mathematics - kar textbooks/class5/5th... · 2019. 8. 19. · pb i h$zm©q>h$ gah$ma j{uv 5...

$: MATHEMATICS - Kar textbooks/class5/5th... · 2019. 8. 19. · PB I H$Zm©Q>H$ gaH$ma J{UV 5 MATHEMATICS (Revised) B¶Îmm nmMdr 5th Standard ‘amR>r ‘mÜ¶‘ Marathi Medium ^mJ$
IPB I

H$Zm©Q>H$ gaH$ma

J{UV

5

MATHEMATICS(Revised)

B¶Îmm nmMdr5th Standard

‘amR>r ‘mÜ¶‘Marathi Medium

^mJ - 2Part - II

Karnataka Text Book Society (R.)100 Feet Ring Road,

Banashankari 3rd Stage, Bengaluru - 85

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^mJ - 2

AZwH«$‘{UH$m

A.Z§ àH$aU n¥îR> H«$‘m§H$

1. 5-A§H$s g§»`m 1-15

2. ~oarO 16-24

3. dOm~mH$s 25-38

4. g§»`oMo Ad`d d g§»`§mÀ`m nQ>r 39-48

5. AnyUmªH$ 49-69

6. H$moZ 70-86

7. dVw©i aMZm 87-97

8. cm§~r 98-106

9. n[a{_Vr Am{U joÌ\$i 107-128

10. _m{hVr g§H$cZ d {ddaU 129-146

CÎmao 147-153

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àH$aU 1JwUmH$ma

`m àH$aUmÀ¶m AÜ``ZmZ§Va Vwåhr ho {eH$mb XmoZ 3 A§H$s g§»¶m§Mm JwUmH$ma Mma A§H$s g§»¶m§Zm 1 d 2, A§H$s g§»òZo JwUZo 5 A§H$s g§»¶m§Zm 1 A§H$s g§»¶oZo JwUZo JwUmH$ma AmYm[aV Vm|S>r CXmhaUo.

AmnUmg _mhrV Amho H$s "JwUmH$ma' hr J{UVmVrc EH$ _wc^yV {H«$`m Amho."JwUmH$ma hr nwZamdVuV ~oarO hmo . EH$mdoir AmnU H$moUË`mhr XmoZ g§»`m§Mm JwUmH$maH$ê$ eH$Vmo.

JwUmH$ma H$amd`mÀ`m XmoZ g§»`mn¡H$s n{hë`m g§» ocm "JwÊ`' d Xþgè`m g§» ocm"JwUH$' Ago åhUVmV. JwÊ` AgUmè`m g§» ocm JwUH$ g§» oZo JwUco AgVm, oUmè`mg§»òcm Ë`m g§»`m§Mm "JwUmH$ma' Ago åhUVmV.

JwÊ¶ JwUH$ = JwUmH$ma

JwUmH$mamMo JwUY_© …1) H$moUË`mhr g§»òbm eyÝ`Zo JwUë¶mg JwUmH$ma eyÝ` ¶oVmo.

CXm. 12 0 = 0., 8 0 = 02) H$moUË`mhr g§»òbm 1 m g§»òZo JwUë¶mg JwUmH$ma Ë`m g§»òBVH$mM ¶oVmo.

CXm. 9 1 = 9, 6 1 = 63) "JwÊ`' d "JwUH$' m§Mo ñWmZ~Xb H$éZ JwUmH$ma Ho$ë¶mg JwUmH$ma g‘mZ ¶oVmo.

CXm. 4 7 = 28, 7 4 = 28.

COiUr Aä`mg …>I. JwUmH$ma H$am.

1) 35 0 4) 1 2352) 164 1 5) 0 1,0013) 100 0 6) 1 55

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>I>I. JwUmH$ma H$am.1) 45 16 4) 18 422) 63 31 5) 83 173) 162 17 6) 234 22

III. Imbrb CXmhaUo gmoS>dm.1) EH$m dhrMr qH$_V 16 Agë`mg 12 døm§Mr qH$_V {H$Vr?2) B. 5 dr _Ü o {eH$Umè`m EH$m {dÚmÏ`mªMr \$s 38 Agë`mg, 128 {dÚmÏ¶mªMr

EHy$U ’$s Mr a¸$_ {H$Vr?3) EH$m emio_YyZ 63 {dÚmWu ghcrgmR>r Joco. àdmg d OodUIMm©H$[aVm àËòH$

{dÚmÏ`mªH$Sy>Z 150 O_m Ho$bo Agë¶mg EHy$U {H$Vr a¸$_ O_m Ho$br?4) Xhm {H$cmo Vm§XimÀ`m EH$m {nedrMr qH$_V 285 Agë`mg Aem 25 {neì`m§Mr

EHy$U qH$_V {H$Vr?5) EH$m emio_Yrc doJdoJù`m ñnYm©_Üò 16 {dÚmÏ`mªZm àW_ nm[aVmo{fH$ d 16

{dÚmÏ`mªZm {ÛVr` nm[aVmo{fH$ XoÊ`mV Amco. àW_ nm[aVmo{fH$mMr a¸$_ 11 d{ÛVr` nm[aVmo{fH$mMr a¸$_ 9 Agë`mg nm[aVmo{fH$mgmR>r {Xbobr EHy$U a¸$_{H$Vr?

