¡gu k„¿epdp„\u 10, 20 Ap¡R>p
L$fhp A\hp 10, 20 Dd¡fhp„ iy„ L$fhy„ Å¡CA¡ ?

52

bpv$bpL$u dpV¡$
v$iL$ R|>V$p L$fuA¡

v$f¡L$ X$bpdp„ 10 `¡_rkg R>¡.

d_¡ 20 d_¡ 4 `¡_rkg d_¡ 25 `¡_rkg
`¡_rkg Å¡BA¡ R>¡. Å¡CA¡ R>¡.
Å¡CA¡ R>¡.
L¡$hu fus¡
Ap`u iL$pi¡ ?

fdp : dpfu `pk¡ 10 `¡_rkg_p b¡ bp¸¼k A_¡ `p„Q `¡_rkg R>¡. s¡dp„\u 7 `¡_rkg
dpfu bl¡_`Zu_¡ Ap`hu R>¡, L¡$hu fus¡ Ap`y„ ?

ei : A¡L$ bp¸¼k R|>Vy„$ L$fu g¡. spfu `pk¡ 10 A_¡ 5 R|>V$u A¡d Ly$g 15 `¡_rkg \i¡,
s¡dp„\u spfu bl¡_`Zu_¡ 7 `¡_rkg Ap`.

15 A¡V$g¡ 32 A¡V$g¡
1 v$iL$ 5 A¡L$d 3 v$iL$ 2 A¡L$d

1 v$iL$ R|>V$p L$fu_¡ 1 v$iL$ R|>V$p L$fu_¡

15 A¡L$d 2 v$iL$ 12 A¡L$d

1 v$iL$ 5 A¡L$d A¡V$g¡ 3 v$iL$ 2 A¡L$d A¡V$g¡
15 A¡L$d 2 v$iL$ 12 A¡L$d

53

bpv$bpL$u v$iL$ R|>V$p L$fu_¡ :    63 − 6 =
22 − 7 =   30 − 9 =

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d
1 12 2 10 5 13

−7 −9 −6
57
15 21
63 − 6 = 57
22 − 7 = 15   30 − 9 = 21   

v$iL$ R|>V$p L$fu_¡ bpv$bpL$u L$f.    37 − 9 =
23 − 5 =   25 − 8 =

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d
1 13 1 −

− −

1

35 - 17 Ap bpv$bpL$u Ap`Z¡ _uQ¡ dyS>b dp„X$Zu L$fu_¡ L$fuiy„.

v$iL$ A¡L$d v$iL$ A¡L$d
15
2 5

3 v$ 5 A¡ 3 7
− 8

1

2 v$ 15 A¡ 1

kfhpmp¡ A\hp bpv$bpL$u L$fsu hMs¡ kyrh^p dpV¡$ \p¡X$u hpf Ap`Z¡ A¡L$d_p Ofdp„ 9 L$fsp„
dp¡V$u k„¿ep gMuA¡ R>uA¡, `Z b^y„ L$pd `su Nep `R>u A¡L$d_p Ofdp„ 9 L$fsp„ dp¡V$u k„¿ep
gMhp_u lp¡su _\u, s¡ rhÛp\}Ap¡_¡ kdÅhhy„.

54

v$iL$ R|>V$p L$fu_¡ bpv$bpL$u L$f. 17 − 9 =

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d 30 − 12 =

− 4 0 − 6 7 − 9 2 51 − 18 =
1 1 2 9 5 3 46 − 17 =
83 − 59 =

74 − 25 =

• cph_pA¡ 43 TpX$ `¥L$u 27 TpX$_¡ `pZu Apàey„. lh¡ L¡$V$gp TpX$_¡ `pZu Ap`hp_y„

bpL$u R>¡ ?

iy„ Apàey„ R>¡ ? Ly$g TpX$ 43 R>¡, 27 TpX$_¡ `pZu Apàey„.

iy„ `|Rey„ R>¡ ? L¡$V$gp TpX$_¡ `pZu Ap`hp_y„ bpL$u R>¡. 43dp„\u 27
iy„ L$fuiy„ ? bpv$bpL$u bpv$ L$fuiy„.

v$iL$ A¡L$d

3 A¡L$ddp„\u 7 A¡L$d 3 13
bpv$ L$fu iL$pe _l]. 3 Ly$g TpX$
dpV¡$ 1 v$iL$ R|>V$p¡ L$fuiy„. 4
s¡\u 13 R|>V$p \i¡. −2 7 TpX$_¡ `pZu Apàey„.
6 TpX$_¡ `pZu Ap`hp_y„ bpL$u R>¡.
1

• NrZs_u Åmudp„ gugu A_¡ gpg f„N_u dmu_¡ 70 kp¡NW$uAp¡ b¡kpX$u R>¡. gugp
f„N_u 42 kp¡NW$uAp¡ R>¡. gpg f„N_u kp¡NW$uAp¡ L¡$V$gu ?

