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Published by baviskards9, 2018-11-19 06:39:20

तिसरी गणित

तिसरी गणित

Keywords: तिसरी गणित

39.00



{ejU ImË`mMm _§Owar H«$_m§H$ : àm{eg§/2014 - 15/2101/ _§Owar/S-505/757, {XZm§H$ 4.2.2014

‘hmamîQ´> amÁ¶ nmR>çnwñVH$ {Z{‘©Vr d Aä¶mgH«$‘ g§emoYZ ‘§S>i, nwUo 411 004.

A

àW_md¥ËVr : 2014 © _hmamîQ>´ amÁ` nmR>çnñw VH$ {Z{_V© r d Aä`mgH«$_ g§emoYZ _S§ >i,
nwU o - 411 004.

_hmamîQ´> amÁ` nmR>çnñw VH$ {Z{_V© r d Aä`mgH«$_ g§emYo Z _§S>imH$S>o
`m nñw VH$mMo gd© hŠH$ amhVrb. `m nwñVH$mVrb H$moUVmhr ^mJ gM§ mbH$,
_hmamîQ>´ amÁ` nmR>çnwñVH$ {Z{_©Vr d Aä`mgH«$_ ge§ moYZ _S§ >i `m§À`m bIo r
nadmZJr{edm` CX²YV¥ H$aVm `Uo ma Zmhr.

J{UV {df` g{_Vr à_Iw g`§ mOo H$ : dgV§ Zm. edo mio
{dXçmg{Md, ^mfVo a
S>m.° e{eH$mV§ A. H$mÌo (AÜ`j) nmR>çnñw VH$ _S§ >i, nUw .o
S>m.° lr_Vr _J§ bm ZmairH$a (gXñ`) g`§ mOo Z ghm`H$ : CÁÁdbm lrH$mV§ JmSo >~mbo o
S>m.° {dZm`H$ _m. gmbo mnay H$a (gXñ`) {df` ghm`H$, J{UV
S>m.° gm.¡ dO¡ `V§ m nmQ>rb (gXñ`) nmR>çnñw VH$ _S§ >i, nUw .o
S>m.° H$o . g~w _« Ê`_ (gXñ`) _Iw nî¥ R> d gOmdQ> : AZKm BZm‘Xma
lr. amOÐ| Jmgo mdr (gXñ`)
lr. à_mXo V.w IM} (gXñ`) H$oOb {‘ñÌr
lr_Vr _J§ b ndma (gXñ`) H$«mn° _mŠg© {S>PmBZ, nUw .o
lr. dgV§ Zm. edo mio (gXñ`$- g{Md)
gX§ rn H$mio r, _~§w B©

J{UV {df` H$m`J© Q gXñ`> {Z{_V© r : gpÀMVmZX§ Am\$io
_»w ` {Z{_V© r A{YH$mar
S>m°. E_. E_. {eH$mao gO§ ` H$m~§ io
S>m°. H¡$bmg ~m|XmS>} {Z{_V© r A{YH$mar
S>m°. O`lr AÌo àemV§ haUo
S>m°. A{Zb d¡Xç {Z{_V© r ghm`H$
lr. ho_§V Xoenm§S>o AjaOiw Ur : J{UV {d^mJ,
lr. ZmJoe _moZo nmR>çnñw VH$ _S§ >i, nUw .o
lr. adtÐ `odbo H$mJX : 70 Or.Eg.E_. _°n{bWmo
lr. nwéfmoËV_ e_m© _Ðw UmXeo  :
lr. gwaoe qeXo
Hw$. ^maVr VmR>o _Ðw H$ :
lr. H$ë`mU qeXo
lr. àXrn JmoS>go àH$meH$
lr. gwYra ZmMUo
lr. amOoe d¡amJS>o {ddHo $ CËV_ Jmgo mdr, {Z`̧ H$
gm¡. d¡embr nmQ>rb nmR>çnñw VH$ {Z{_V© r _S§ >i,
lr. _méVr ~mañH$a à^mXdo r, _~§w B-© 25.

B

C

amîQ´>JrV
OZJU_Z-A{YZm`H$ O` ho

^maV-^m½`{dYmVm &
n§Om~, {g§Yw, JwOamV, _amR>m,
Ðm{dS>, CËH$b, ~§J,
{d§Ü`, {h_mMb, `_wZm, J§Jm,
CÀN>b Ob{YVa§J,
Vd ew^ Zm_o OmJo, Vd ew^ Am{eg _mJo,
Jmho Vd O`JmWm,
OZJU _§JbXm`H$ O` ho,
^maV-^m½`{dYmVm &
O` ho, O` ho, O` ho,
O` O` O`, O` ho &&

D

à{Vkm

^maV _mPm Xoe Amho. gmao ^maVr` _mPo ~m§Yd AmhoV.
_mÂ`m Xoemda _mPo ào_ Amho. _mÂ`m XoemVë`m g_¥X²Y Am{U
{d{dYVoZo ZQ>boë`m na§nam§Mm _bm A{^_mZ Amho. Ë`m na§nam§Mm
nmB©H$ hmoÊ`mMr nmÌVm _mÂ`m A§Jr `mdr åhUyZ _r gX¡d à`ËZ
H$arZ.
_r _mÂ`m nmbH$m§Mm, JwéOZm§Mm Am{U dS>rbYmè`m _mUgm§Mm
_mZ R>odrZ Am{U àË`oH$mer gm¡OÝ`mZo dmJoZ.
_mPm Xoe Am{U _mPo Xoe~m§Yd `m§À`mer {ZîR>m amIÊ`mMr
_r à{Vkm H$arV Amho. Ë`m§Mo H$ë`mU Am{U Ë`m§Mr g_¥X²Yr
hçm§VM _mPo gm¡»` gm_mdbo Amho.

E

àñVmdZm

"~mbH$m§À`m _mo\$V d gŠVrÀ`m {ejUmMm A{YH$ma A{Y{Z`_ - 2009' Am{U "amîQ´>r` Aä`mgH«$_
AmamIS>m - 2005' S>moiçm§g_moa R>odyZ _hmamîQ´> amÁ`mV "àmW{_H$ {ejU Aä`mgH«$_ - 2012 ' V`ma H$aÊ`mV
Ambm. `m emgZ_mÝ` Aä`mgH«$_mda AmYm[aV J{UV B`ËVm n{hbr Vo B`ËVm AmR>drÀ`m nmR>çnwñVH$m§Mr ZdrZ
_mbm 2013-2014 `m embo` dfm©nmgyZ Q>ßß`mQ>ßß`mZo nmR>çnwñVH$ _§S>i àH$m{eV H$aV Amho. `m _mboVrb
J{UV B`ËVm {VgarMo ho nmR>çnwñVH$ Amnë`m hmVr XoVmZm Amåhm§bm {deof AmZ§X dmQ>Vmo.

gd© AÜ``Z-AÜ`mnZ à{H$« `m ~mbH$| {ÐV Agmdr, H¥${VàYmZVm d kmZaMZmdmXmda ^a {Xbm Omdm,
àmW{_H$ {ejUmÀ`m AIoarg {dXçmÏ`m©Zo {H$_mZ j_Vm àmßV H$amì`m, VgoM {ejUmMr à{H«$`m a§OH$ Am{U
AmZ§XXm`r ìhmdr, hm ÑpîQ>H$moZ g_moa R>odyZ `m nwñVH$mMr aMZm H$aÊ`mV Ambr Amho.

{dXçm϶mª‘ܶo {ZgJ©V: Agbobr {MÌm§Mr AmdS> Am{U ñdV: H$mhrVar H$aÊ`mMr YS>nS> bjmV KoD$Z ho
nwñVH$ {MÌê$n Am{U H¥${VàYmZ R>odÊ`mMm à`ËZ Ho$bm Amho. {MÌo eŠ`Vmo ~mobH$s Am{U J{UVmVrb g§H$ënZm
ñnîQ> H$aÊ`mg gmhmæ`^yV R>aVrb Aer AmhoV.

J{UV g§~moYm§Mr COiUr ìhmdr, Ë`m§Mo {ñWarH$aU ìhmdo, ñd`§-AÜ``Z gwb^ ìhmdo åhUyZ nwñVH$mV
loUr~X²Y (Graded) "ñdmÜ`m`' Am{U "g§dmXm§Mm' g_mdoe H$aÊ`mV Ambm Amho. ñdmÜ`m`m§_Yrb àíZ
{dXçmÏ`mªZr ñdà¶ËZmZo gmoS>dmdo Aer Anojm Amho. ñdmÜ`m` H$§ Q>midmUo hmDo $ Z`Vo `mgmR>r Ë`m§_Ü`o {d{dYVm
AmUÊ`mMm à`ËZ H$o bm Amh.o

àË`oH$ nmR>mÀ`m g§X^m©V {ejH$m§Zr Or ^mfm {dXçmÏ`mªg_moa _m§S>mdr Aer Anojm Amho, Vr
nmR>çnwñVH$mV {Xbr Amho; VgoM {ejH$m§gmR>r doJiçm gyMZm H$mhr n¥îR>m§da {Xë`m AmhoV. AÜ`mnZ OmñVrV
OmñV H¥${VàYmZ ìhmdo `mgmR>r gyMZm d CnH«$_ XoÊ`mV Ambo AmhoV.

ho nmR>çnwñVH$ OmñVrV OmñV {ZXm}f d XO}Xma ìhmdo, `m ÑîQ>rZo _hmamîQ´>mÀ`m gd© ^mJm§Vrb {ZdS>H$
{ejH$, VgoM H$mhr {ejUVÁk d {df`VÁk `m§À`mH$Sy>Z `m nwñVH$mMo g_rjU H$ê$Z KoÊ`mV Ambo Amho.
{ejH$, nmbH$ `m§À`mH$Sy>Z Ambobr nÌo, d¥ËVnÌm§VyZ N>mnyZ Ambobr Q>r>H$mË_H$ narjUo `m§Vrb gyMZm§Mm
{dMma ho nmR>çnwñVH$ V`ma H$aVmZm Ho$bm Amho. `m gdmªZr {Xboë`m ghH$m`m©~X²Xb _§S>i Ë`m§Mo Am^mar Amho.
Amboë`m gyMZm d A{^àm` `m§Mm J{UV {df` g{_VrZo `mo½` Vmo {dMma H$ê$Z `m nwñVH$mbm A§{V_ ñdê$n
{Xbo Amho.

_§S>imMr J{UV {df` g{_Vr, H$m`©JQ>, lr. {d. {X. JmoS>~mobo ({Z_§{ÌV) d {MÌH$ma `m§À`m
AmñWmnyd©H$ n[al_m§VyZ ho nwñVH$ V`ma Pmbo Amho. _§S>i `m gdmªMo _Z:nyd©H$ Am^mar Amho.

{dXçmWu, {ejH$ d nmbH$ `m nwñVH$mMo ñdmJV H$aVrb Aer Amem Amho.

nwUo (M§. am. ~moaH$a)
{XZm§H$ : 4 {S>g|~a, 2013 g§MmbH$

13 AJ«hm`U>, 1935 _hmamîQ´> amÁ` nmR>çnwñVH$ {Z{_©Vr d

Aä`mgH«$_ g§emoYZ _§S>i, nwUo.