EH$m 3 A§H$s g§»òMm Xþgè`m 3 A§H$s g§»òer JwUmH$ma.CXmhaU 1 …

156 d 267 `m g§»`m§Mm JwUmH$ma H$am.JwUmH$mamV gm_mdcoco Q>ßno1) 267 6 hm JwUmH$ma H$am. JwUmH$ma

1602 hm n{hë`m AmS>ì`m n§º$sV gwQ>oñWmZmnmgyZ S>mdrH$S>o ñWmZdma {chm.

2) AmVm 267 5 = 1335 hm JwUmH$maXþgè`m n§º$sV XeH$ ñWmZmnmgyZ S>mdrH$S>o

2 6 7 1 5 61 6 0 2

1 3 3 52 6 74 1 6 5 2

n{hbr n§º$sXþgar n§º$s{Vgar n§º$s

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Ë¶m Ë¶m ñWmZmda {chm.3) 267 1 = 267 hm JwUmH$ma eVH$

ñWmZmnmgyZ S>mdrH$S>o Ë¶m, Ë¶m ñWmZmda{chm.

4) `m {VÝhr n§{º$Vrc A§H$ ñWmZdma {_idm. 267 156 = 41,652.

CXmhaU 2 …

EH$m dhr_Üò 192 nmZo AmhoV. Aem 250 døm_Üò AgUmè¶m EHy$U nmZm§Mrg§»¶m {H$Vr?

døm§Mr g§»`m = 250

EH$m dhrVrc nmZm§Mr g§»`m = 192

250 døm§_Yrc EHy$U nmZm§Mr g§»`m

= 250 192

= 48,000

250 døm§Vrc nmZm§Mr g§»`m = 48,000

4 A§H$s g§» obm 1 AWdm 2 A§H$s g§» oZo JwUZo.CXmhaU 1 …

2,468 `m g§»òcm 7 Zo JwUmQ>ßnm 1 cm

JwUmH$ma 8 7 = 56 mn¡H$s 6 hogwQ>o ñWmZr {chÿZ 5 ho XeH$ ñWmZrhmVMo {chm.

2 5 0

1 9 2

5 0 0

2 2 5 0 0 2 5 0

4 8 0 0 0

JwÊ` 2 4 6 8JwUH$ 7JwUmH$ma 6

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Q>ßnm 2 am6 7 = 42 hm JwUmH$ma H$am.`mV 5 {_idm. 42 + 5 = 47XeH$ ñWmZr 7 hm A§H$ {chÿZeVH$ ñWmZr 4 hm A§H$ hmVMo{chm.

Q>ßnm 3 am4 7 = 28 hm JwUmH$ma H$ê$Z¶m JwUmH$mamV 4 hmVMo {_idm. 4 + 28= 32 `mn¡H$s 2 hoeVH$ ñWmZr {chÿZ 3 ho ghóñWmZr hmVMo {chm.

Q>ßnm 4 am2 7 = 14 ¶m JwUmH$mamV hmVMo3 {_idm. 3 + 14 = 17 ho 17S>mdrH$S>rc eodQ>À`m XmoZ ñWmZmV{chm.

2,468 bm 7 Zo JwUë¶mg Ë¶m§Mm JwUmH$ma 17,276 `oVmo.CXmhaU 2 …

1,376 d 34 Mm JwUmH$ma H$am.

JwUmH$mamV gm_mdcoco Q>ßno

1) 1,376 cm 4 Zo JwUm. Amcocm JwUmH$magwQ>o ñWmZmnmgyZ S>mdrH$S>o n{hë`m n§º$sV{chm.

1,376 4 = 5,504

2 4 6 8 71 7 2 7 6

2 4 6 8 7

7 6

5

2 4 6 8 7

2 7 6

4

3

1 3 7 6 3 4

n{hbr n§[º$ 5 5 0 4Xþgar n§[º$ 4 1 2 8 0

4 6 7 8 4

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2) 1376 cm 3 Zo JwUm. Amcocm JwUmH$ma XeH$ ñWmZmnmgyZ S>mdrH$S>o Xþgè`mn§º$sV {chm.

1,376 3 = 4,128.

3) XmoÝhr n§º$sVrc àË`oH$ ñWmZmVrc A§H$mMr ~oarO H$am.

1,376 34 = 46,784

CXmhaU 3 …

EH$m H$nS>çm§À`m H$maImÝ`mV XaamoO 2,718 nmoemI V`ma Ho$co OmVmV. Va 23{XdgmV H$maImÝ`mV V`ma Pmcoë`m nmoemIm§Mr g§»`m {H$Vr?