• õhfp `pk¡ 92 dZL$p lsp. s¡dp„\u 59 dZL$p s¡Z¡ `fu_¡ Apàep. lh¡ õhfp `pk¡
L¡$V$gp dZL$p hÝep li¡ ?

• dçduA¡ qv$hpmudp„ 67 O|Ofp A_¡ 48 L$Qp¡fu s¥epf L$fu. O|Ofp L$fsp„ L$Qp¡fu
L¡$V$gu Ap¡R>u R>¡ ?

• õ_¡lk„d¡g_dp„ rS>ëgp `qfjv$_u ipmp_p 81 rhÛp\}Ap¡ `¥L$u
78 rhÛp\}Ap¡A¡ cpN gu^p¡. sp¡ L¡$V$gp rhÛp\}Ap¡A¡ õ_¡l
k„d¡g_dp„ cpN gu^p¡ _l] ?

55

rk½$p - _p¡V$p¡ Ap¡mMuA¡

ei A_¡ fdp dçdu kp\¡ dpdp_p Npd¡ Nep. ApS>¡ Npddp„ epÓp R>¡. b„_¡ epÓpA¡
S>hp dpV¡$ _uL$þep. dpdpA¡ b„_¡_¡ kp¡ ê$r`ep Apàep.
fdp _„vy$L$pL$p_u vy$L$p_¡ NC. kp¡ ê$r`ep_p R|>V$p dp„Áep. _„vy$L$pL$pA¡ s¡_¡ _uQ¡ dyS>b
R|>V$p Apàep.

12
Mpgu Qp¡fkdp„ D`f_p âÐe¡L$ rk½$p A\hp _p¡V$p¡_u qL„$ds gM.
s„y ÓZ Sy>v$p Sy>v$p âL$pf¡ 100 ê$r`ep R|>V$p L$fu v¡$.

5566

Qpgp¡ bÅfdp„ S>CA¡.

Adpfp Npd_u Ap vy$L$p_ Å¡.
Al] `p¡sp_p lp\¡ hõsy gC hõsy_u qL„$ds blpf S>sp„ `l¡gp„ `¡V$udp„ S>dp L$fphhp_u
R>¡.

Ÿ_¡ A¡L$ v$X$p¡ A_¡ A¡L$ dp¡V$f gu^u.
s¡Z¡ `¡V$udp„ ê$r`ep S>dp L$ep®.
kp¡_uA¡ A¡L$ Y$]Ngu A_¡ A¡L$ cdfX$p¡ gu^p¡.
s¡Z¡ `¡V$udp„ ê$r`ep S>dp L$ep®.
v¡$hp„i¡ b¡ L¡$mp A_¡ A¡L$ Ágpk v|$^ gu^y„.
s¡Z¡ `¡V$udp„ ê$r`ep S>dp L$ep®.
`fuA¡ A¡L$ _p¡V$ A_¡ b¡ `¡_rkg gu^u.
s¡Z¡ `¡V$udp„ ê$r`ep S>dp L$ep®.
sy„ _½$u L$f : s_¡ Ap vy$L$p_dp„\u iy„ iy„ h¡Qpsy„ g¡hy„ Ndi¡ ? hõsy
gu^p `R>u sy„ `¡V$udp„ L¡$V$gp ê$r`ep S>dp L$fui ?

57

g„bpC dp`uA¡

Qpgp¡ dp`uA¡ : ei_¡ s¡_p Ap¡fX$pdp„ Aæepk dpV¡$ A¡L$ V¡$bg Å¡CA¡ R>¡. c]s_¡
AX$pX$u_¡ S>¡ S>ÁepA¡ V¡$bg d|L$hp_y„ R>¡ s¡ S>Áep_u g„bpC ei¡ _p_u gpL$X$u hX¡$ dp`u.
s¡ Qpf gpL$X$u L$fsp„ \p¡X$u h^pf¡ lsu.

s¡V$gu g„bpC_y„ V¡$bg `k„v$ L$fhp dpV¡$ ei vy$L$p_dp„ Nep¡. Ðep„ s¡Z¡ A_¡L$ V¡$bg Å¡ep.
S>¡ gpL$X$u hX$¡ S>Áep dp`u lsu s¡ S> gpL$X$u V¡$bg_u g„bpC dp`u. ei L$ey„ V¡$bg `k„v$
L$fi¡, s¡ _uQ¡_p rQÓp¡ `f\u L$C fus¡ L$lu iL$pe ? ei¡ `k„v$ L$f¡g V¡$bg _uQ¡_p
Qp¡fkdp„ f„N `|f.