F

F {ejH$m§er {hVJwO F

o nmR>çnwñVH$ ho `m ñVamdarb AÜ``Z-AÜ`mnZ à{H«$`oVrb A{Ve` _hËËMmMo gmYZ Amho.
AmnUm§g Amnë`m n[agamVrb {d{dY AZw^d d {dXçm϶mªMo ñdV:Mo AZw^d ¶m§Mm Cn¶moJ H$ê$Z
AܶmnZ H$aVm `mdo `mÑîQ>rZo `m nmR>çnwñVH$mMr aMZm Ho$br Amho. Ë`mV {Xboë`m nwT>rb ~m~tMm
AmdOy©Z Cn`moJ H$amdm.

o Ioi, JmUr, JmoîQ>r, àm˶{jH$, CnH«$‘ B˶mXtÀ¶m gmhmæ¶mZo J{UVmVrb g§H$ënZm, g§~moY ñnîQ>
H$amdo.

o àm˶{jH$m§Mm A{YH$m{YH$ dmna H$ê$Z J{UV {df¶mMo AܶmnZ H$amdo.
o {MÌ{ZarjU, ‘{U‘mim§Mm dmna ¶m§gma»¶m {d{dY CnH«$‘m§VyZ ‘Zmoa§OH$Vm dmT>dmdr.
o {dXçmWu ñdV: H$go {eHy$ eH$Vrb, ˶m§Zm ‘mhrV Agboë¶m ‘m{hVrMm Cn¶moJ H$ê$Z, ˶m§Zm

{eH$ʶmgmR>r H$er ‘XV H$aVm ¶oB©b ¶m ÑîQ>rZo AܶmnZ H$amdo. ˶mgmR>r {MÌH$mS>©, g§»¶mH$mS>©,
‘{U‘mim Ago {d{dY e¡j{UH$ gm{h˶ dmnamdo.
o AܶmnZ H$aVmZm XeH$mMo JQ> H$aUo, gwQ>o H$aUo ¶m§gma»¶m H¥$Vr à˶j H$ê$Z ¿¶mì¶m.
o ~oarO-dOm~mH$s ¶m§gma»¶m g§»¶m§darb {H«$¶m ‘Ur, IS>o, {~¶m B˶mXtÀ¶m gmhmæ¶mZo H$ê$Z ¿¶mì¶m.
o gmYmaUV: XaamoO EH$m n¥îR>mdarb nmR>çm§emÀ`m g§X^m©Zo AÜ``Z-AZw^d XçmdoV.
o n¥îR>mdarb nmR>çm§emÀ¶m g§X^m©Zo {dXçm϶mªer àíZmoËVaê$nmZo MMm© H$amdr. e¡j{UH$ gm{h˶mÀ¶m
‘XVrZo Aܶ¶Z-AZw^d Xçmdo.
o g§~§{YV n¥îR>mdarb H¥$Vt~m~V {dXçm϶mªer MMm© H$amdr / ñnîQ>rH$aU Xçmdo / ñnîQ> gyMZm Xçmì¶m.
o {dXçm϶mªZm nopÝgbrZo H¥$Vr H$aʶmg gm§Jmdo. H¥$Vr nyU© H$aʶmgmR>r Amdí¶H$ dmQ>ë¶mg JQ>mVrb
ghH$mè¶m§er MMm© H$aʶm~m~V gyMZm Xçmdr.
o {dXçmWu H¥$Vr H$aV AgVmZm {ejH$m§Zr JQ>mJQ>m§V {\$ê$Z H¥$VrMo {ZarjU H$amdo. Amdí`H$ VoWo
_mJ©Xe©Z H$amdo.
o {dXçmÏ`mªZr H¥$Vr nyU© Ho$ë`mZ§Va à˶oH$mÀ¶m H$m¶m©Mr nmhUr H$amdr. AmT>iboë¶m MwH$m, C{Udm,
ÌwQ>t~m~V MMm© H$ê$Z ˶m XþéñV H$ê$Z ¿¶mì¶m.
o n¥îR>mda {Xboë¶m CnH«$‘m§À¶m ‘XVrZo gamd H$ê$Z ¿¶mdm.
o JaOoZwgma nyaH$ CnH«$‘ / gm{h˶ ¶m§À¶m ‘XVrZo gamd ¿¶mdm.
o Xþgè¶m {Xder AmYrÀ¶m n¥îR>mdarb nmR>çm§emÀ¶m g§X^m©Vrb àíZ {dMmê$Z nmR>çm§emMo AmH$bZ
Pmë¶mMr ImÌr H$amdr.
o AYyZ‘YyZ ‘mJo nyU© Pmboë¶m nmR>çm§emda AmYm[aV {dMmaàdV©H$ àíZ {dMmê$Z CËVao Xoʶmg
{dXçm϶mªZm àd¥ËV H$amdo.
o AS>MUt~m~V àíZ {dMmaʶmg {dXçm϶mªZm àd¥ËV H$amdo. àíZ {dMmaʶmMr gd¶ {dH${gV H$amdr.
o g§»¶m§Mo dmMZ-boIZ, VgoM ‘ZmVë¶m ‘ZmV ~oarO-dOm~mH$s H$aʶmMr j‘Vm {dH${gV H$aʶmÀ¶m
ÑîQ>rZo gmV˶mZo à¶ËZ H$amdo.
o diUXma A§H$boIZ VgoM CXmhaUm§Mr ‘m§S>Ur hr H$m¡eë¶o {dH${gV hmoVrb ¶m ÑîQ>rZo à¶ËZ H$amdo.

G

AZwH«$_{UH$m

{d^mJ n{hbm

B ^m¡{_{VH$ AmH¥$Ë`m§Mr AmoiI ....................................... 1 Vo 4
B g§»¶mkmZ ................................................................5 Vo 18
B ~oarO : {~ZhmV˦mMr ...............................................1 9 Vo 21
B dOm~mH$s : {~ZhmV˦mMr ..........................................2 2 d 23
B JwUmH$ma ...............................................................2 4 Vo 32
B ZmUr d ZmoQ>m ........................................................3 3 d 34
B ‘mnZ ...................................................................3 5 Vo 42

{d^mJ Xþgam

B AmH¥${V~§Y .............................................................4 3 Vo 46
B g‘{‘Vr ................................................................4 7 Vo 49
B ~oarO : hmV˦mMr ....................................................5 0 Vo 54
B dOm~mH$s : hmV˦mMr ................................................5 5 Vo 60

B JwUmH$ma ................................................................6 1 Vo 66
B ^mJmH$ma ................................................................6 7 Vo 73
B H$mb‘mnZ ...............................................................7 4 d 75
B {XZX{e©H$m ..............................................................7 6 d 77
B AnyUmªH$ ................................................................7 8 Vo 83
B ‘m{hVrMo ì¶dñWmnZ ..................................................8 4 Vo 88

H

{d^mJ n{hbm

^m¡{_{VH$ AmH¥$Ë`m§Mr AmoiI   

COiUr

n Mm¡H$moZ, {ÌH$moU, dVw©i

{d{dY Mm¡H$moZ {d{dY {ÌH$moU dVw©io

F Imbrb {MÌo nmhÿZ ˶mVrb ^m¡{‘{VH$ AmH¥$Ë`m AmoiIm d H$mT>m. Ë`m§Mr Zmdo {bhm.

{MÌo

AmH¥$Vr Am¶V
AmH¥$VrMo Zmd

F darb {MÌmVrb {ÌH$moU, dVw©io, Mm¡H$moZ AmoiIm. {ÌH$moU bmb, Mm¡H$moZ {Ziçm d dVw©io
{ndiçm a§JmZo a§Jdm.

- {ejH$m§gmR>r : nwR²>R>çmMo da {Xbobo d BVahr AZoH$ doJdoJio AmH$ma H$mnyZ Q>o~bmda R>odmdo. ˶m§Mo {ÌH$moU, Am`V,
Mm¡ag d dVw©i Ago dJuH$aU H$ê$Z ¿`mdo. `m§n¡H$s H$mhr AmH$mam§Mo darb àH$mam§V dJuH$aU hmoUma
Zmhr, ho {dXçmÏ`mªÀ¶m bjmV AmUyZ Xçmdo.

1

H$S>m d H$monao

~\$s©Mm VwH$S>m nmhm.
~\$uMm VwH$S>m Mm¡H$moZr Amho.
Mm¡H$moZmbm Mma H$S>m d Mma H$monao AgVmV.

Q>o~bmÀ`m n¥îR>^mJmMo {ZarjU H$am.
F Q>o~bmÀ`m n¥îR>^mJmbm {H$Vr H$S>m AmhoV ?
F Q>o~bmÀ`m n¥îR>^mJmbm {H$Vr H$monao AmhoV ?
F Q>o~bmÀ`m n¥îR>^mJmMm AmH$ma H$moUVm ?

n Am`V


eoOmar XmIdë¶mà‘mUo EH$ Am¶VmH$ma H$mJX ¿`m.
F Am¶Vmbm H$S>m {H$Vr d H$monao {H$Vr ?

AmVm g_moamg_moarb H$S>m EH$_oH$s¨er OmoS>Ê`mgmR>r H$mJXmbm Aer
_Ymo_Y KS>r Kmby.

nmhm ! OmñV bm§~rMr H$S> g_moaÀ`m H$S>oer V§VmoV§V OwiVo.

H$_r bm§~rMr H$S> g_moaÀ`m H$S>oer V§VmoV§V OwiVo.

Am`VmÀ`m g_moamg_moaÀ`m H$S>m g_mZ bm§~rÀ`m AgVmV.

n Mm¡ag

é_mbmMo {ZarjU H$ê$.
hm Mm¡ag Amho.

F Mm¡agmbm H$S>m d H$monao {H$Vr ?

é‘mbmMr AmS>dr d C^r KS>r KmbyZ g‘moamg‘moaÀ¶m H$S>m
g‘mZ bm§~rÀ¶m AmhoV H$m Vo nmhm.

AmVm é_mbmMo g_moamg_moarb H$monao EH$_oH$m§er OwiVmV H$m,
ho nmhʶmgmR>r Aer KS>r Kmby.

H$monao OwiVmV d bJVÀ`m H$S>mhr EH$_oH$s§er OwiVmV.
AmVm é_mbmMr nwÝhm KS>r Kmbm. gd© H$S>m EH$‘oH$s¨er OwiVmV.

2

Mm¡agmÀ`m Mmahr H$S>m g_mZ bm§~rÀ`m AgVmV.
é‘mbmMr KS>r KmVë¶mda {ÌH$moU {‘imbm, ho bjmV ¿¶m.

n {ÌH$moU
F {ÌH$moUmbm H$S>m {H$Vr ? H$monao {H$Vr ?
n[agamV Amnë¶mbm hm AmH$ma Hw$R>o Hw$R>o {XgVmo, Vo emoYm.
H$mS>çm§Mm dmna H$ê$Z Imbrb AmH$ma V`ma H$am.
Mm¡H$moZ , Am`V , Mm¡ag , {ÌH$moU.

F Imbrb VŠVm nyU© H$am.

AmH¥$Vr AmH¥$VrMo Zmd H$S>m§Mr g§»`m H$monè`m§Mr g§»`m

- {ejH$m§gmR>r : a§JrV H$mJXmMo Am¶V, Mm¡ag, {ÌH$moU ¶m AmH$mam§Mo VwH$S>o H$mnyZ R>odmdo. ˶m§Mo JwUY‘© {dXçm϶mªZm
Vnmgʶmg gm§Jmdo. dVw©imMr H$S> hr dH«$mH$ma AgVo d dVw©imbm H$monao ZgVmV, ho {dXçm϶mªÀ¶m
bjmV AmUyZ Xçmdo.

3

n nmM VwH$S>çm§Mm Q>°ZJ«°_ V`ma H$aÊ`mMr nX²YV
EH$ Mm¡agmH¥$Vr H$mJX ¿`m.

Ë`m H$mJXmbm KS>çm KmbyZ Mm¡agmMm _Ü` emoYm. VgoM Mmahr 12 3
H$S>m§À¶m _Ü`q~Xÿ§da IwUm H$am. AmH¥$VrV XmIdë`mà_mUo aoKm 4
H$mTy>Z Mm¡agmMm _Ü` d H$S>m§Mo _Ü` OmoS>m. 5
AmH¥$VrV XmIdë¶mà‘mUo aoKm§da H$mnyZ nmM VwH$S>o V`ma H$am.
n eoOmarb Q>°ZJ«°_Mm Cn`moJ H$ê$Z Imbrb àíZm§Mr CËVao emoYm. 12
3
F Vw‘À¶m Q>°ZJ«°‘‘ܶo {H$Vr {ÌH$moU AmhoV ?
54
F gd© {ÌH$moU gmaIo AmhoV H$m ?