àË oH$ {Xder V`ma hmoUmè`m nmoemIm§Mr g§»`m = 2,718

H$maImÝ`mMo H$m_mMo {Xdg = 23

23 {XdgmV V`ma hmoUmè`m nmoemIm§Mr g§»`m = 2,718 23

= 62,514

23 {XdgmV EHy$U 62,514 nmoemI V¶ma Pmbo. 2 7 1 8 2 3

8 1 5 4 5 4 3 6 0 6 2,5 1 4

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5 A§H$s g§»òcm 1 A§H$s g§»òZo JwUUoCXmhaU 1…

10,843 cm 8 Zo JwUmJwUmH$ma : 10,843 8 =86,74410,843 cm 8 Zo JwUyZ òUmamJwUmH$ma gwQ>o ñWmZmnmgyZ S>mdrH$S>on{hë`m AmS>>ì`m AmoirV {chm. 10,843 8 = 86,744

CXmhaU 2 …21,807 cm 4 Zo JwUm

JwUmH$ma : 21,807 4 =87,22821,807 cm 4 Zo JwUyZ òUmamJwUmH$ma gwQ>o ñWmZmnmgyZ S>mdrH$S>on{hë`m n§º$sV ñWmZdma {chm. 21,807 4 = 87,228

JwÊ` 1 0 8 4 3JwUH$ 8JwUmH$ma 8 6 7 4 4

2 1 8 0 7 4

8 7 2 2 8

ñdmÜ¶m¶ 1.1I. JwUmH$ma H$am

1) 146 173 2) 178 1423) 163 134 4) 183 2085) 150 107 6) 248 2127) 316 100 8) 100 523

A

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II. JwUmH$ma H$am1) 2,861 9 2) 3,947 73) 7,254 6 4) 6,041 55) 8,028 8 6) 4,395 9

III. JwUmH$ma H$am1) 9,025 10 2) 2,549 203) 3,746 23 4) 4,756 195) 2,439 31 6) 1,258 137) 1,028 37 8) 2,375 16

IV. JwUmH$ma H$am1) 21,497 3 2) 15,746 53) 11,048 7 4) 10,039 9

V. Imbrb CXmhaUo gmoS>dm :

1) {gÕmßnm ho \$imMo ì`mnmar AgyZ Vo g§Í`m§Mr {Z`m©V H$aVmV. EH$m noQ>r_Ü`o 144g§Ìr AgUmè`m 259 noQ>çm Ë`mZr {Z`m©V Ho$ë`m. Va Ë`mZr {Z`m©V Ho$coë`m g§Í`m§MrEHy$U g§»`m {H$Vr?

2) EH$ g§a{jV AaÊ¶m‘Ü¶o AmS>ì¶m am§JoV 160 d Cä¶m am§JoV 108 PmS>m§Mr bmJdS>Ho$br Amho. Va {VWo bmJdS> Ho$boë¶m PmS>m§Mr EHy$U g§»¶m {H$Vr?

3) EH$m gm`H$c {dH«o$Ë`mZo 27 gm`H$cr IaoXr Ho$ë`m AmhoV. EH$m gm`H$cMrqH$_V ` 2,067 Agë`mg Ë`mZo Úmd`mMr EHy$U a¸$_ {H$Vr?

4) EH$m eoVH$è`mZo Amnë`m eoVmV 23 q¹$Q>>c Jhÿ {nH${dcm. Ë`mZo Vo Jhÿ 1,935à{V q¹$Q>c `m XamZo {dH$ë`mg Ë`mcm {_iUmar a¸$_ {H$Vr?

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àH$aU 2mJmH$ma

`m àH$aUmÀ¶m AÜ``ZmZ§Va Vwåhr ho {eH$mb. {Xcoë`m g§»`ocm à_m{UV mJmH$ma H«$‘dma nÕVrZo mJVm oB©c. EH$m 5 A§H$s g§»¶obm 1 qH$dm 2 A§H$s g§»`oZo à_m{UV mJmH$ma H«$‘dma

nÕVrZo mJVm oB©c. g§» oÀ`m mJmH$mamg§~§Yr Vm|S>r CXmhaUo gmoS>{dVm oVrc.

_mJrc B`Îmo_Ü o AmnU g_mZ gXñ` AgUmè`m g§»¶mMo JQ> nÕVrZo d nwZamdVuVdOm~mH$sÀ`m nÕVrZo mJmH$ma H$aÊ`mg§~§Yr Aä`mg Ho$cocm Amho.Imcrc CXmhaUm§Mo {ZarjU H$am -1. JQ> nÕVrZo mJmH$ma …

àË oH$ JQ>mV 4 M|Sy> AgVrc Aem[aVrZo, EHy$U 32 M|Sy>Mo AmnU JQ> Ho$ë`mg, EHy$U 8JQ> hmoVmV.