L$ey„ V¡$bg
gJ ?

2 gpL$X$u 3 gpL$X$u 4 gpL$X$u 5 gpL$X$u ei¡ 5 gpL$X$u gp„by„
V¡$bg ip dpV¡$ `k„v$
L$e¯y ?

5588

fdp_¡ s¡_p hN®_p v$fhpÅ `f A_¡ ipmp_p dy¿e âh¡iÜpf `f awg_p lpf gNpX$hp_p
R>¡. s¡ dpV¡$ s¡Z¡ ÓZ ÅX$p v$p¡fp gphu hN®_p v$fhpÅ_u `lp¡mpC A_¡ ipmp_p dy¿e
âh¡iÜpf_u g„bpC dp`u. v$f¡L$ lpf dpV¡$ b¡ h¢s h^pf¡ gp„bp¡ v$p¡fp¡ L$pàep¡. b¡ h¢s h^pf¡
gp„bp¡ v$p¡fp¡ ip dpV$¡ gu^p¡ ?

L$fu Sy>Ap¡ :
• sd_¡ ipmp_p hN® A_¡ dy¿e âh¡iÜpf dpV¡$ sp¡fZ s¥epf

L$fhp dpV¡$ L¡$V$gu v$p¡fu Å¡Ci¡ ?
• Bdpfs b„^psu lp¡e s¡hp bp„^L$pd_p õ\m¡ rinL$/hpgu

kp\¡ S>C_¡ s¡Ap¡ dp` i¡_p hX¡$ A_¡ L¡$hu fus¡ g¡ R>¡ s¡ Sy>Ap¡.
59

hS>_ L$fuA¡

_uQ¡ Ap`¡gu hõsyAp¡ `¥L$u cpf¡ hõsy _uQ¡_u hõsyAp¡ `¥L$u lgL$u hõsy _uQ¡_p

_uQ¡ Ap`¡gp Qp¡fkdp„ f„N `|f. Qp¡fkdp„ f„N `|f.

tQVy$ A_¡ rbËz$ A¡ b¡ riepm fpÓ¡ Qpgu_¡ S>sp lsp. s¡d_¡ A¡L$ Np¡m_u cugu dmu.
b„_¡_¡ M|b Ap_„v$ \ep¡.

d_¡ Np¡m M|b cph¡ R>¡. _p, lz„ dp¡V$p¡ R>y>. lz„ kfMp
lz„ cpN `pX$ui. cpN `pX$ui.

cp¡gy f]R> s¡d_p¡ TOX$p¡ Å¡sp¡ lsp¡. s¡ s¡d_u dv$v¡$ Apìep¡.

Af¡, A¡L$buÅ kp\¡ TOX$p¡ s¡ L$C fus¡ ?
_l], lz„ b„_¡_¡ kfMp¡ Np¡m
hl¢Qu Ap`ui.

cp¡gy f]R> s¡d_u dv$v$ dpV¡$ A¡L$ hõsy gC Apìep¡.
kdp_ hl¢QZu L$fhp dpV¡$ cp¡gyA¡ iy„ L$e¯y ?
L$prR>ep¡ ipL$_y„ hS>_ i¡_p hX¡$ L$f¡ R>¡ ? ................

âÐen hõsy QL$pku hS>__u syg_p L$fhp_u L©$rs L$fphhu.

6600

* _uQ¡_p ÓpS>hp„ Sy>Ap¡. v$f¡L$ ÓpS>hp„dp„_u cpf¡ A_¡ lgL$u hõsy L$lp¡.

L$qfepZp_u vy$L$p_dp„ S>C_¡ rhrh^ hõsyAp¡_y„ hS>_ L¡$hu fus¡ L$fhpdp„ Aph¡ R>¡ s¡ Å¡.
hõsy_y„ hS>_ L$fhp dpV¡$ h`fpsp ÓpS>hp_p rhrh^ âL$pf Å¡.

h^y dprlsu : `l¡gp„_p kdedp„ hõsy_y„ hS>_ L$fhp dpV¡$ ¼ep dp` hp`fhpdp„ Aphsp
lsp. s¡_u dprlsu d¡mhp¡.

ÓpS>hp_u dv$v$\u hõsy_y„ hS>_ L$fhp_u L©$rs L$fphhu. rhÛp\}Ap¡_¡
`p¡sp_y„ ÓpS>h„y Ås¡ s¥epf L$fhp L$l¡hy„.