F XmoZ {ÌH$moU OmoSy>Z EH$ Mm¡ag V¶ma H$aVm ¶oB©b H$m ?

F XmoZ {ÌH$moU OmoSy>Z ‘moR>m {ÌH$moU V¶ma hmoB©b H$m ?

F ¶mV {H$Vr Mm¡ag AmhoV ? {H$Vr Mm¡H$moZ AmhoV ?

F {MÌmVrb {R>nŠ`m§À`m H$mJXmda H$mT>boë¶m AmH¥$Ë`m AmoiIm. Ë`m§n¡H$s {ÌH$moU bmb a§JmZo,
Mm¡ag {Ziçm a§JmZo d Am`V {haì`m a§JmZo a§Jdm.

- {ejH$m§gmR>r : {dXçmÏ`mªZm XmoarÀ¶m gmhmæ¶mZo dVw©i, Am`V, Mm¡ag, {ÌH$moU ho AmH$ma H$am¶bm gm§Jmdo.
doJdoJio Q>°ZJ«°‘ {‘idyZ ˶m§nmgyZ doJdoJiçm AmH¥$˶m V¶ma H$aʶmg {dXçm϶mªZm àmoËgmhZ Xçmdo.

4

g§»`mkmZ

F Imbrb gmaUrV 1 Vo 10 ¶m g§»`m§À¶m Mm¡H$Q>r bmb a§JmZo, 11 Vo 20 `m g§»`m§À¶m Mm¡H$Q>r
{haì`m a§JmZo, ..... `mà_mUo {d{dY a§Jm§Mm dmna H$ê$Z gd© Mm¡H$Q>r a§Jdm.

99 19 78 45 59 80 67 98 46 47

18 82 79 8 40 39 97 5 68 26

51 4 58 88 13 75 17 95 52 16

83 81 71 34 87 1 96 38 25 27

32 77 2 76 12 63 53 60 9 37

65 10 100 14 64 24 11 94 93 36

31 72 41 55 29 54 22 35 3 48

84 30 15 6 86 23 62 61 70 69

57 66 56 73 33 89 7 42 92 49

44 85 28 74 20 50 90 91 21 43

n 26 Vo 99 g§»`m§Mo Ajar boIZ
26 gìdrg 27 gËVmdrg 28 AR²>R>mdrg 29 EH$moUVrg 30 Vrg
31 EH$Vrg 32 ~ËVrg 33 VohVrg 34 Mm¡Vrg 35 nñVrg
36 N>ËVrg 37 gXVrg 38 AS>Vrg 39 EH$moUMmirg 40 Mmirg
41 EHo$Mmirg 42 ~oMmirg 43 ÌoMmirg 44 MìdoMmirg 45 n§MoMmirg
46 eohoMmirg 47 gËVoMmirg 48 AR²>R>oMmirg 49 EH$moUnÝZmg 50 nÝZmg
51 EH$mdÝZ 52 ~mdÝZ 53 ÌonÝZ 54 MmonÝZ 55 n§MmdÝZ
56 N>ßnÝZ 57 gËVmdÝZ 58 AR²>R>mdÝZ 59 EH$moUgmR> 60 gmR>
61 EH$gîQ> 62 ~mgîQ> 63 ÌogîQ> 64 Mm¡gîQ> 65 nmgîQ>
66 ghmgîQ> 67 gXþgîQ> 68 ASw>gîQ> 69 EH$moUgËVa 70 gËVa
71 EH$mhËVa 72 ~mhËVa 73 ͶmhËVa 74 Mm¡è¶mhËVa 75 n§MmhËVa
76 ehmËVa 77 gË˶mhËVa 78 AR²>R>çmhËVa 79 EH$moUE|er 80 E|oer
81 E³¶mE|er 82 ã¶mE|er 83 ͶmE|er 84 Mm¡è¶mE|er 85 n§MmE|er
86 ehmE|er 87 gË˶mE|er 88 AR²>R>çmE|er 89 EH$moUZìdX 90 ZìdX
91 E³¶mÊUd 92 ã¶mÊUd 93 ͶmÊUd 94 Mm¡è¶mÊUd 95 n§MmÊUd
96 ehmÊUd 97 gË˶mÊUd 98 AR²>R>çmÊUd 99 Zì¶mÊUd

- {ejH$m§gmR>r : \$aerda g§»`m {bhÿZ qH$dm g§»`mH$mS>} R>odyZ Ë`m^modVr {dXçmÏ`mªZm C^o H$ê$Z H«$_mZo g§»`m
emoYÊ`mMm Ioi ¿`mdm.

5

eVH$mMr AmoiI Z§Xy : _r EH$ eVH$ Ymdm H$mT>ë`m.
Q>moZr : `m e§^a Jmoiçm AmhoV.

gb_m : _r `m ~m§JS>çm _moOë`m. gmoZy : _r EH$ eoH$S>m åhUOoM
Ë`m 10 XeH$ AmhoV. 100 g§Ìr AmUbr.

VmB© : Vw‘Mo à˶oH$mMo åhUUo ~amo~a Amho. VrM g§»¶m à˶oH$mZo doJdoJiçm àH$mamZo
gm§{JVbr. eVH$ åhUOo e§^a EH$H$ qH$dm ZwgVo e§^a, Xhm XeH$ åhUOo e§^a, eoH$S>m
åhUOo e§^a Am{U EH$eo åhUOo XoIrb e§^a.

e

gmoZyZo `m _mioVrb 100 _Ur ~Q>ì`mV KmVbo. hm Pmbm eVH$mMm ~Q>dm.

XeH$ H$mS>çm
åhUOo 1 eVH$ H$mS>çm.

20 én¶m§À¶m 5 ZmoQ>m
ååhhUU OOoo 1 eVH$ éné`no.`o,


6

nyU© eVH$

9 _Ur Am{U 1 _Ur {_iyZ 10 _Ur.

10 dñVy§Mm g_yh åhUOo EH$ XeH$.

X E 99 hr XmoZ A§H$s gdmªV _moR>r g§»`m

9 9 Amho. {VÀ¶mV 1 {_idë¶mda 100

+ 1 hr VrZ A§H$s g§»`m V`ma Pmbr.

1 0 0

100 ¶m VrZ A§H$s g§»¶oV XeH$mÀ¶m S>mdrH$S>o ZdrZ ñWmZ eVH$mMo Amho.

100 åhUOo e X E 100 hr VrZ A§H$s g§»`m Amho.
1 0 0

e e XmoZeo e e e VrZeo

e e e e Mmaeo e e e e e nmMeo

e e e e e e e e e ZD$eo

X X X X X X X X X X 10 XeH$ åhUOo 1 eVH$
åhUOo EH$eo (100)

X X X X X X X X X X 20 XeH$ åhUOo 2 eVH$

X X X X X X X X X X åhUOo XmoZeo (200)

X X X X X X X X X X 40 XeH$ åhUOo 4 eVH$
X X X X X X X X X X åhUOo Mmaeo (400)
X X X X X X X X X X
50 XeH$ åhUOo 5 eVH$
XX X X X X XX XX åhUOo nmMeo (500)
X X X X X X X X X X 7

XX X X X X XX XX

X X X X X X X X X X
X X X X X X X X X X

XX X X X X XX XX

VrZ A§H$s g§»`m : AmoiI g§»¶m $
F [aH$må¶m Mm¡H$Q>tV g§»¶m Ajam§V {bhm.
eVH$ XeH$ EH$H$ A§H$m§V Ajar
ISy> boIZ boIZ

e 1 0 1 101 EH$eo EH

e 1 0 2 102 EH$eo XmoZ

e 1 0 3 103

e 1 0 4 104

e 1 0 5 105

e 1 0 6 106

e 1 0 7 107

e 1 0 8 108

e 1 0 9 109

e 1 1 0 110

- {ejH$m§gmR>r : 100 ISy>§Mm ~m°³g, 10 ISy>§Mo nmH$sQ> d gwQ>o ISy> ¶m§Mm Cn¶moJ H$ê$Z g§»¶m {b{hʶmg gm§Jmdo.

8

VrZ A§H$s g§»`m : AmoiI

F gmaUrV XmIdë¶mà‘mUo ‘{UVmam§‘ܶo ¶mo½¶ VodT>o ‘Ur Kmbm. g§»¶m A§H$m§V d Ajam§V
{bhm.

e e X XXX X 254 XmoZeo
e e e ee e X MmonÝZ
eX E
eX E 617 ghmeo
gVam

e e e e X XX eX E
eX E
e e e ee e e

X XXX

eeeee eee eX E
eX E
X XXXX XXX eX E
eX E
eeeee

XXX X
X XXXX e e e e
XX XXXXXXX

e

- {ejH$m§gmR>r : àË`oH$s 100 _Ur Agbobo ~Q>do, àË`oH$s 10 _Ur Agboë`m _mim d H$mhr gwQ>o _Ur KoD$Z
{dXçmÏ`mªZm 3 A§H$s g§»`m V`ma H$aʶmg Xçmì`m. ~Q>do, _mim, gwQ>o _Ur `m§À`m OmJm ~Xbë`m,
Var g§Ho$VmZwgma `mo½` arVrZo g§»`m {b{hÊ`mMm Iyn gamd ¿`mdm.

9

VrZ A§H$s g§»`m : boIZ d dmMZ
F Mm¡H$Q>tV `mo½` g§»`m ^am d g§»`m dmMm.

101 211 321 431 541 651 761 871 981

102 212 432 652 762 872 982

103 213 323 543

104 214 434 544 764 874

105 325 435 655 875 985

216 766

107 217 327 437 547 657 877

328 438 768 988
109 219 659

110 220 330 440 550 770 880 990

F {Xboë¶m A§H$m§À¶m g‘yhmVrb àË`oH$ A§H$ EH$XmM dmnê$Z VrZ A§H$s g§»`m V`ma H$am.

1 123, 132, 213, 231, 312, 321
2 3

3
305, 350, 530, 503
05
035, 053 `m VrZ A§H$s g§»`m ZmhrV ho bjmV ¿`m, H$maU ˶m g§»¶m XmoZM A§H$

dmnê$Z 35, 53 Aem {b{hVmV. 4 3
61

7 8 A§H$s g§»`m ¿`6m. 2 9 5 ~XbyZ ZdrZ 0 7 H$am,
H$moUVrhr VrZ Ë`mVrb eVH$ñWmZMm A§H$ g§»`m V`ma
VgoM XeH$ d EH$H$ñWmZMo A§H$ ~XbyZ ZdrZ g§»`m V`ma H$am.

- {ejH$m§gmR>r : Wmn åhUOo eVH$, Q>mir åhUOo XeH$, MwQ>H$s åhUOo EH$H$ Ago g‘OyZ g§»`m V`ma H$amì`m.

10

_mJMr g§»`m, nwT>Mr g§»`m

F Imbrb g§»`mnQ²>Q>çm§Vrb g§»`m dmMm.

99 100 101 102 103 104 105 106 107 108 109 110


215 216 217 218 219 220 221 222 223 224 225 226

399 400 401 402 403 404 405 406 407 408 409 410

F darb g§»`mnQ²>Q>çm§À`m _XVrZo bJVMr nwT>Mr g§»`m {bhm.

D 105, D 220, D 409, D 219,

F darb g§»`mnQ²>Q>çm§À`m _XVrZo bJVMr _mJMr g§»`m {bhm.

D , 400 D , 107 D , 218 D , 110

F darb g§»`mnQ²>Q>çm§À`m _XVrZo bJVMr _mJMr d bJVMr nwT>Mr g§»`m {bhm.

D , 217 , D , 100 , D , 409 ,

F {Xboë`m g§»`oÀ¶m bJVMr nwT>Mr g§»`m Ë`m g§»`onojm {H$VrZo _moR>r AgVo ?

F {Xboë`m g§»`oÀ¶m bJVMr ‘mJMr g§»`m Ë`m g§»`onojm {H$VrZo bhmZ AgVo ?

F 435 ‘ܶo 1 {‘idyZ `oUmar g§»¶m H$moUVr ?