32 ÷ 4 = 82. nwZamdVuV dOm~mH$sÀ`m nÕVrZo mJmH$ma …

32 - 4 = 28 20 - 4 = 16 8 - 4 = 428 - 4 = 24 16 - 4 = 12 4 - 4 = 024 - 4 = 20 12 - 4 = 8dOm~mH$s EHy$U 8 doim Amho. 32 ÷ 4 = 8

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99

COiUr Aä`mg …I. Imcr {Xcoë`m dñVy§Mo, gXñ` g§»`m g_mZ AgUmè`m JQ>mV {d^mJUr H$ê$Z

Ë`m JQ>m^modVr Jmoc H$am d Vw_Mo CÎma àíZmg_moa {Xcoë`m Mm¡H$Q>rV {chm.CXmhaU …-

6 ÷ 3 =

1) 10 ÷ 5 =

2) 20 ÷ 4 =

3) 15 ÷ 3 =

4) 9 ÷ 3 =

II. "nwZamdVuV dOm~mH$s' À`m nÕVrZo Imcrc mJmH$ma H$am.1) 12 ÷ 42) 25 ÷ 53) 42 ÷ 74) 30 ÷ 105) 75 ÷ 15

AmVm AmnU mJmH$mamMr doJir nÕV {eHy$."^mJmH$ma' hr JwUmH$ma {H«$ oÀ`m {déÕ AgUmar {H«$`m Amho.

8 4 = 32 32 ÷ 4 = 8 32 ÷ 8 = 4Ooìhm JQ>mVrc gXñ`m§Mr g§»`m chmZ AgVo, Voìhm darc nÕVrZo mJmH$ma H$aUo

g§mono OmVo.g_Om, Oa AmnUm§g 84 m g§»`og 4 Zo mJmd`mMo Amho. Aemdoir hr nÕV

àXrK© d doiImD$ H§$Q>midmUr VgoM H$ï>Xm`H$ R>aVo. åhUyZ Zoh_r dmnaÊ`mOmoJrgmonr d ghOnUo "^mJmH$ma H$amd`mMr à_m{UV nÕV' gd©Ì dmnacr OmVo.

2

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1010

AmVm AmnU ^mJmH$ma H$amd`mÀ`m à_m{UV nÕVr~Ôc g_OmdyZ KoD$.CXmhaU 1 …

84 m g§» ocm 4 Zo mJm.2 1 ^mJmH$ma

^mOH$ 4) 8 4 ^mÁ` 8

0 440 eof (~mH$s)

^mJmH$mamV gm_mdcoco Q>ßno1) g§» oVrc gdm©V _moR>çm ñWmZmVrc (S>mdrH$S>rc) A§H$mnmgyZ ^mJmH$ma {H«$ ocm

gwédmV H$amdr. darc g§» oV 8 hm A§H$ XeH$ ñWmZr Amho. Ë`mnmgyZ ^mJmH$ma{H«$ ocm gwédmV H$amdr.

2) 4 2 = 8 ^mJmH$ma H$aVmZm 2 hm A§H$ mJmH$ma {chmd`mÀ`m {R>H$mUr{chÿZ ^mÁ` g§»ò_Yrc XeH$ ñWmZÀ`m 8 `m g§»òImcr 8 hr g§»`m {chm.

3) 8 _YyZ 8 dOm H$am. 8 - 8 = 0 ~mH$s 0 {chm.4) gwQ>o ñWmZMm 4 hm A§H$ Imcr ¿`m.

4 1 = 4 ^mJmH$ma {chmd`mÀ`m {R>H$mUr 1 hr g§»`m {chm d 4 `mg§»òImcr 4 hr g§»`m {chm.

5) 4 _YyZ 4 dOm H$am 4 - 4 = 0 hr ~mH$s eof {chmd`mÀ`m {R>H$mUr {chm.¶m nÕVrbm à‘m{UV ^mJmH$mamMr H«$‘dma (AëJmo[aX‘) nÕV åhUVmV.

CXmhaU 2 …à_m{UV mJmH$ma nÕVrZo 49 m g§» ocm 2 Zo mJm

2 4 ^mJmH$ma^mOH$ 2) 4 9 ^mÁ`

4 0 9

81 ~mH$s

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1111

à_m{UV mJmH$ma nÕVr_Ü o gm_mdcoco Q>ßno1) g§»¶oVrb gdm©V ‘moR>çm ñWmZmVrb A§H$mnmgyZ mJmH$ma {H«$¶obm gwédmV H$amdr.

darb g§»¶oV 4 hm A§H$ XeH$ ñWmZr Amho.2) 2 2 = 4 2 ho mJmH$mamÀ`m {R>H$mUr {chm d 4 hr g§»`m mÁ` g§» oVrc

S>mdrH$S>rc n{hë`m g§» oÀ`m Imcr {chm.3) 4 - 4 = 0 hr dOm~mH$s H$ê$Z ~mH$s 0 {chm.4) gwQ>oñWmZMr 9 hr g§»`m Imcr ¿`m. 2 4 = 8 åhUyZ mJmH$mamÀ`m {R>H$mUr

4 {chm.5) gwQ>oñWmZÀ`m 9 m A§H$m_YyZ 8 hr g§»`m dOm H$am 9 - 8 = 1 hr g§»¶m

eof {c{hÊ`mÀ`m {R>H$mUr {chm.