61

^pfL$sp dp`uA¡

* S>¡ hpkZdp„ h^y `pZu kdpi¡ s¡_u _uQ¡_p Qp¡fkdp„ f„N `|f.

ei A_¡ fdp fkp¡X$pdp„\u Sy>v$p Sy>v$p hpkZ gC Apìep. s¡d_u `pk¡ A¡L$ dN, A¡L$
bpgv$u, A¡L$ Ágpk lsp¡.

s¡dZ¡ Ap b^p„ hpkZ A¡L$ hX¡$ `pZu\u cep®.

ei : fdp L$l¡ Å¡BA¡, ¼ep hpkZdp„ kp¥\u h^y `pZu kdpey„ ?
fdp : .................
lh¡ sy„ L$l¡, ¼ep hpkZdp„ kp¥\u Ap¡Ry>„ `pZu kdpey„ ?
ei : .................

D`f âdpZ¡ Sy>v$p Sy>v$p ApL$pf_p hpkZ hp`fu_¡ L©$rs L$fhu.

6622

Qpgp¡ L©$rs L$fuA¡ : sd¡ sdpfp fkp¡X$pdp„\u Sy>v$p Sy>v$p âL$pf_p hpkZ c¡Np L$fp¡. Ap
b^p„ hpkZdp„ `pZu cfhp dpV¡$ A¡L$ S> hpV$L$u_p¡ D`ep¡N L$fp¡. v$f¡L$ hpkZdp„ L¡$V$gu
hpV$L$u `pZu kdpi¡ s¡_y„ A_ydp_ L$fp¡ A_¡ `R>u âÐen ê$`¡ `pZu cfu A_ydp_
QL$pkp¡.

L$ey„ `pÓ cfpey„ ? s¡ cfhp dpV¡$ A„v$pS>¡ L¡$V$gu Ap cfhp dpV¡$ Qp¡½$k L¡$V$gu

hpV$L$u `pZu Å¡Bi¡ ? hpV$L$u `pZu_u S>ê$f `X$u ?

L©$rs : • D^fk_u v$hp_u iuiu_p Y$p„L$Z `f àgp[õV$L$_y„ A¡L$
_p_L$Xy„$ Y$p„L$Z Aph¡ R>¡. s¡ Y$p„L$Z hX¡$ v$hp dp`hpdp„
Aph¡ R>¡.

• A¡L$ Ágpk A\hp A¡L$ L$` gp¡. s¡dp„ L¡$V$gp Y$p„L$Z `pZu
kdpe R>¡ s¡ Sy>Ap¡.

63

dprlsu_y„ ìehõ\p`_

_uQ¡ L¡$fu_p rQÓ `f drl_p_p _pd Apàep R>¡. v$f¡L$ rQÓ `f s¡ s¡ drl_p_p
qv$hkp¡_u k„¿ep gM.

ÅÞeyApfu a¡b°yApfu dpQ® A¡râg d¡ S|>_

Sy>gpC Ap¸NõV$ kàV¡$çbf Ap¸¼V$p¡bf _h¡çbf qX$k¡çbf

D`f_y„ rQÓ Å¡C_¡ hp¼e `|Z® L$f. R>¡.
1) rQÓdp„ Ly$g drl_p_p _pdp¡ Apàep R>¡.
2) 31 qv$hk_p Ly$g drl_p R>¡.
3) 30 qv$hk_p Ly$g drl_p R>¡.
4) 28 A\hp 29 qv$hk_p drl_p R>¡.
5) d¡ drl_p `R>u Aphsp¡ 31 qv$hk_p¡ â\d drl_p¡

Ap hj®_y„ spfurMey„ (L¸$g¡ÞX$f) Å¡C_¡ _uQ¡_p Qp¡fk cf.

1) Ap hj£ fdTp_ Cv$ drl_pdp„ R>¡.

2) _pspg drl_pdp„ R>¡.

3) Ap hj£ lp¡mu drl_pdp„ R>¡.

4) dpfp¡ S>Þdqv$hk drl_pdp„ R>¡.

5) dlpfpóV²$qv$_ _p fp¡S> R>¡.

6) rinL$qv$_ _p fp¡S> R>¡.