F 435 _YyZ 1 H$‘r H$ê$Z ¶oUmar g§»¶m H$moUVr ?

F bJVMr nwT>Mr d bJVMr _mJMr g§»`m {bhm.

D 118 , 119 , 120 D , 200 , D , 391,

D , 599 , D , 800 , D , 707,

F {Xboë¶m g§»¶oÀ¶m nwT>rb H$moU˶mhr VrZ g§»`m {bhm.

D 555, 600 , 650 , 977 D 399, ,,

F {Xboë¶m g§»¶oÀ¶m ‘mJrb H$moU˶mhr VrZ g§»`m {bhm.

D 99 , 312 , 407 , 500 D , , , 601

- {ejH$m§gmR>r : 100, 199, 300, 499, 201, 590 `m§gma»`m g§»`m§À`m _mJrb d nwT>rb g§»`m gm§JÊ`mMm gamd
¿`mdm.

11

bhmZ-_moR>onUmgmR>r {MÝhm§Mm dmna < , >

F g§»¶m§Mm bhmZ-‘moR>onUm R>adm.

g§»¶m 8, 2 77, 59 39, 9 14, 35 67, 32
bhmZ g§»¶m
‘moR>r g§»¶m

n {MÝhm§Mm Cn¶moJ Y Y Y
Y Y Y
Y YY
Y YY
Y Y

5 > 2 Mo dmMZ : 5 ‘moR>o 2 nojm 2 < 5 Mo dmMZ : 2 bhmZ 5 nojm

27   40 91  49

27 < 40 Mo dmMZ : 27 bhmZ 40 nojm. 91 > 49 Mo dmMZ : 91 ‘moR>o 49 nojm.

F Imbrb Mm¡H$Q>tV >, < ¶m§n¡H$s ¶mo½¶ {MÝh {bhm.

10 > 9 9 10 5 3  3 5

50 49 49 50 23 25 73 75

500 499 499 500 500 300 600 400

Q>moZr : {Xboë`m XmoÝhr g§»¶m XmoZ A§H$s AgVrb, Va Ë`m§Mm bhmZ-‘moR>onUm Amnë¶mbm
R>adVm ¶oVmo; nU EH$ g§»¶m XmoZ A§H$s Am{U EH$ g§»¶m VrZ A§H$s Agob Va ?

VmB© : AmYr XmoZ A§H$s g§»¶m§n¡H$s gJiçm§V ‘moR>r g§»¶m gm§J ~a§ !
Q>moZr : gmon§ Amho. gJiçm XmoZ A§H$s g§»¶m§V 99 hr gdmªV ‘moR>r g§»¶m Amho.
99 nojm ‘moR>r bJVMr g§»¶m Amho 100. Vr Va VrZ A§H$s g§»¶m Amho.
VmB© : ‘J Vwåhm§bm g‘Ob§ Zm, XmoZ A§H$s g§»¶m 99 qH$dm {VÀ¶mnojm bhmZ AgVo, åhUyZ

Vr 100 nojm bhmZ AgVo. VrZ A§H$s g§»¶m 100 qH$dm {VÀ¶mnojm ‘moR>r AgVo.
Q>moZr : ¶mdê$Z bjmV ¶oV§, H$s VrZ A§H$s g§»¶m XmoZ A§H$s g§»¶onojm ‘moR>rM AgVo.
gb‘m : VgmM {dMma Ho$bm, Va XmoZ A§H$s g§»¶m, EH$ A§H$s g§»¶onojm ‘moR>rM AgVo Zm ?
VmB© : ~amo~a !

12

bhmZ-_moR>onUm (nwT>o Mmby)

Z§Xÿ : VrZ A§H$s XmoZ g§»¶m AgVrb, Va ˶m§n¡H$s bhmZ-‘moR>r g§»¶m H$er AmoiIm¶Mr?
VmB© : WmoS>r gmonr CXmhaU§ nmhÿ. 500 d 300 ¶m g§»¶m nmhm. ¶mVrb H$moUVr g§»¶m ‘moR>r

Amho ?
gb‘m : 5 eVH$ 3 eVH$m§nojm ‘moR>o AmhoV, åhUyZ 500 > 300.
VmB© : AmVm 325 d 625 ¶m g§»¶m nmhm. BWo XmoÝhr g§»¶m§Vrb XeH$ g‘mZ d EH$H$hr

g‘mZ AmhoV; nU 6 eVH$ ho 3 eVH$m§nojm ‘moR>o AmhoV, åhUyZ 625 > 325.
Q>moZr : XmoZ g§»¶m§‘ܶo eVH$, XeH$, EH$H$ gJio doJdoJio Agbo, Va H$m¶ H$am¶M§ ?
Z§Xÿ : 495 Am{U 812 ¶m g§»¶m nmhm.
VmB© : 495 ‘ܶo eVH$mÀ¶m KamVbm A§H$ Amho 4. Vmo 812 À¶m eVH$mÀ¶m A§H$mnojm bhmZ

Amho, ho ‘hËËdmM§ Amho. AmnU AmYr 495 Z§Va bJoM ¶oUmar nyU© eVH$s g§»¶m nmhÿ.
Q>moZr : Vr Amho 500 Am{U 495 < 500.
VmB© : 812 ¶m g§»¶oMm eVH$ Amho 8. Amnë¶mbm ‘mhrV Amho, H$s 500 < 800 Am{U

800 < 812, åhUyZ 495 < 812. ho g‘Ob§ H$m ?
Q>moZr : hmo, Agm {dMma Ho$bm, Va Vo AdKS> Zmhr.
Z§Xÿ : åhUOo VrZ A§H$s XmoZ g§»¶m {Xë¶m, Va {OMm eVH$ñWmZMm A§H$ ‘moR>m, Vr OmñV

‘moR>r.

F bhmZ-_moR>r g§»`m R>adm.

721 589 423 723 600 497

gb‘m : nU XmoÝhr g§»¶m§À¶m eVH$m§À¶m Kam§Vrb A§H$ g‘mZ AgVrb Va H$m¶ H$am¶Mo ?
718 d 720 ¶m g§»¶m nmhm.
VmB© : hoXoIrb gmono Amho. eVH$ g‘mZ Agbo, Va XeH$ d EH$H$mZo V¶ma Pmboë¶m g§»¶m

nmhm.
gmoZy : 720 d 718 ¶m§‘ܶo 20 d 18 Mr VwbZm H$am¶Mr Zm ? 20 > 18 åhUyZ

720 > 718.
VmB© : ~amo~a Amho. XmoZ g§»¶m§‘Yrb eVH$ñWmZMo A§H$ g‘mZ AgVrb, Va {OMm

XeH$ñWmZMm A§H$ _moR>m Agob, Vr g§»¶m ‘moR>r. eVH$ d XeH$ñWmZMo A§H$ g_mZ
Agbo, Va EH$H$ñWmZMm A§H$ nmhÿZ Hw$R>br g§»¶m ‘moR>r Amho Vo R>adm.

F {Xboë¶m g§»¶m§À¶m OmoS>çm§‘ܶo < , > ¶m§n¡H$s ¶mo½¶ Vo {MÝh {bhm.

427 267, 150 501, 813 79,  300 624

13

MT>Vm - CVaVm H«$‘

Q>moZr, gmoZy, gb‘m d Z§Xÿ `m§Zm J{UV {df¶mV Imbrbà_mUo JwU {_imbo.

Q>moZr 70, gb‘m 87, gmoZy 79, Z§Xÿ 85.

`m gdmªMo JwU MT>Ë`m H«$_mZo d CVa˶m H«$‘mZo [bhm.

MT>Vm H«$‘ : 70, 79, 85, 87 CVa>Vm H«$‘ : 87, 85, 79, 70

F Imbrb g§»¶m§Mm MT>Vm d CVaVm H«$_ bmdm.

g§»¶m MT>Vm H«$_ CVaVm H«$_

55, 63, 40, 80

69, 9, 59, 70

14, 29, 47, 39

F 122, 360, 325 `m g§»`m§Mm F 801, 617, 847, 799 `m g§»`m§Mm

MT>Vm d CVaVm H«$_ bmdm. MT>Vm d CVaVm H«$_ bmdm.

gdmªV bhmZ g§»`m : 122 gdmªV bhmZ g§»`m : 617

gdmªV _moR>r g§»`m : 360 AmVm Caë`m 801, 847, 799

MT>Vm H«$_ : 122, 325, 360 `m§Vrb gdmªV bhmZ g§»`m : 799

hm 122 < 325 < 360 Agmhr Z§Va Caë`m : 801, 847

{b{hVmV. `m§n¡H$s bhmZ g§»`m 801 d Z§VaMr g§»`m 847.

CVaVm H«$_ : 360, 325, 122 MT>Vm H«$_ : 617, 799, 801, 847

hm 360 > 325 > 122 Agmhr CVaVm H«$_ : 847, 801, 799, 617

{b{hVmV.

F g§»¶m§Mm MT>Vm H«$‘ d CVaVm H«$‘.

{Xboë`m g§»`m MT>Vm H«$‘ CVaVm H«$‘

217, 211, 215 211, 215, 217 217, 215, 211
500, 400, 100, 600 100, 400, 500, 600 600, 500, 400, 100

519, 419, 619 419, 519, 619 619, 519, 419
785, 757, 8, 81 8, 81, 757, 785 785, 757, 81, 8
15, 100, 81, 167 15, 81, 100, 167 167, 100, 81, 15

F Imbrb g§»¶m MT>˶m d CVa˶m H«$‘mZo {bhm.

D 117, 69, 50, 8 D 217, 271, 270 D 365, 73, 12, 116
D 527, 8, 324, 63
D 912, 27, 356 D 315, 215, 515 D 285, 407, 589, 360
D 909, 990, 999
D 88, 78, 75 D 500, 501, 499

D 888, 788, 688 D 105, 107, 101, 102

14

{Xboë¶m A§H$m§nmgyZ gdmªV bhmZ d gdmªV ‘moR>r g§»¶m

VmB© : 2, 3, 5 ¶m A§H$m§nmgyZ VrZ A§H$s g§»¶m V¶ma H$ê$¶m.
gmoZy : EH$ A§H$ EH$XmM ¿¶m¶Mm H$m ?
Q>moZr : hmo. ZmhrVa IynM g§»¶m V¶ma hmoVrb. 222, 232, 233, 323, 333, 235, 253

Aem {H$VrVar g§»¶m V¶ma hmoVrb.
gb‘m : à˶oH$ A§H$ EH$XmM dmnabm, Va ‘mÌ 235, 253, 325, 352, 532, 523 EdT>çmM

g§»¶m V¶ma hmoVrb.
VmB© : AmVm ¶m§Vë¶m g§»¶m§Mr VwbZm H$ê$Z bhmZ-‘moR>çm g§»¶m R>adm ~a§ !
Q>moZr : ¶m g§»¶m§n¡H$s 532 Am{U 523 ¶m g§»¶m§À¶m eVH$ñWmZMm A§H$ gdmªV ‘moR>m Amho.