XeH$ ñWmZmVrc g§» ocm àW_ H$m mJmdo?42 ÷ 3 hm ^mJmH$ma Ü`mZmV ¿`m42 ÷ 3

= (40 + 2) ÷ 3= (30 + 12) ÷ 3= (30 ÷ 3) + (12 ÷ 3)= 10 + 4= 14

CXmhaU 3 …lr{Zdmg Odi 32 Mm°H$coQ> AmhoV. Ë`mZo Vo Amnë`m 8 {_Ìm§Zm g_à_mUmV

dmQ>bo. Va àËòH$ {_Ìmcm {_iUmè`m Mm°H$coQ>Mr g§»`m {H$Vr?lr{Zdmg Odirc Mm°H$coQ>Mr EHy$U g§»`m = 32 (^mÁ`){_Ìm§Mr g§»`m = 8 (^mOH$)AmVm 32 m g§»òcm 8 Zo mJm. åhUOo AmnUm§g àËòH$ {_Ìmcm {_iUmè`mMm°H$coQ>Mr g§»`m {_ioc.^mJmH$ma Amåhmbm CÎma XoB©b.

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1212

32÷8 m mJmH$mamV Agboë`m nm`Ý`m

1)3 hr g§»`m 8 nojm chmZ Amho. åhUyZg§»`oVrc nwT>rb A§H$ ^mJmH$mamgmR>r¿`m. åhUOo g§»`m "32' hmoB©c.

2)8 4 = 32 åhUyZ mJmH$mamÀ`m {R>H$mUr4 hr g§»`m {chm Am{U mÁ` AgUmè`mg§»`oÀ`m Imcr 32 {chm.

3)^mÁ` 32 _YyZ 32 dOm H$am. 32 - 32 = 0AmVm eof ñWmZmda "0' hr g§»`m {chm.

àË oH$ {_Ìmcm Mma Mm°H$coQ> {_iVrc.Imcrc H$moï>H$mMo {ZarjU H$am -

eodQ>À`m aH$mÝ`mVrc g§» oMr qH$_V hr Xþgè`m aH$mÝ`mVrc mÁ`À`m qH$_Vrer

g_mZ Amho. darc VŠË`mdê$Z AmnU Ago AZw_mZ H$mTy> eH$Vmo {H$,

(^mOH$ mJmH$ma) + ~mH$s = mÁ`.

^mÁ` = (^mOH$ ^mJmH$ma) + ~mH$sho à_m{UV ^mJmH$mamMo gyÌ Amho.Vwåhr XmoZ g§»`mMm ^mJmH$ma ho gyÌ dmnê$Z nS>Vmim H$éeH$Vm.

A.H«$. mÁ` mOH$ mJmH$ma ~mH$s ^mOH$ mJmH$ma + ~mH$s1 16 3 5 1 3 5 + 1 = 15 + 1 = 16

2 26 4 6 2 4 6 + 2 = 24 + 2 = 26

3 40 5 8 0 5 8 + 0 = 40 + 0 = 40

4 75 7 10 5 7 10 + 5 = 70 + 5 = 75

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1313

CXmhaU 4 …à_m{UV mJmH$mamÀ`m nÕVrZo 125 cm 5 Zo mJm.

2 55)1 2 5 1 0

0 2 52 50 0

^mJmH$mamV gm_mdcoco Q>ßno1) 1 ho 5 nojm chmZ AmhoV. åhUyZ 125 `m g§»`oVrc S>mdrH$S>rc XmoZ A§H$

¿`m. åhUOoM g§»`m 12 hmoB©c2) 5 2 = 10 åhUyZ mJmH$mamÀ`m {R>H$mUr 2hm A§H$ {chm d mÁ` g§» oÀ`m Imcr

10 {chm.3) 12 _YyZ 10 dOm H$am 12 - 10 = 2

2 hr g§»`m ~mH$s {chmd`mÀ`m OmJr {chm.4) AmVm nwT>rc A§H$ 5 hm Imcr ¿`m. g§»`m 25 hmoB©c. 5 5 = 25. åhUyZ

^mJmH$mamÀ`m {R>H$mUr 5 hm A§H$ {chm d 25 hm A§H$ mÁ` g§» oÀ`m Imcr {chm.5) 25 _YyZ 25 dOm H$am. 25 - 25 = 0.