6644

spfp hN®_p rhÛp\}Ap¡_¡ s¡d_p¡ S>Þdqv$hk ¼ep drl_p_u L$C spfuM¡ R>¡ s¡ `|R>.
_uQ¡ dyS>b s¡_u _p¢^ s¥epf L$f.

drl_p ÅÞeyApfu a¡b°yApfu dpQ® A¡râg d¡ S|>_
S>Þd- dpep, Ards, l¡dp, d¡fu, huZp, aprsdp, T¥_p,
qv$hk s_ep kprlg, d^y, h¡v$p„s, h¡v eyN

L$_L$ _ufS> iL$ug
drl_p Sy>gpC Ap¸NõV$ kàV¡$çbf Ap¸¼V$p¡bf _h¡çbf qX$k¡çbf
S>Þd- Q„vy$, Bhp, Å¡k¡a, S>e, `v¹$dp,
qv$hk op_, âZh Q¥spgu frTep, fp¥_u

bLy$g d¥r\gu

_uQ¡_p âñp¡_p dp¥rML$ S>hpb Ap`p¡.
1) Q¥spgu A_¡ Å¡k¡a_p¡ S>Þdqv$hk L$ep drl_pdp„ R>¡ ?
2) A¡râg drl_pdp„ L¡$V$gp gp¡L$p¡_p¡ S>Þdqv$hk R>¡ ?
3) ¼ep drl_pdp„ kp¥\u h^pf¡ gp¡L$p¡_p¡ S>Þdqv$hk R>¡ ?
4) ¼ep drl_pdp„ L$p¡C_p¡ `Z S>Þdqv$hk _\u ?
5) ÅÞeyApfu drl_pdp„ L$p¡_p¡ L$p¡_p¡ S>Þdqv$hk R>¡ ?

qfep, s¡ spfp¡ S>Þdqv$hk d¢ Ofdp„ hX$ugp¡_¡ âZpd
L¡$hu fus¡ ES>ìep¡ ? L$ep®. b`p¡f¡ A_p\-
Af¡ hpl qfep ! M|b S> Apîddp„ S>C_¡ Mphp_u
kfk. d¢ dpfp S>Þd- hõsyAp¡ Ap`u. kp„S>¡ rdÓp¡
qv$hk¡ A¡L$ TpX$ hpìey„. kp\¡ `pV$} L$fu.

65

ApL©$rsb„^

_uQ¡ Ap`¡gp ApL©$rsb„^_y„ r_funZ L$f. `qfkfdp„ Ap`Z_¡ Aphp A_¡L$
ApL©$rsb„^ Å¡hp dm¡ R>¡.

6666

L©$rs :
c]X$p_¡ L$p`u s¡_¡ f„Ndp„ X|$bpX$u L$pNm `f Ås¡ A¡L$ ApL©$rsb„^ s¥epf L$f.

_uQ¡_p rQÓdp„ v$ip®h¡g ApL©$rsb„^ `|Z® L$f. 14

4 6 10
2

_uQ¡_p ApL©$rsb„^_y„ r_funZ L$fu_¡ Mpgu S>Áepdp„ ep¡Áe Anf A\hp k„¿ep
gM.

A VMA VMA V

131313

100 010 001 100

kuspam, QuLy$_p„ bu_¡ õhÃR> A_¡ L$p¡fp„ L$fu c¡Np„ L$fhp„ A_¡ s¡d_p„ ApL©$rsb„^ s¥epf L$fhp„
L$l¡hy„. ApL©$rsb„^ dpV¡$ hV$pZp, hpgp¡m_p v$pZp_p¡ `Z D`ep¡N L$fu iL$pe.

67

_uQ¡_p ApL©$rsb„^ `|Z® L$f. 45
15 20 25

bpmL$p¡_¡ ApL©$rsb„^_p _d|_p Ap¡mMhp L$l¡hy„. Ap dpV¡$ k„¿ep hX¡$
s¥epf \sp ApL©$rsb„^_p rhrh^ âL$pfp¡ rhi¡ rhÛp\}Ap¡ kp\¡ QQp®
L$fp¡.

68

NyZpL$pf `|h®s¥epfu

TV$`V$ NZ ! bl¡_ : Al] v$f¡L$ fL$pbudp„ L¡$V$gp `¡fy R>¡ ?

ei : b¡

bl¡_ : Ap Qpf fL$pbudp„ dmu_¡ Ly$g L¡$V$gp

`¡fy R>¡ ?

fdp : 2 + 2 + 2 + 2 A¡d kfhpmp¡ L$fuA¡

sp¡ ApW `¡fy R>¡.

bl¡_ : ^pfp¡ L¡$, Aphu ApW$ fL$pbu lp¡e sp¡ Ly$g L¡$V$gp `¡fy \pe ?

ei : sp¡ 2_¡ ApW$ hpf gB b^p_p¡ kfhpmp¡ L$fhp¡ `X$i¡. 2 + 2 + 2 + 2 +

2 + 2 + 2 + 2_p¡ kfhpmp¡ \pe 16. `Z Ap kfhpmp¡ L$fhpdp„ sp¡ OZp¡

kde gpÁep¡.