¶m XmoZ g§»¶m§‘ܶo VwbZm H$aVmZm 32 hr g§»¶m 23 nojm ‘moR>r, åhUyZ 532 > 523.
åhUOo 2, 3, 5 ¶m A§H$m§nmgyZ V¶ma Pmboë¶m g§»¶m§n¡H$s 532 hr g§»¶m gdmªV ‘moR>r.
gb‘m : BWo V¶ma Pmboë¶m g§»¶m§n¡H$s eVH$ñWmZr 2 Agboë¶m g§»¶m§n¡H$s 235 d 253 ‘ܶo
35 < 53 ¶mdê$Z 235 < 253.
VmB© : em~mg !
Z§Xÿ : {Xboë¶m A§H$m§nmgyZ gd© g§»¶m V¶ma Z H$aVm, EH$X‘ gdmªV bhmZ d gdmªV ‘moR>r
g§»¶m V¶ma H$aVm ¶oB©b H$m ?
Q>moZr : hmo. gdmªV ‘moR>çm g§»¶oVrb eVH$ñWmZMm A§H$ gdmªV ‘moR>m AgUmaM. Caboë¶m XmoZ
A§H$m§Mr g§»¶m V¶ma H$aVmZm ‘moR>çm g§»¶ogmR>r ˶m§Vbm ‘moR>m A§H$ XeH$ñWmZr ¶oB©b.
gmoZy : åhUOo ‘moR>çm§V ‘moR>r g§»¶m V¶ma H$aVmZm {Xbobo A§H$ CVa˶m H«$‘mZo {bhmdo.
Ogo, Amnë¶m CXmhaUmV gdmªV ‘moR>r g§»¶m 532.
gb‘m : {Xboë¶m VrZ A§H$m§nmgyZ bhmZm§V bhmZ g§»¶m H$er V¶ma H$am¶Mr Vo ‘r gm§Jy H$m ?
eVH$ñWmZr gdmªV bhmZ A§H$ {bhm¶Mm. EH$H$ñWmZr gdmªV ‘moR>m d Cabobm
XeH$ñWmZr {bhm¶Mm. WmoS>³¶mV, {Xbobo A§H$ MT>˶m H«$‘mZo {b{hbo, H$s VrZ A§H$s
gdmªV bhmZ g§»¶m V¶ma hmoB©b. Ogo ¶oWo 235.
gmoZy : nU {Xboë¶m A§H$m§‘ܶo eyݶ Agob, Va Ag§M H$am¶M§ H$m ?
VmB© : Zmhr. Vg§ Ho$b§ Va Vr g§»¶m VrZ A§H$s Z hmoVm XmoZ A§H$s hmoB©b. CXmhaUmgmR>r 5,0,2
ho A§H$ nmhm. eVH$ñWmZr eyݶ Agob, Va 025, 052 ¶m g§»¶m V¶ma hmoVmV; nU ˶m
25 d 52 Aem XmoZ A§H$m§‘ܶo {b{hVm ¶oVmV, åhUyZ ˶m XmoZ A§H$s AmhoV.
Z§Xÿ : {Xboë¶m A§H$m§‘ܶo 0 Agob Va eyݶoVa (eyݶ gmoSy>Z BVa) A§H$m§n¡H$s bhmZ A§H$
eVH$ñWmZr R>ody¶m.
gb‘m : eyݶ XeH$ñWmZr {bhÿZ Cabobm A§H$ EH$H$ñWmZr {bhm¶bm hdm.
VmB© : ~amo~a. Ogo 5, 0, 2 ¶m A§H$m§Zr ~Zdbobr gdmªV bhmZ VrZ A§H$s g§»¶m 205 Amho.

F {Xboë¶m A§H$m§nmgyZ gdmªV bhmZ d gdmªV ‘moR>r VrZ A§H$s g§»¶m {bhm.

D 9, 4, 6 D 7, 0, 4 D 3, 9, 5 D 8, 5, 9

15

g§»¶oMo {dñVm[aV ê$n

VmB© : 824 _Ü`o {H$Vr eVH$, {H$Vr XeH$ AmhoV d {H$Vr EH$H$ AmhoV ?
gmoZy : 824 åhUOo 8 eVH$ 2 XeH$ d 4 EH$H$.
Q>moZr : åhUOo 824 = 800 + 20 + 4.
Z§Xÿ : nU ¶mM nX²YVrZo 203 H$go {bhm`Mo ?
gb_m : 203 = 200 + 3
VmB© : Vo ~amo~a Amho, nU 203 = 200 + 0 + 3 ho {dñVm[aV ê$n OmñV gmoB©Mo Amho,

H$maU BWo eVH$ñWmZMm, XeH$ñWmZMm A§H$ d EH$H$ñWmZMm A§H$ H$moUVm ho MQ>H$Z
g‘OVo. ¶mMà‘mUo 80 Mo 80 + 0 Ago {dñVm[aV ê$n hmoB©b.

"9' hr EH$ A§H$s g§»¶m KoVbr, Va {VMo {dñVm[aV ê$n "9' hoM Amho.

F Imbrb g§»¶mMr {dñVm[aV ê$no {bhm.

D 998 D 34 D 287 D 534 D 76 D 301 D 90 D 45 D 13

VmB© : {dñVm[aV ê$n {Xb§ Agb§, Va ˶mdê$Z g§»¶m {b{hVm ¶oB©b H$m ?
500 + 30 + 7 ho {dñVm[aV ê$n nmhm.
gb_m : ‘r à¶ËZ H$aVo.
500 + 30 + 7 = 537
VmB© : em~mg !

F {dñVm[aV ê$nmdê$Z g§»`m {bhm.

D 700 + 0 + 5 D 400 + 60 + 7 D 800 + 0 + 0
D 30 + 9 D 200 + 10 + 1 D 100 + 50 + 0
D 40 + 4 D 300 + 0 + 6

ñWm{ZH$ qH$_V

VmB© : 400 + 40 + 7 ho {dñVm[aV ê$n H$moU˶m g§»¶oMo Amho ?
Z§Xÿ : gmono Amho, 447.
gb_m : J§_VM Amho. EH$Xm 400 gmR>r 4 hm A§H$ dmnabm, Va Z§Va 40 gmR>r 4 hm A§H$

dmnabm.
VmB© : A§H$mMr OmJm qH$dm ñWmZ {VMr qH$_V R>adVo, ho bjmV ¿¶m. eVH$ñWmZÀ`m 4 Mr

qH$_V 400 Amho, Va XeH$ñWmZÀ`m 4 Mr qH$_V 40 Amho. EH$H$ñWmZÀ¶m 7 Mr
qH$‘V _mÌ 7 M Amho. A§H$mMr ˶m§À¶m ñWmZmZwgma Or qH$‘V AgVo {Vbm ˶m
A§H$mMr ñWm{ZH$ qH$‘V åhUVmV.

16

VmB© : 576 `m g§»`oV 5 Mr ñWm{ZH$ qH$_V 500 Am{U 7 Mr ñWm{ZH$ qH$_V 70, Va 6 Mr

ñWm{ZH$ qH$_V 6 EdT>r Amho. ho g‘Ob§ Zm ? AmVm hr H$mhr CXmhaU§ nmhm.

9 3 4 7 0 5

ñWm{ZH$ qH$_V 900 30 4 ñWm{ZH$ qH$_V 700 0 5

e X E e X E

4 4 4 6 3 9

4 600

40 ñWm{ZH$ qH$_V 30

400 9

F Imbrb g§»`m§Vrb AYmoao{IV A§H$m§Mr ñWm{ZH$ qH$_V {bhm.
919 , 135 , 20 , 305 , 480 , 32

n g§»¶m Am{U {dñVm[aV ê$n : àm˶{jH$

VmB© : VrZ A§H$s g§»¶m Am{U {VMo {dñVm[aV ê$n àm˶{jH$mZo XmIdVm ¶oVo. ˶mgmR>r eoOmar

4 00 + 3 0 + 5 XmIdë¶mà‘mUo EH$ H$mJXr nQ²>Q>r KoD$Z
{VMo gmV gmaIo ^mJ H$am. ‘Zmer EH$
VrZ A§H$s g§»¶m R>adm. g‘Om 435. ¶m

g§»¶oMo {dñVm[aV ê$n ˶m H$mJXr nQ²>Q>rda

da XmIdë¶mà‘mUo {bhm.

Z§Va R>iH$nUo XmIdboë¶m aoKm§da nQ²>Q>rbm {MÌmV

XmIdë¶mà‘mUo KS>çm Kmbm. 43 5

435 KS>çm KmVë¶mZo "00 +' Am{U "0 +' ho
PmH$bo OmVrb Am{U 435 hr g§»¶m

{Xgob.


¶mà‘mUo KS>çm KmVboë¶m nQ²>Q>rda g§»¶m Am{U KS>çm CbJS>boë¶m nQ²>Q>rda {VMo {dñVm[aV

ê$n {XgVo.

- {ejH$m§gmR>r : `mà_mUo KS>rnQ²>Q>çm V`ma H$ê$Z {d{dY VrZ A§H$s g§»`m§Mo {dñVm[aV ê$n d A§H$m§À`m ñWm{ZH$
qH$_Vr g_OyZ KoÊ`mMr g§Yr Xçmdr.

17

1000 `m g§»`oMr AmoiI

h e ee XX X h e X E
e ee XX X 1 1 1
e ee XX X 9 9 9
+ 1
e X 10 10 10
1 0 0 0

AmnU hmVÀ¶mMr ~oarO H$ê$Z 99 + 1 = e§^a (100) hmoVmV, ho nm{hbo Amho. AmVm
999 + 1 hr ~oarO Cä`m _m§S>UrV H$ê$. 9 EH$H$ + 1 EH$H$ ho 10 EH$H$ hmoVmV. Ë`m§Mm EH$
XeH$ (hmVMm) hmoVmo. 9 XeH$ + 1 XeH$ {_iyZ 10 XeH$ hmoVmV. Ë`m§Mm EH$ eVH$ (hmVMm)
hmoVmo. 9 eVH$ + 1 eVH$ {_iyZ 10 eVH$ hmoVmV. Ë`mVyZ nwÝhm EH$ hmVMm ¶oVmo. Ë`mÀ`mgmR>r
Zdo ñWmZ V`ma H$ê$. Ë`mbm hOmamMo ñWmZ åhUVmV. 1000 ¶m g§»¶oV hOma ñWmZr 1 Am{U
BVa gd© ñWmZm§V 0 Amho. ¶m g§»¶oMo dmMZ "EH$ hOma' Ago H$aVmV.



EH$m ‘mioV 10 _Ur. Aem 100 ‘mim§‘ܶo EHy$U 1000 _Ur AmhoV.
åhUyZ 100 XeH$ åhUOo gwX²Ym 1000.

18

  ~oarO : {~ZhmVÀ`mMr  

eee ee

ee e

Q>moZrH$S>o à˶oH$s 100 _Ur Agbobo 3 ~Q>do AmhoV. ~Q>do.
gmoZyH$S>o VgoM 5 ~Q>do AmhoV. EHy$U ~Q>do {H$Vr ? 8

XmoKm§Odirb ~Q>ì`m§_Yrb EHy$U _Ur {H$Vr ? 800 _Ur.

F Q>moZrOdi 100 én`m§À`m 2 ZmoQ>m, 10 én`m§Mr EH$ ZmoQ> Amho d 1 én`mMr 5 ZmUr AmhoV.
gmoZyOdi 100 én`m§Mr EH$ ZmoQ>, 10 én`m§À`m 3 ZmoQ>m d 1 én`mMr 2 ZmUr AmhoV,
Va XmoKm§H$S>o {_iyZ 100 én`m§À`m EHy$U ZmoQ>m {H$Vr ? 10 én`m§À`m EHy$U ZmoQ>m {H$Vr ?
1 én`mMr EHy$U ZmUr {H$Vr ?

F {MÌmdê$Z V`ma Ho$boë`m CXmhaUmMo {ZarjU H$am. CXmhaU nyU© H$am. Ë`mgmR>r EH$H$m§V
EH$H$, XeH$m§V XeH$ d eVH$m§V eVH$ {_idm.
e X E

e 1 e 2 X 1 E 1 2 1
+ +
e e 2 e 1 X 3 E 2 1 3

e e e

F {MÌo nmhÿZ g§»¶m {bhm d ~oarO H$am. e X E
e e e +
e X E +
e X E

e X E



19

F nwT>rb ~oaOm H$am d {ZarjU H$am.

+ 2504 + 2504 + 708 + 780 + 7153 + 13
75

74 74

g§»¶m§Mm H«$‘ ~Xbbm Var ~oarO VrM ¶oVo.

F nwT>rb CXmhaUo gmoS>dm.

D 376 + 2 D 403 + 64 D 125 + 144 D 513 + 365
D 20 + 436
e X E
3 7 6
+ 2
3 7 8

D 142 + 6 D 205 + 4 D 540 + 35

F C^r _m§S>Ur H$ê$Z ~oarO H$am.