0 hm A§H$ ~mH$s {chmd`mÀ`m {R>H$mUr {chm.Vmim

^mÁ¶ = (^mOH$ ^mJmH$ma) + ~mH$s125 = (5 25) + 0125 = 125 + 0125 = 125

CXmhaU 5 …218 m g§» ocm 2 Zo mJm.

1 0 92 ) 2 1 8

2 0 1

0 1 81 80 0

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1414

^mJmH$mamV gm_mdcoco Q>ßno -

1) 2 1 = 2 åhUyZ 1 hr g§»`m ^mJmH$mamÀ`m {R>H$mUr {chm Am{U g§»òVrc^mÁ`mÀ`m Imcr 2 hr g§»`m {chm.

2) 2 _YyZ 2 dOm H$am. 2 - 2 = 0, ~mH$s 0 {chm.3) 1 hm A§H$ Imcr ¿`m. AmVm 1 2 = 2 nU 2 hr g§»`m 1 m g§»ònojm _moR>r

Amho. 2 0=0, 0 hr 1 nojm bhmZ Amho. åhUyZ ^mJmH$mamÀ`m {R>H$mUr 0hr g§»`m {chÿZ 1 `m ^mÁ` g§»òÀ`m Imcr 0 hr g§»`m {chm.

4) 1 _YyZ 0 dOm H$am. 1 - 0 = 1. AmVm hm A§H$ ~mH$s {chmd`mÀ`m{R>H$mUr {chm.

5) g§» oVrc 8 hm A§H$ Imcr ¿`m. g§»`m 18 hmoB©c. 2 9 = 18. åhUyZ 9 hm A§H$^mJmH$mamÀ`m ñWmZr {chm d ^mÁ` 18 _YyZ 18 hr g§»`m dOm H$am.18 - 18 = 0

6) 0 hr g§»`m ~mH$s {chmd`mÀ`m {R>H$mUr {chm .Vmim

^mÁ¶ = (^mOH$ ^mJmH$ma) + ~mH$s218 = (2 109) + 0218 = 218 + 0218 = 218

CXmhaU 6 …à_m{UV mJmH$mamÀ¶m nÕVrZo 185 cm 12 Zo mJm.

1 5 Q> Vmim 12) 1 8 5 ^mÁ¶ = (^mOH$ ^mJmH$ma)+ ~mH$s

1 2 185 = (12 15) + 50 6 5 185 = 180 + 5

6 0 185 = 1850 5

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C M Y K

1515

CXmhaU 7 …648 bm 15 Zo mJm.

4 3Q> Vmim 15) 6 4 8 ^mÁ¶ = (^mOH$ ^mJmH$ma)+ ~mH$s

6 0 648 = (15 43) + 34 8 648 = 645 + 34 5 648 = 6480 3

CXmhaU 8 …EH$m emioÀ¶m ghcrMm EHy$U IM© ` 7,225 Amho. Ë`m ghcrcm EHy$U 17

{dÚmWu OmUma AmhoV Va ghcrgmR>r àË`oH$ {dÚmÏ`m©Zo Úmd`mMr a¸$‘ {H$Vr?

ghcrcm OmUmè¶m {dÚmÏ`mªMr g§»`m = 17

ghcrMm EHy$U IM© = ` 7,225

àË¶oH$ {dÚmÏ¶mªZo Úmd¶mMr a¸$‘ = ` 7,225 ÷ 17= ` 425

àË`oH$ {dÚmÏ`m©Zo Úmd`mMr a¸$_ ` = 425

Vmim^mÁ¶ = (^mOH$ ^mJmH$ma) + ~mH$s

7,225 = (17 425) + 0

7,225 = 7,225 + 0

7,225 = 7,225CXmhaU 9 …

A{ZVmZo 25 {dÚmÏ¶mªZm dmQ>Ê`mg EHy$U 1,123 ‘mog§~r AmUbr AmhoV. Vr

gd© {dÚmÏ`mªZm dmQ>ë`mZ§Va A{ZVmOdi {H$Vr ‘mog§~r {e„H$ amhVrc?

4 2 517) 7 2 2 5

6 8 0 4 2 3 4 0 8 5

8 50 0

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C M Y K

1616

A{ZVmZo AmUcobr EHy$U ‘mog§~r = 1,123

{dÚmÏ`mªMr g§»`m = 25

àËòH$ {dÚmÏ`m©cm {_iUmè`m ‘mog§ã¶m§Mr g§»`m = 1123 ÷ 25 = 44

àËòH$ {dÚmÏ`m©cm 44 ‘mog§~r {_iVrb

A{ZVm Odi [e„H$ am{hbobr ‘mog§~r = 23

^mJmH$mamV gm_mdcoco Q>ßno -1) 11 hr g§»`m 25 nojm chmZ Amho. åhUyZ g§»òVrc S>mdrH$S>rc n{hco VrZ

¿`m Ë`m_wio ^mÁ` 112 hmoB©c.