bl¡_ : Ap fus¡ AL¡ $S> k¿„ ep_¡ afu afu gC_¡ kfhpmp¡ L$fhp_p¡ lpe¡ , sp¡ OqX$ep

D`epN¡ u \pe R>.¡ Ap`Z¡ s¡ iuMui.„y sd¡ \pX¡ $p OqX$ep `pL$p L$fu gp.¡ TV$`V$

kfhpmp¡ L$fu iL$ip.¡ rQÓp¡ `f\u OqX$ep L$¡hu fus¡ se¥ pf \pe R>,¡ s¡ Å.¡

rQÓp¡ Å¡ A_¡ NZu_¡ gM.

1)

  + + + +   = 
2)

      +    +     = 
3)

  +    = 

6699

4)

     +     +     +    = 
5)

      +     +     = 
6)

     +     +     +     = 

Qpgp¡ fduA¡ :

1)  L¡$V$gu fL$pbu R>¡ ?

 A¡L$ fL$pbudp„ L¡$V$gp k„sfp„ ?

 Ly$g L¡$V$gp k„sfp„ ?

 4 hpf ÓZ A¡V$g¡ 3 + 3 + 3 + 3 = 12

2) bpNdp„ Nygpb_p fp¡` lpfbÝ^ hpìep R>¡.

 Ly$g lpf L¡$V$gu ?

 A¡L$ lpfdp„ L¡$V$gp fp¡` ?

 Ly$g L¡$V$gp fp¡` ?

 A¡V$g¡ 3 + 3 + 3 + 3 + 3 =

A¡V$g¡ `p„Q hpf ÓZ gB_¡ L$f¡gp¡ kfhpmp¡

A¡_¡ Ap`Z¡ 3 × 5 = 15 A¡d gMuiy„. s¡_„y

hp„Q_ "ÓZ NyÎep `p„Q bfpbf 15' A¡d

L$fuiy„.

"×' Ap rQŒ NyZpL$pf dpV¡$ h`fpe R>¡.

A¡L$ S> k„¿ep_¡ afu afu gC kfhpmp¡ L$fuA¡ sp¡ s¡ k„¿ep_p¡ OqX$ep¡

s¥epf \pe R>¡.

70

OqX$ep s¥epf L$fuA¡

2_p¡ OqX$ep¡ :

2 × 1 b¡ A¡L$ hpf 2 b¡ A¡L$p b¡
2 × 2 b¡ b¡ hpf 4 b¡ vy$ Qpf
2 × 3 b¡ ÓZ hpf 6 b¡ sfu R>
2 × 4 b¡ Qpf hpf 8 b¡ Qp¡L$ ApW
2 × 5 b¡ `p„Q hpf 10 b¡ `„Qp v$k
2 × 6 b¡ R> hpf 12 b¡ R>„N bpf
2 × 7 b¡ kps hpf 14 b¡ ksp Qp¥v
2 × 8 b¡ ApW$ hpf 16 b¡ AW$p kp¡m
2 × 9 b¡ _h hpf 18 b¡ _hp AY$pf
2 × 10 b¡ v$k hpf 20 b¡ v$p_ huk

71

3_p¡ OqX$ep¡ :

3×1 ÓZ, 3 ÓZ A¡$L$p ÓZ ÓZ A¡$L$p ÓZ
A¡L$ hpf

3×2 ÓZ, 6 ÓZ vy$ R> ÓZ vy$ R>
b¡ hpf

3×3 ÓZ, 9 ÓZ sfu _h ÓZ sfu _h
ÓZ hpf

3×4 ÓZ, 12 ÓZ Qp¡L$ bpf ÓZ Qp¡L$ bpf
Qpf hpf

3×5 ÓZ, 15 ÓZ `„Qp `„v$f ÓZ `„Qp `„v$f
`p„Q hpf

3×6 ÓZ, R> 18 ÓZ R>„N ÓZ R>„N
hpf AY$pf AY$pf

3×7 ÓZ, 21 ÓZ ksp ÓZ ksp
kps hpf huk A¡L$ A¡L$huk

3×8 ÓZ, 24 ÓZ AW$p ÓZ AW$p
ApW$ hpf huk Qpf Qp¡huk

3×9 ÓZ, 27 ÓZ _hp ÓZ _hp
_h hpf huk kps kÑphuk

3 × 10 ÓZ, 30 ÓZ v$p_ Óuk ÓZ v$p_ Óuk
v$k hpf

hp„Q_ L$fsu hMs¡ "ÓZ ksp huk A¡L$' A_¡ ÓZ ksp A¡L$huk' Ap `¥L$u A¡L$ S>
hp„Q_ A`¡rns R>¡.

huk A¡L$, huk kps A¡ fus¡ hp„Q_ h^y kpfy„ fl¡i¡ L$pfZL¡$ s¡ fus¡ gMhy„ `Z h^y
kfm R>¡.