D 664 + 220 D 421 + 351 D 713 + 205 D 122 + 324 D 207 + 102

D 270 + 312 D 450 + 230 D 541 + 320 D 400 + 300 D 22 + 342

F AmS>ì`m _m§S>UrZo Ho$bobr Imbrb ~oarO Aä¶mgm.

e X E e X E e X E





4 2 1 + 3 5 1 = 7 7 2


F AmS>ì`m _m§S>UrZo ~oarO H$am. D 527 + 261 D 623 + 215 D 203 + 302
20

VrZ g§»`m§Mr ~oarO

F ~oarO H$am. E 2 ‘ܶo 3 {‘idbo, 5 Ambo.
_m`mZo XþH$mZmVyZ 2 én`m§Mo ImoS>a~a, 3 én`m§Mr 2 5 ‘ܶo 4 {‘idbo, 9 Ambo.
nopÝgb d 4 én`m§Mo a§JrV ISy> KoVbo, Va + 3
{VZo XþH$mZXmambm {H$Vr én`o Xçmdo? + 4
2 + 3 = 5
ImoS>a~aMo 2 én`o d nopÝgbMo 3 én`o {_iyZ 9
5 én`o Pmbo. ¶m 5 én¶m§V ISy>Mo 4 én`o

{_idbo, H$s 9 én`o hmoVrb. åhUOoM 2 + 3 + 4 = 9
åhUyZ _m`mZo XþH$mZXmambm 9 én¶o Xçmdo.

F H$nmQ>mV JmÊ`m§Mr 3 nwñVHo$, JmoîQ>tMr 21 nwñVHo$ d {MÌm§Mr 14 nwñVHo$ X E
AmhoV, Va H$nmQ>mVrb EHy$U nwñVHo$ {H$Vr ? 2 1
+ 1 4
21 + 14 + 3 = 38 + 3
H$nmQ>mV EHy$U 38 nwñVHo$ AmhoV. $ 3 8

F nwT>rb CXmhaUo gmoS>dm.

D X E D X E D X E D X E

++ 233 052 ++ 121 152 ++ 5 023 ++ 21 5
2
1



D 453 + 104 + 112 D 105 + 3 + 20 D 202 + 34 + 11

e X E

4 5 3
++
1 0 4
1 1 2

D 143 + 2 + 2 D 3 + 42 + 233
D 200 + 10 + 1 D 451 + 224 + 112 D 104 + 2 + 3
D 352 + 313 + 21 D 5 + 12 + 372 D 400 + 40 + 4
D 303 + 444 + 122

21

  dOm~mH$s : {~ZhmVÀ`mMr  

F {MÌ nmhm. CXmhaU Aä¶mgm. F {MÌmdê$Z CXmhaUmMr ‘m§S>Ur H$am d gmoS>dm.

X E X E

- 2 3
1 2

1 1

F
e e X E E E - e X E
2 1 3 àW‘ EH$H$m§VyZ EH$H$ dOm H$ê$.
1 1 1 Z§Va XeH$m§VyZ XeH$ dOm H$ê$.

1 0 2 Z§Va eVH$m§VyZ eVH$ dOm H$ê$.

F A{OVH$S>o 257 én`o AmhoV. Ë`mZo _ZmoObm 150 én`o {Xbo, Va A{OVH$S>o {H$Vr én`o
Cabo, ho Imbrb {MÌmdê$Z R>adm.



F {H«$Ho$Q> _°M_Ü`o B§½b§S>Zo 245 Ymdm H$mT>ë`m. ^maVmZo 123 Ymdm H$mT>ë`m, Va B§½b§S>er
~amo~ar H$aʶmgmR>r ^maVmbm AmUIr {H$Vr Ymdm H$mT>mì`m bmJVrb ?

B§½b§S>er ~amo~ar hmoÊ`mgmR>r ^maVmÀ`m 245 Ymdm ìhmì`m e X E

bmJVrb; åhUOo 123 À`m nwT>o AmUIr {H$Vr Ymdm H$mT>ë`m, H$s - 12 4 5
245 Ymdm hmoVrb, ho emoYmdo bmJob. 2 3

åhUOo 123 + = 245. Mm¡H$Q>rVrb g§»`m emoYmdr 1 2 2

bmJob. hr g§»`m 245 _YyZ 123 dOm Ho$ë`mg {_iob.

22

F dOm~mH$s H$am.

D e X E D e X E D e X E
- 5 4 25 - 47 43 98 - 28
5 3
0 2

5 4 3

D e X E D e X E D e X E
- 21 13 47 - 3 6 63 - 4 53 55



D e X E D e X E D e X E
- 4 5 8 - 58 9 9 - 49 5 5
4 4 2 3 1 5



F C^r ‘m§S>Ur H$ê$Z dOm~mH$s H$am.

D 654 - 200 D 674 - 242 D 772 - 341

e X E
5
- 62 0 4
0

F ‘moR>çm g§»¶oVyZ bhmZ g§»¶m dOm H$am.

D 315, 517 D 470, 340 D 300, 700

AmS>ì`m _m§S>UrZo dOm~mH$s

e X E e X E
3 4 5 - 2 4 3 = 102 dOm~mH$s H$aVmZm EH$H$m§VyZ EH$H$, XeH$m§VyZ XeH$
d eVH$m§VyZ eVH$ dOm H$amdo.

F AmS>ì`m _m§S>UrZo dOm~mH$s H$am.

417 - 305, 504 - 201, 779 - 250, 420 - 220

23

  JwUmH$ma  

{ejH${XZmbm VmBªZm XoʶmgmR>r \w$bm§Mm JwÀN> V¶ma Ho$bm. ˶mgmR>r Q>moZr, gmoZy, gb‘m, Om°Z
d Z§Xÿ `m§Zr àË`oH$s 2 \w$bo AmUbr. Ë`m \w$bm§Mm EH$ gw§Xa JwÀN> gmoZyZo V`ma Ho$bm.

VmB© : N>mZ ! {H$Vr gw§Xa Am{U _moR>m JwÀN> Pmbm Amho !
EHy$U {H$Vr \w$bm§Mm JwÀN> Amho hm ?
Q>moZr : àË`oH$mZ§ AmUbobr XmoZ Aer nmMOUm§Mr {_iyZ Xhm \w$b§ Pmbr.
Om°Z : àË`oH$mMr 2 \w$b§ Aer EHy$U nmMOUm§Mr ’w$b§ åhUOo 5 doim 2 KoD$Z Ho$bobr ~oarO

2 + 2 + 2 + 2 + 2 = 10.
VmB© : 2 + 2 + 2 + 2 + 2 ho 2  5 Ago {b{hVmV.
10 hm 2 Am{U 5 `m§Mm JwUmH$ma Amho.
AmVm BWo {MÌo AmhoV. ˶mV {H$Vr ’$io AmhoV ‘moOy¶m.

gmoZy : EH$m AmoirV 4 qb~o,Aem XmoZ Amoir. Q>moZr : EH$m AmoirV 4

4 Mr XþßnQ> åhUOo 8 qb~o. H$mH$S>çm, Aem

4 hr g§»`m XmoZ doim KoD$Z Ho$bobr Mma Amoir.

~oarO åhUOo 4 Mr XþßnQ>. 4 Mr 4 nQ,>

åhUOo

16 H$mH$S>çm.


gb‘m : EH$m AmoirV Mma noê$,
Aem VrZ Amoir åhUOo
4 Mr {VßnQ> 12.

Om°Z : EH$m AmoirV Mma Am§~o, Aem
10 Amoir.

4 Mr XhmnQ> åhUOo 40 Am§~o.

24

JwUmH$ma gb‘m

D

Q>moZr gmoZy Z§Xÿ
àË`oH$mH$S>o 3 M|Sy> åhUOo EHy$U M|Sy> {H$Vr ?
3 + 3 + 3 + 3 = 12
Mma doim 3 KoD$Z Ho$bobr ~oarO, åhUOo 3 Mr Mma nQ>,
åhUOo 3  4 = 12 (3 MmoH$ 12).
D `mà_mUo nwT>rb CXmhaUmVrb Mm¡H$Q>r> nyU© H$am.

àË`oH$ Q>monbrV ghm Am§~o, Va VrZ Q>monë¶m§‘Yrb Am§~o {H$Vr ?

6 + 6 + 6 = ghmMr nQ> åhUOoM 6  = (6 {ÌH$ )

D 3 _wbm§Mm EH$ JQ> `mà_mUo 7 JQ> H$ê$Z _wbo C^r hmoVr, Va EHy$U _wbo {H$Vr ?

3 Mr nQ> , VrZ gmVo , 3  =

F {MÌ nmhm d darbà‘mUo CXmhaU V`ma H$ê$Z gmoS>dm.

D EH$m dhrMr qH$_V 5 é. Aem 9 dhçm§Mr qH$_V {H$Vr ?
5 hr g§»¶m 9 doim KoD$Z Ho$bobr ~oarO åhUOo> 5  9.
5  9 = 45.
åhUyZ 9 dhçm§Mr qH$_V 45 én`o.

VmB© : nmT>o åhUOo H«$_mZo Ho$bobo JwUmH$maM AmhoV. Ë`m§Mm Cn`moJ H$ê$Z AmnU nwT>o _moR>çm
g§»`m§Mm JwUmH$ma H$aUma AmhmoV.

AmnU 2, 3, 4, 5 Am{U 10 Mo nmT>o åhUy.

25

JwUmH$ma ~oarO ê$nmV {H$Vr {H$Vr JwUmH$ma EHy$U
dñVwê$nmV doim nQ> ê$n dñVy

2 + 2 + 2 + 2 + 2 XmoZ, 2 Mr 25 10
nmM  doim nmMnQ>

5+5 ... , 5 Mr ...  ...
XmoZ doim ... nQ>

... + ... + ... + ..., ... Mr ...  ...
... + ... nmM  doim ... nQ>

.................... Xhm, 10 Mr ...  ... .......
VrZ doim ... nQ>

.................... Mma, ....... ...  ... .......
ghm doim

.................... ....... ....... ...  ... .......
26

6 Mm nmT>m

6, EH$ doim 61=6
ghm EHo$ ghm

6, XmoZ doim 6  2 = 12
ghm XþUo ~mam

6, VrZ doim 6  3 = 18
ghm {ÌH$ AR>am

6, Mma doim 6  4 = 24
ghm MmoH$ Mmodrg

6, nmM doim 6  5 = 30
ghm nmMo Vrg

6, ghm doim 6  6 = 36
ghm gmho N>ËVrg

6, gmV doim 6  7 = 42
ghm gmVo ~oMmirg

6, AmR> doim 6  8 = 48
ghm AmR>o AR²>R>oMmirg

6, ZD$ doim 6  9 = 54
ghm Zdo MmonÝZ

6, Xhm doim 6  10 = 60
ghm Xmho gmR>

27

7, 8 d 9 Mm nmT>m
6 À`m nmT>çmà_mUo 7, 8, 9 Mm nmT>m V`ma H$ê$.