2) 25 4 = 100 4 hm A§H$ ^mJmH$mamÀ`m {R>H$mUr {chÿZ 100 hm A§H$

^mÁ` g§»òÀ`m Imcr {chm.

3) 112 _YyZ 100 dOm H$am. 112 - 100 = 12. AmVm 12 hm A§H$ ~mH$s

{chmd`mÀ`m {R>H$mUr {chm.

4) AmVm 3 hm A§H$ Imcr ¿`m. g§»`m 123 hmoB©c. 25 4 = 100. åhUyZ

^mJmH$mamÀ`m {R>H$mUr 4 hr g§»`m {chm d 100 hr g§»`m ^mÁ` 123 `m

g§» oÀ`m Imcr {chm.

5) 123 _YyZ 100 dOm H$am. 123 - 100 = 23 hm A§H$ ~mH$s {chmd`mÀ`m

{R>H$mUr {chm.Vmim

^mÁ¶ = (^mOH$ mJmH$ma)+ ~mH$s1,123 = (25 44) + 231,123 = 1100 + 231,123 = 1,123

4 425) 1 1 2 3

1 0 0 0 1 2 3 1 0 0 0 2 3

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C M Y K

1717

CXmhaU 10 …56,083 m g§» ocm 11 Zo mJm.

5 0 9 8 8 Vmim11) 5 6 0 8 3 ^mÁ¶ = (^mOH$ ^mJmH$ma) + ~mH$s

5 5 8 3 56,083 = (11 5,098) + 5 1 0 8 3 56,083 = 56,078 + 5 0 0 8 3 56,083 = 56,0831 0 8 8

9 9 80 9 3

8 85

CXmhaU 11 …10,005 m g§» ocm 2 Zo mJm.

5 0 0 2 8 Vmim 2) 1 0 0 0 5 ^mÁ¶ = (^mOH$ ^mJmH$ma) + ~mH$s

1 0 8 3 10,005 = (2 5002) + 10 0 0 8 3 10,005 = 10004 + 1

0 8 3 10,005 = 10,005 0 0 8

0 80 5 41

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C M Y K

1818

ñdmÜ¶m¶ 2.1I. Imcrc g§»`m§À`m mJmH$ma {H«$ o_YyZ {_iUmam mJmH$ma d ~mH$s H$mT>m.

1) 48 ÷ 62) 36 ÷ 33) 55 ÷ 44) 72 ÷ 7

II. Imcrc g§»`m§À`m mJmH$ma {H«$ o_YyZ {_iUmam mJmH$ma d ~mH$s H$mT>m.1) 232 ÷ 42) 474 ÷ 63) 255 ÷ 114) 527 ÷ 12

III. Imcrc g§»`m§À`m mJmH$ma {H«$ o_YyZ {_iUmam mJmH$ma d ~mH$s H$mT>m.1) 1,653 ÷ 82) 1,325 ÷ 23) 1,435 ÷ 154) 2,647 ÷ 13

IV. Imcrc g§»`m§À`m mJmH$ma {H«$ o_YyZ {_iUmam mJmH$ma d ~mH$s H$mT>m.1) 24,658 ÷ 22) 14,005 ÷ 73) 32,745 ÷ 104) 12,056 ÷ 12

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C M Y K

1919

V.Imcrc CXmhaUo gmoS>dm.

1) EH$m qeß`mOdi EHy$U 18 _r. H$mnS> Amho. Ë`m_YyZ Vmo 9 eQ>© {edVmo. Va EH$eQ>© {edÊ`mg cmJUmao H$mnS> {H$Vr?

2) EH$m _moQ>magm`H$crcm 240 {H$._r. A§Va OmÊ`mg 5 {cQ>a noQ´>moc cmJVo. Va1 {cQ>a noQ´>mocZo Vr _moQ>magm`H$c {H$Vr {H$._r. A§Va OmB©c?

3) lrYaZo 946 XoD$Z 11 ~mhþë`m IaoXr Ho$ë`m. Va lrYaZo IaoXr Ho$coë`m EH$m~mhþcrMr qH$_V {H$Vr?

4) EH$m ì`º$sMo dm{f©H$ CËnÞ ` 90,912 Agë`mg Ë`m ì`{º$Mo _m{gH$ CËnÞ{H$Vr?