Ap fus¡ 4_p¡ OqX$ep¡ `Z kfmsp\u s¥epf L$fu iL$pi¡.

72

ei : ApS>¡ lz„ TpX$ `f\u Qpf `¡fy sp¡X$u gpìep¡ Ry>„. 4 _p¡ OqX$ep¡
fdp : Ap`Z¡ s¡_p¡ D`ep¡N L$fu_¡ 4_p¡ OqX$ep¡ s¥epf L$fuA¡. 4×1= 4
ei : aL$s Qpf `¡fy hp`fu_¡ 4_p¡ ApMp¡ OqX$ep¡ s¥epf L$fuiy„? 4×2=
4×3=
s¡ dpV¡$ h^y `¡fy _l] Å¡CA¡?
bl¡_ : h^pf¡ `¡fy_u S>ê$f _\u. Ap`Z¡ b^p„ c¡Np„ dmu_¡ Ap

OqX$ep¡ s¥epf L$fuiy„. Ap `¡fy A¡L$ lpfdp„ fpMuA¡. ei, 4 × 4 =

sy„ Ap `¡fy_¡ A¡L$ hpf NZ. `R>u 4 × 1 = 4 "Qpf A¡Ly$ 4 × 5 =
Qpf' A¡ guV$u gM.

4×6=

(ei¡ s¡d L$ey¯.) 4×7=

bl¡_ : lh¡ fdp sy„ ApS> `¡fy_¡ buÆ hpf NZ, `Z 4 `R>u 4 × 8 =
NZ. (fdpA¡ `p„Q, R>, kps, ApW$ A¡d NÎep A_¡
OqX$ep_u buÆ guV$u gMu. 4 × 2 = 8 "Qpf vy$ ApW$'.) 4×9=

fdp : lh¡ ei sy„ ApNm_u guV$u s¥epf L$f. 4 × 10 =

(`R>u ei¡ s¡S> `¡fy_¡ ApW$ `R>u ÓuÆ hpf NÎep. 10 _p¡ OqX$ep¡
4 × 3 = 12 "Qpf sfu bpf' A¡ guV$u gMu.) 10 × 1 = 10
ei : lh¡ d_¡ kdÅey„ L¡$ dpÓ Qpf `¡fy afu afu_¡ NZu_¡

4_p¡ OqX$ep¡ L¡$hu fus¡ s¥epf L$fpe. ApNm_p¡ OqX$ep¡ 10 × 2 =

lz„ S> s¥epf L$fui. 10 × 3 =
fdp : v$k_p¡ OqX$ep¡ s¥epf L$fhp¡ sp¡ h^y kfm R>¡ ! s¡_p 10 × 4 =

dpV¡$ NZhy„ `Z `X$i¡ _l].

bl¡_ : lp ! L$pfZ L¡$ 10_p¡ A¡L$ v$iL$ lp¡e R>¡ s¡ Ap`Z¡ 10 × 5 =

ÅZuA¡ R>uA¡. 10 × 6 =
10 × 7 =
A¡L$ v$iL$ = 10 A¡V$g¡ L¡$ 10 × 1 = 10, "v$k A¡L$p 10 × 8 =
v$k'

b¡ v$iL$ = 20 A¡V$g¡ 10 × 2 = 20, "v$k vy$ huk'
A¡d L$fsp„ L$fsp„ v$k v$iL$ = 100
10 × 9 =

A¡V$g¡ 10 × 10 = 100, "v$k v$p_ kp¡.' 10 × 10 =

73

5_p¡ OqX$ep¡ s¥epf L$f. s¡_p dpV¡$ 5 spfp A\hp 5 awg_p rQÓp¡ v$p¡f.