7  1 = 7 8  1 = 8 9  1 = 9
7  2 = 14 8  2 = 16 9  2 = 18
7  3 = 21 8  3 = 24 9  3 = 27
7  4 = 28 8  4 = 32 9  4 = 36
7  5 = 35 8  5 = 40 9  5 = 45
7  6 = 42 8  6 = 48 9  6 = 54
7  7 = 49 8  7 = 56 9  7 = 63
7  8 = 56 8  8 = 64 9  8 = 72
7  9 = 63 8  9 = 72 9  9 = 81
7  10 = 70 8  10 = 80 9  10 = 90

~oaOoÀ`m gmhmæ`mZo nmT>m

VmB© : 6 Mm nmT>m V`ma H$aVmZm 6 Mo 4 Mm 2 Mm ~oarO 6 Mm nmT>m
XmoZ ^mJ H$ê$. Ogo, 6 = 4 + 2. nmT>m nmT>m

AmVm 4 d 2 Mm nmT>m KoD$Z Ë`m§Mr 4 2 4 + 2 = 6 6  1 = 6

~oarO H$ê$Z 6 Mm nmT>m V¶ma 8 4 8 + 4 = 12 6  2 = 12
H$ê$. 12 6 12 + 6 = 18 6  3 = 18
Q>moZr : 6 Mm nmTm Ogm 4 d 2 À`m 16 8 16 + 8 = 24 6  4 = 24
nmT>çmZo V`ma H$aVm `oVmo, Vgm

Vmo 5 d 1 À`m gmhmæ¶mZohr V`ma 20 10 20 + 10 = 30 6  5 = 30
H$aVm `oB©b Zm ?
VmB© : ~amo~a. _mhrV Agboë`m XmoZ 24 12 24 + 12 = 36 6  6 = 36
28 14 28 + 14 = 42 6  7 = 42
nmT>çm§À`m ~oaOoZo ZdrZ nmTo V`ma

H$aVm `oVmV. 32 16 32 + 16 = 48 6  8 = 48

Q>moZr : _J 7 Mm nmT>m 4 d 3 À`m 36 18 36 + 18 = 54 6  9 = 54
nmT>çm§Zr V`ma H$aVm `oB©b. 20 40 + 20 = 60 6  10 = 60
40

- {ejH$m§gmR>r : 8 d 9 Mo nmT>o XmoZ nmT>çm§À`m ~oaOoÀ`m gmhmæ`mZo V`ma H$ê$Z ¿`mdo. XmoZ nmT>çm§À`m dOm~mH$sÀ`m
gmhmæ`mZohr nmT>o V`ma H$aVm `oVmV, ho bjmV AmUyZ Xçmdo.

28

9 À¶m nmT>çmMr J§‘V 09
VmB© : ‘r Vwåhm§bm 9 À`m nmT>çmMr EH$ J§_V gm§JVo. 18
9, 8, 7, ..... Aem 0 n`ªV g§»`m CbQ> H«$_mZo EH$H$ñWmZr {bhm. 27
36
Ë`m§À`m AmYr XeH$ñWmZr 0, 1, 2, ...... 9 `m g§»`m H«$_mZo {bhm. Pmbm 45
9 Mm nmT>m V`ma ! Amho H$s Zmhr J§_V ! 54
gmoZy : Aao dm ! AOyZ EH$ J§‘V ‘m¶m bjmV Ambr Amho. nmT>çmV ¶oUmè¶m 63
à˶oH$ g§»¶oVrb XeH$ d EH$H$ñWmZÀ¶m A§H$m§Mr ~oarO ZD$M Amho. 72
81
90
F Imbrb gmaUrV 5  3 = 15 ho XmIdbo Amho. [aH$må¶m Mm¡H$Q>tV ¶mo½¶ g§»¶m ^am.

 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10

3369

448 16

5 5 10 15 20 25

6 36

7 49

8 64

9 81
10 10 100

- {ejH$m§gmR>r : àË`oH$ {dXçmÏ`m©bm 1 Vo 100 Mr gmaUr V`ma H$aÊ`mg gm§Jmdr. Ë`m gmaUrV àË`oH$ {dXçmÏ`m©bm
EH$ nmT>m XoD$Z Ë`mV `oUmè`m g§»`m a§JdÊ`mg gm§Jmdo. V`ma hmoUmè`m AmH¥${V~§YmMo {ZarjU
H$aÊ`mg gm§Jmdo.

29

F Imbrb JwUmH$ma H$am.
 36  53  75  83  64  78



F Imbr {Xboë`m {MÌm§dê$Z JwUmH$mamMr CXmhaUo V`ma H$am d gmoS>dm.

D Imbrb {MÌmdê$Z V`ma Pmbobo CXmhaU :



EH$m AmoirV 6 \w$bo, Va Aem 4 AmoitVrb \w$bo {H$Vr ?

EH$m AmoirVrb \w$bo
 Amoir

EHy$U \w$bo

D

M|Sy>, Va ~m°Šg_Yrb EHy$U M|Sy> {H$Vr ?
EH$m ~m°Šg_Ü`o

D


D

- {ejH$m§gmR>r : EH$ A§H$s XmoZ g§»`m dmnê$Z JwUmH$mamMr CXmhaUo V`ma H$ê$Z, gmoS>dyZ ¿`mdr.

30

JwUmH$mamgmR>r nmT>çm§Mm Cn`moJ

D qMQy>Zo dmT>{XdgmgmR>r EH$ noZ 5 én`m§g `mà_mUo 6 noZ§ KoVbr, Va Ë`mbm XþH$mZXmambm

EHy$U {H$Vr én`o Xçmdo bmJVrb ?

Õ EHy$U qH$_V _mhrV H$ê$Z KoÊ`mgmR>r 5 Mm nmT>m,  56 noZ§ noZMr qH$_V
nmM gmho n`ªV åhUmdm bmJob. EH$m

nmM gmho Vrg åhUOoM 5  6 = 30 30 EHy$U én`o
EHy$U 30 én`o Xçmdo bmJVrb.

D EH$m am§JoV 8 PmS>o, Aem 5 am§Jm§V {H$Vr PmS>o ?

Õ am§Jm 5, àË`oH$ am§JoV PmS>o 8.

AH$amRm`> nMmrM{oH«$M`mmi:rgJ wUmH$ma. 8 Mm nmT >m dmnê$.  5 am§Jm
8 àË`oH$ am§JoVrb PmS>o
EHy$U PmS>o
EHy$U PmS>o = 40 4 0

D EH$m S>ã`mV 9 bmSy>. Aem 7 S>ã`m§V {H$Vr bmSy> _mdVrb ?

H$am`Mr {H«$`m : JwUm H$ma  7 S>~o
9 Mm nmTm åhUy. 9 EH$m S>ã`mVrb bmSy>

ZD$ gmVo EHy$U bmSy>

D EH$m gßVmhmV 7 {Xdg, Va 4 gßVmhm§V {H$Vr {Xdg ?

Õ 7 Mm nmT>m åhUy.  4 gßVmh
gmV MmoH$ 7 EH$m gßVmhmVrb [Xdg

EHy$U {Xdg

D EH$m AmoirV 8 ’$aí`m,

Va 3 AmoitV {H$Vr 8 EH$m AmoirVrb ’$aí`m  3 Amoir
’$aí`m ?  3 Amoir 8 EH$m AmoirVrb ’$aí`m

EHy$U ’$aí`m EHy$U ’$aí`m

D EH$m noê$Mr qH$‘V 6 én¶o Amho.

Q>moZr, gmoZr, Z§Xÿ d gb‘m ¶m Mm¡Km§Zm à˶oH$s  6 EH$m noê$Mr qH$‘V
EH$ noê$ XoʶmgmR>r {H$Vr én¶o bmJVrb ? 4 ‘wbo

EHy$U én¶o

31

JwUmH$mamMo JwUY‘©

  3 5
5 3




35 = 53

F nwT>rb JwUmH$ma H$am d {ZarjU H$am.

65= 83= 76= 92=
29=
56= 38= 67=

g§»`m§Mm H«$_ ~Xbbm Var JwUmH$ma VmoM `oVmo.

Ogo : 6  5 = 5  6 ; 8  3 = 3  8 ; 7  6 = 6  7 ; 9  2 = 2  9

F eyÝ`mMm JwUmH$ma JwUY_© 2 + 2 + 2 + 2 åhUOoM 2  4 = 8
1 + 1 + 1 + 1 åhUOoM 1  4 = 4
0 + 0 + 0 + 0 åhUOoM 0  4 = 0


H$moUË`mhr g§»`oZo "eyݶ' bm JwUbo qH$dm "eyÝ`mZo' H$moUË`mhr g§»`obm
JwUbo, Va JwUmH$ma "eyÝ`' `oVmo. 0  4 = 4  0 = 0

F Imbrb JwUmH$ma H$am.

24= = 4  2 7  0 = = 0  7 9  8 = =89

73= = 3  7 8  0 = = 0  8 6  3 = =36

n Jwʶ, JwUH$, JwUmH$ma

6 JwÊ` 5 JwÊ` VmB© : 6  5 `m JwUmH$mamV 6 `m n{hë`m
 5 JwUH$  6 JwUH$ g§»`obm AmnU JwUVmo Vmo JwÊ` Am{U 5 `m

30 JwUmH$ma 30 JwUmH$ma Xþgè`m g§»`oZo JwUVmo Vmo JwUH$ Am{U Ambobo
CËVa 30 åhUOo JwUmH$ma hmo`. ˶mMà‘mUo

5  6 ¶m JwUmH$mamV 5 hm Jwʶ, 6 hm JwUH$ d 30 hm JwUmH$ma Amho.

32

ZmUr d ZmoQ>m

F Imbrb ZmoQ>m§Mr {MÌo nmhm. ˶m§Mr _yë`o Mm¡H$Q>tV {bhm.

`m ZmoQ>oMo _yë` én`o Amho. `m ZmoQ>oMo _yë` én`o Amho.

`m ZmoQo>Mo _yë` `m ZmÊ`mMo _yë` `m ZmÊ`mMo _yë`

én`o Amho. én`o Amho. én`m Amho.

F [aH$må`m Mm¡H$Q>tV EHy$U aŠH$_ (_yë`) {bhm.

D
650

én`o

D





én`o

D


én`o

33

Q>moZr : _mÂ`mH$S>o 3 ZmoQ>m AmhoV, Ë`m§Mr EHy$U qH$_V 75 én`o Amho. EHy$U
gb‘m : _mÂ`mH$S>o gwX²Ym 75 én`o AmhoV nU _mÂ`mH$S>o 5 ZmoQ>m AmhoV.
Q>moZr : Ag§ H$g§ hmoB©b ?
Q>moZrOdiÀ`m ZmoQ>m Aem AmhoV.

én`o

Am{U gb‘mOdiÀ¶m ZmoQ>m Aem AmhoV. én`o



EHy$U



åhUOo XmoKm§Mohr åhUUo ~amo~a Amho.
g§Oy : ‘m¶mH$S>o 100 én¶m§Mr 1 ZmoQ>, 20 én`m§À`m 4 ZmoQ>m Am{U 1 én¶mMr 6 ZmUr

AmhoV, Va _mÂ`mH$S>o {H$Vr én`o AmhoV ?

amOy : åhUOo EHy$U 186 én`o AmhoV.
A{ZVm : _mÂ`mH$S>o 4 ZmoQ>m AmhoV. Ë`m§Mr EHy$U qH$_V 170 én`o Amho, Va Ë`m ZmoQ>m

H$moUË`m ?
` 100 ` 50 ` 10 ` 10

F 170 én¶o AmUIr doJiçm àH$mao 4 ZmoQ>m§À`m gmhmæ`mZo XoVm ¶oVrb H$m ?



- {ejH$m§gmR>r : {dXçmÏ`mªZm H$mS>mªda g§»`m {bhÿZ ZmoQ>m V`ma H$aÊ`mg gm§Jmdo d Ë`m§À`m AmYmao Ioi ¿`mdo.

34

   _mnZ 

bm§~r
VmBªZr Z§Xÿ d gmoZy ¶m§Zm Q>o~bmMr bm§~r ‘moOm¶bm gm§{JVbo.


Z§Xy : `m Q>o~bmMr bm§~r 11 {dVr EdT>r Amho.
gmoZy : Q>o~bmMr bm§~r _mÂ`m 12 {dVr EdT>r Amho.
gb‘m : Vwåhr XmoKm§Zr {dVrZ§M _moOb§, Var XmoKm§À`m _moOÊ`mV \$aH$ H$m nS>bm?
Q>moZr : XmoKm§Mr drV gmaIr Amho H$m ?
Z§Xÿ : _mPr drV gmoZyÀ`m {dVrnojm _moR>r Amho, åhUyZ Ag§ Pmb§.
VmB© : _r EH$mM bm§~rÀ`m XmoZ H$mJXr nQ²>Q>çm XmoKm§Zmhr XoVo. Ë`m§Zr hr bm§~r _moOm ~a§ !