A¡L$ hpf NZu_¡ 5 5
b¡$ hpf NZu_¡ 5+5 10
ÓZ hpf NZu_¡ 10 + 5 15
15 + 5 20

R> hpf NZu_¡ 25 + 5 30

\p¡X$u Nçds :

A¡L$ Ecu lfp¡mdp„ 3 A¡L$ ApX$u lpfp¡mdp„ 4
Ly„$X$p, A¡hu 4 Ecu Ly„$X$p, A¡hu 3 ApX$u lpf
lfp¡m. Ly$g Ly„$X$p 12
A¡V$g¡ L¡$, 4 hpf 3 = Ly$g 12 Ly„$X$p
A¡V$g¡ L¡$, 3 hpf 4 =
3 × 4 = 12
4 × 3 = 12

Nçds R>¡ _¡ ! fdpA¡ NÎep sp¡ `Z 12 Ly„$X$p. ei¡ NÎep sp¡ `Z 12 Ly„$X$p. A¡V$g¡
4 hpf 3 L¡$ 3 hpf 4 gBA¡ sp¡ `Z S>hpb 12 S> Aph¡.

fdp A_¡ ei_u S>¡d, 3 × 8 = 8 × 3 A¡ rQÓ v$p¡fu_¡ QL$pku
Å¡.

74

2×1 =2 OqX$ep 4×1 =4
2×2 =4 3×1 =3 4×2 =8
2×3 =6 3×2 =6 4×3 = 12
2×4 =8 3×3 =9 4×4 = 16
2×5 = 10 3 × 4 = 12 4×5 = 20
2×6 = 12 3 × 5 = 15 4×6 = 24
2×7 = 14 3 × 6 = 18 4×7 = 28
2×8 = 16 3 × 7 = 21 4×8 = 32
2×9 = 18 3 × 8 = 24 4×9 = 36
2 × 10 = 20 3 × 9 = 27 4 × 10 = 40
3 × 10 = 30

5×1 =5 10 × 1 = 10
5×2 = 10 10 × 2 = 20
5×3 = 15 10 × 3 = 30
5×4 = 20 10 × 4 = 40
5×5 = 25 10 × 5 = 50
5×6 = 30 10 × 6 = 60
5×7 = 35 10 × 7 = 70
5×8 = 40 10 × 8 = 80
5×9 = 45 10 × 8 = 90
5 × 10 = 50 10 × 10 = 100

75

hpspd® p„ NZy pL$pf

ei_p Of¡ fdp A_¡ buÅ `p„Q rdÓp¡ fdhp A¡L$W$p \ep lsp. Ly$g ....... bpmL$p¡
lsp. Npddp„\u ei_p kyf¡idpdp Apìep lsp, s¡dZ¡ bpmL$p¡_¡ N°uL$fpÅ_p¡ dyNV$
b_phsp iuMìey„.

L$pX®$ `¡`f_u `Ë$uAp¡ gC s¡_p `f hp„L$u
Q|„L$u f¡MpAp¡ v$p¡fu.

hp„L$u Q|„L$u f¡Mp L$p`u_¡ b¡ cpN L$ep®.

`R>u bpmL$p¡A¡ A¡L$ A¡L$ cpN `f C[ÃR>s
rQÓ v$p¡fu s¡dp„ f„N `|ep®.
`R>u kyf¡idpdpA¡ õV¡$`g `u_ gNphu dyNV$ b_phu Apàep.

A¡L$ `Ë$udp„\u b¡ dyNV$ s¥epf \pe sp¡ Ly$g L¡$V$gu `Ë$uAp¡_u S>ê$f `X$u ?
v$f¡L$ bpmL$p¡A¡ dyNV$ `l¡fu gu^p. h^¡gp¡ dyNV$ dpdp_p dp\p `f d|¼ep¡.

fdpA¡ L$üy„, ""Ap`Z¡ Np¡m QL$suAp¡ hX¡$ Ap`Zu Ap„Nmu `f b¡k¡
A¡hu _p_u V$p¡`uAp¡ s¥epf L$fu, Ðepf¡ A¡L$ QL$sudp„\u ÓZ V$p¡`uAp¡
s¥epf \C. lh¡ v$f¡L$ S>Z_p A¡L$ lp\_u Ap„NmuAp¡ dpV$¡ V$p¡`u s¥epf
L$fuA¡ sp¡ kps bpmL$p¡_p Ap„Nmp dpV¡$ L¡$V$gu V$p¡`uAp¡ Å¡Ci¡ ? ei¡
L$üy„, ""kl¡gy„ R>¡. L$pfZL¡$ Ap`Z_¡ `p„Q_p¡ OqX$ep¡ AphX¡$ R>¡.''

s¡V$gu _p_u V$p¡`uAp¡ s¥epf L$fhp dpV¡$ L¡$V$gu Np¡m QL$suAp¡
Å¡Ci¡ s¡ L$l¡.

7766

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प्रकाशने.

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विभागीय भांडारे संपरक् क्रमांक : पणु े -  २५६५९४६५, कोल्हापूर-  २४६८५७६, मुंबई (गोरेगाव)
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