Z§Xÿ : Q>o~bmMr bm§~r `m 9 nQ²>Q>çm§EdT>r Amho.
gmoZy : _r _moOë`mda gwX²Ym 9 nQ²>Q>çmM ^abr.
Z§Xÿ : Amåhm§bm {Xboë`m nQ²>Q>çm gma»`mM bm§~rÀ`m hmoË`m, åhUyZ bm§~r gmaIrM Ambr.
gb_m : åhUOo EH$mM dñVyMr bm§~r gma»`mM gmYZmZ§ _moObr Va Vr g_mZ ^aVo.
gmoZy : _bm ISy>Mr bm§~r _moOm`Mr Agob, Va hr nQ²>Q>r Cn`moJr nS>ob H$m? hr nQ²>Q>r Va

ISy>nojm OmñV bm§~ Amho.
35

VmB© : AmnU `m H$mJXmÀ`m nQ²>QrÀ`m KS>çm Kmby Am{U {VMo gmaIo ^mJ H$ê$. {VÀ`m
Pmboë`m bhmZ ^mJm§Mm Cn`moJ Amnë`mbm ISy>Mr bm§~r _moOÊ`mgmR>r hmoB©b.

Q>moZr : ¶m nQ²>Q>rÀ¶m VrZXm KS>çm KmbyZ 8 g‘mZ ^mJ H$ê$.

gb_m : `m nQ²>Q>rOdi _r ISy> R>odVo.
`m ISy>Mr bm§~r nmM bhmZ ^mJm§EdT>r Amho.
Z§Xÿ : `m nQ²>Q>rMm Cn`moJ H$ê$Z àdoeX²dmamÀ`m XmoZ Im§~m§Vrb A§Va _moOy`m H$m ?
gb_m : ZH$mo. hr H$mJXr nQ²>Q>r IynM H$_r bm§~rMr Amho.
VmB© : _mÂ`mH$S>o EH$ bm§~ Xmoar Amho. Vr A§Va _moOÊ`mgmR>r dmnê$.

Z§Xÿ : AmnU `m XmoarÀ`m gmhmæ`mZ§ `m àdoeX²dmamÀ`m XmoZ Im§~m§Vrb A§Va _moOy.
Q>moZr : àdoeX²dmamÀ`m XmoZ Im§~m§Vrb A§Va 3 Xmoè`m§EdT>§ Amho.
VmB© : OmñV bm§~r _moOÊ`mgmR>r OmñV bm§~rM§ gmYZ KoU§ gmoB©M§ AgV§. H$_r bm§~r

_moOÊ`mgmR>r H$_r bm§~rM§ gmYZ KoU§ gmoB©M§ AgV§, ho AmVm g‘Ob§ Zm ?

36

VmB© : H$moUË`mhr _mUgmZ§ H$mnS> _moOb§ Var Ë`mMr bm§~r g_mZM Agbr nm{hOo, åhUyZ
H$mnS>mÀ`m XþH$mZm_Ü`o àË`oH$ XþH$mZXma H$mnS> _moOÊ`mgmR>r EH$ _moR>r nQ²>Q>r dmnaVmo.

`m nQ²>Q>rMr bm§~r EH$ _rQ>a AgVo. _rQ>a ho bm§~r _moOÊ`mM§ à_m{UV EH$H$ Amho.
1 _rQ>aMo 100 g_mZ ^mJ Ho$bo, H$s àË`oH$ ^mJ EH$ g|{Q>_rQ>aMm AgVmo.

1 _rQ>a = 100 g|{Q>_rQ>a
gb_m : `mnydu AmnU àdoeX²dmamÀ`m XmoZ Im§~m§Vrb A§Va XmoarÀ`m gmhmæ`mZ§ _moOb§ hmoV§. Vo

nQ²>Q>rÀ¶m gmhmæ¶mZ§ _rQ>a d g|{Q>_rQ>a_Ü`o nwÝhm _moOy.
Z§Xÿ : XmoZ Im§~m§Vrb A§Va 3 _rQ>a 80 g|{Q>_rQ>a Amho.
Q>moZr : _mPm XmXm H$_r A§Va _moOÊ`mgmR>r H§$nmgnoQ>rVrb bhmZ nQ²>Q>r dmnaVmo.
VmB© : `m nQ²>Q>rda _moR>çm IwUm§Odi 1, 2, 3, 4 ..... Ag§ {b{hbob§ AgV§. ¶m g§»¶m

g|{Q>‘rQ>a XmIdVmV. XmoZ _moR>çm IwUm§_Ü`o bhmZ-bhmZ IwUm AgVmV. ˶m IwUm
g|{Q>‘rQ>ahÿZ bhmZ EH$H$ XmIdVmV.

Z§Xÿ : `m à_m{UV nQ²>Q>rZ§ AmnU ISy>Mr bm§~r nwÝhm _moOy.
gb_m : `m ISy>Mr bm§~r 8 g|{Q>_rQ>a Amho.

37

_rQ>a-g|{Q>_rQ>a

‘rQ>a ho 1 g|{Q>‘rQ>aÀ¶m 100 nQ> AgVo. ‘moR>o A§Va ‘moOʶmgmR>r ‘rQ>a ho à_m{UV EH$H$
dmnaVmV.

‘rQ>anQ²>Q>r

F Imbrb A§Va/bm§~r g|{Q>‘rQ>a‘ܶo ‘moOmb H$s ‘rQ>a‘ܶo Vo gmaUrV {bhm

nopÝgbrMr bm§~r dhrMr bm§~r

XmoZ B‘maVt‘Yrb A§Va ‘mo~mBbMr bm§~r

añ˶mMr é§Xr XmoZ Im§~m§Vrb A§Va

F Imbrb A§Vao Vwåhr à‘m{UV EH$H$mV ‘moOm d {‘Ìm§Zm ‘moOm¶bm gm§Jm. nañnam§Mr ‘mno

nS>Vmim. ’$aH$ Pmë¶mg nwÝhm ‘moOm.

D emioÀ¶m g§ajH$ q^VrMr bm§~r D nwñVH$mMr bm§~r D d¥ËVnÌmMr bm§~r

D Q>o~bmMr bm§~r D ìham§S>çmMr bm§~r D Q>o~bmMr O{‘ZrnmgyZMr C§Mr

F ‘mhrV H$ê$Z ¿¶m.

D AmB©À¶m gmS>rMr bm§~r D ~m~m§À¶m eQ>©bm bmJUmè¶m H$mnSmMr bm§~r>

D VmB©À¶m AmoT>UrMr bm§~r D Q>m°dobMr bm§~r D é‘mbmMr bm§~r

F Imbrb _moOUrMm A§XmO H$am. A§XmO ~amo~a H$s MyH$ ¶mMm à˶j ‘moOyZ nS>Vmim ¿¶m.

Zmd A§XmOo à˶j nQ²>Q>rZo /Q>onZo _moOyZ

^|S>rMr bm§~r
JdmarÀ¶m e|JoMr bm§~r
{‘aMrÀ¶m amonmMr C§Mr
ÁdmarÀ¶m YmQ>mMr C§Mr
dS>m˦m PmS>mMm Koa
AmdmamVrb XmoZ PmS>m§_Yrb A§Va

- {ejH$m§gmR>r : dJm©_Ü`o _rQ>a, g|{Q>‘rQ>aÀ¶m IwUm Agbobr nQ²>Q>r q^Vrda bmdyZ {dXçmÏ`mªZm EH$_oH$m§Mr C§Mr

_moOÊ`mMr g§Yr Xçmdr.


38

‘mnZ : dOZ (dñVw‘mZ)
gmoZy : `m M|Sy>M§ dOZ 17 JmoQ>çm Amho.

Z§Xÿ : Ë`mM M|Sy>M§ dOZ _mÂ`mH$S>rb 10 JmoQ>çm ^ab§.


gb_m : Ag§ H$g§ Pmb§ ? EH$mM M|Sy>M§ dOZ doJdoJi§ H$g§ ?
Q>moZr : gmoZyZ§ AmUboë`m JmoQ>çm bhmZ hmoË`m Am{U Z§XÿZ§ AmUboë`m JmoQ>çm _moR>çm hmoË`m,

åhUyZ Ag§ KS>b§ Agob.
VmB© : Aao, Ag§ KS>V§ åhUyZM Va XþH$mZmV dOZ _moOÊ`mMr à_m{UV EH$H§$ åhUOo _mn§

AgVmV.

EH$mM dñVyMo dOZ à_m{UV _mnm§À`m gmhmæ`mZo H$moUrhr Ho$bo Var Vo g_mZM ^aVo.
{H$bmoJ«°_ ho dOZ _moOÊ`mMo à_m{UV EH$H$ Amho.

_bm 1 {H$bmoJ«°_ _bm 5 {H$bmoJ«°_
gmIa Xçm. Jhÿ hdo AmhoV.

_bm 2
{H$bmoJ«°_
Ádmar hdr

Amho.

39

{Xboë`m dñVy§Mo dOZ 1 {H$bmoJ«°_nojm H$_r H$s OmñV Amho, `mMm A§XmO H$am d XþH$mZmV
OmD$Z ImÌr H$ê$Z ¿`m.


dñVyMo Zmd A§XmOo dOZ 1 {H$bmoJ«°_ / àË`j _moOyZ
1 {H$bmoJ«°_nojm H$_r /
1 {H$bmoJ«°_nojm OmñV

{_R>mMm nwS>m
JwimMm _moR>m IS>m

50 {~pñH$Q>o
nmM dmQ>çm gmIa

Q>moZr : AmB©bm {eam H$aÊ`mgmR>r AYm© {H$bmoJ«°_ gmIa hdr hmoVr. KamV Va 1 {H$bmoJ«°_ gmIaoMm nwS>m

hmoVm.

gb_m : _J Vy H$m` Ho$b§g ?

Q>moZr : _r Vr 1 {H$bmoJ«°_ gmIa VamOyÀ`m XmoÝhr nmaS>çm§V WmoS>r WmoS>r Q>mH$V Jobmo Am{U nmaS>r

g_mZ nmVirV amhVrb Ag§ nm{hb§. `mà_mUo EH$ {H$bmoJ«°_ gmIaoMo XmoZ g_mZ ^mJ

Pmbo, åhUOo àË`oH$ nmaS>çmVrb gmIa AYm© {H$bmoJ«°_ Pmbr. Vr AmB©bm {Xbr.

gb_m : _mÂ`m AmB©bmhr AYm© {H$bmoJ«°_ dOZmMr dñVy ~è`mM doim bmJVo.

Q>moZr : _r Vwbm AYm© {H$bmoJ«°_ dOZmM§ _mn V`ma H$ê$Z XoVmo. AYm© {H$bmoJ«°_ gmIa EH$m

nmaS>çmV R>odyZ Xþgè`m nmaS>çmV VodT>çm dOZmMo bhmZ-bhmZ IS>o R>odyZ EH$m é_mbmV

~m§YyZ R>odVmo. Vo Pmb§ AYm© {H$bmoJ«°_M§ _mn.

gb_m : åhUOo `mà_mUo Amnë`mbm nmd {H$bmoJ«°_ dOZmM§ ‘mnhr V`ma H$aVm `oB©b.

F EH$ {H$bmoJ«°_Mo _mn d VamOy `m§À`m gmhmæ`mZo nwT>rb dOZm§Mo Vm§Xÿi/Jhÿ/Ádmar _moOm.

D 2 {H$bmoJ«°_ D 5 {H$bmoJ«°_ D 3 {H$bmoJ«°_ D AYm© {H$bmoJ«°_

F Vw_Mo dOZ {H$Vr Vo nmhm. dJ©{_Ìmnojm dOZ {H$Vr H$_r/OmñV Vo gm§Jm.

F {d{dY àH$maÀ`m dOZH$mQ>çm§Mr _m{hVr ¿`m. dmna H$ê$Z nmhm.

D pñà¨JH$mQ>m D BboŠQ´>m°{ZH$ H$mQ>m D Xm§S>rMm H$mQ>m (VamOy)

D _mUgmMo dOZ H$aVmV Vmo H$mQ>m

40


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