JwUmH$ma d mJmH$ma m XmoÝhr {H«$`m§Mm A§V^m©d Agcocr CXmhaUo -CXmhaU 1 …

EH$m Y_m©Xm`r g§ñWoZo 175 XoUJrXmam§H$Sy>Z àË`oH$s ` 125 à_mUo XoUJr O_mHo$cr. O_m Pmcocr a¸$_ 7 emim§Zm g_à_mUmV dmQ>ë`mg àË oH$ emiocm{_iUmar a¸$_ {H$Vr?XoUJrXmam§Mr g§»`m = 175àË`oH$s O_m Ho$cocr XoUJr = ` 125 O_m Pmcocr EHy$U a¸$_ = ` 175 125

= ` 21,875a¸$_ dmQ>md`mÀ`m emim§Mr g§»`m = 7 àË oH$ emiocm {_iUmar a¸$_ = 21,875 ÷ 7

= ` 3,125

Oa ` 21,875 hr a¸$‘ 7 emim§Zm g‘mZ dmQ>ë¶mg àË¶oH$ emiobm {‘iUmar a¸$‘= ` 3,125

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C M Y K

2020

CXmhaU 2 …AaÊ` ImË`mZo EH$m IoS>çm_Üò Cä¶m 96 am§Jm Am{U AmS>ì¶m 80 am§Jm ‘Ü¶o

PmS>o cmdcr. IoS>çm_Yrc 12 ì`º$sZr Ë`m PmS>m§Mr XoI^mb H$aÊ¶mMr O~m~XmarpñdH$maë`mg, àËòH$ ì`º$scm {H$Vr PmS>m§Mr XoI^mb H$amdr cmJoc?AaÊ` ImË`mH$Sy>Z cmdcoë`m PmS>m§Mr g§»`m = 96 80

= 7,680 PmS>oO~m~Xmar pñdH$macoë`m ì`º$s¨Mr g§»`m = 12àËòH$ ì`º$sZo XoI^mb H$amd`mÀ`m PmS>m§Mr g§»`m = 7,680 ÷ 12

= 640 PmS>o. àË oH$ ì¶º$sZo XoI^mb H$amd¶mÀ¶m PmS>m§Mr g§»¶m = 640

ñdmÜ¶m¶ 2.2

I. gmoS>dm :1) EH$m g§Í`mÀ`m ~mJoV g§Í`mMr 82 PmS>o AmhoV. ~mJoVrc eoVH$è`mZo àËòH$

PmS>mMr 60 g§Ìr VmoSy>Z Vr àËòH$ noQ>r_Üò 12 g§Ìr `mà_mUo âcr. VaVmoS>cocr gd© g§Ìr âÊ`mgmR>r {H$Vr noQ>çm cmJVrc?

2) EH$m emioVrc 15 {dÚmWu ghcrgmR>r Joco hmoVo. Ë`mZr ` 9 à{V {H$._r. `mXamZo dmhZ R>adyZ 325 {H$._r. Mm àdmg Ho$cm. Va àË oH$ {dÚmÏ`m©Zo Úmd`mMra¸$_ {H$Vr?

3) A{ZVmOdi EH$ Jm` Amho Vr XaamoO 8 {cQ>a XÿY XoVo. EH$ {cQ>a XþYmMrqH$_V 18 Amho. EH$ _{hZm (30 {XdgmMm) XÿY {dHy$Z oUmar a¸$_ A{ZVmZoAmnë`m 4 _wcm_Üò g_à_mUmV dmQ>ë`mg àËòH$ _wcmcm {_iUmar a¸$_{H$Vr?

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C M Y K

2121

àH$aU 3~m¡{ÕH$ A§H$J{UV

`m àH$aUmÀ¶m AÜ``ZmZ§Va Vwåhr ho {eH$mb A§XmO H$aÊ¶mÀ¶m nÕVr~m~V ñnï>rH$aU XoVm oB©c. A§XmOo qH$‘V gm§JÊ¶mÀ¶m nÕVr~m~V ñnï>rH$aU XoVm oB©c. XmoZ 5 A§H$s g§»`m§À`m ~oaOoMr Xeghó ñWmZmÀ¶m Odinmg A§XmO H$aVm

oB©c. XmoZ 5 A§H$s g§»¶m§À¶m dOm~mH$sÀ¶m Xeghó ñWmZmÀ¶m Odinmg A§XmO

H$aVm ¶oB©b. XmoZ 5 A§H$s g§»`m§À`m JwUmH$mamMm Xeghó ñWmZmÀ`m n`ªV Odinmg

A§XmO H$aVm oB©c. XmoZ g§»`m§À`m mJmH$mam~m~V A§XmO H$aVm oB©c.

A§XmO H$aUo d OdiMr qH$‘VdV©_mZnÌmVrc XmoZ H$mÌUo Imcr {Xcocr AmhoV. Vr dmMm -

darc ~mV_r_Ü o gm§{JVcoë`m g§» oBVHo$M cmoH$ Ë`m{R>H$mUr hmoVo Ago AmnU åhUyeH$Vmo H$m? CXmhaU 1 _Ü o gm§{JVë`mà_mUo ~amo~a 4,700 {dÚmÏ`m©ZrM {dkmZ àXe©ZmcmoQ> {Xcr H$m?

CXmhaU 2 _Üò gm§{JVë`mà_mUo ~amo~a 80,000 cmoH$M {Za{lV Pmco AmhoV H$m?CXmhaUmV gm§{JVcoë`m g§» oBVHo$M cmoH$ VoWo ZgVrc. _wcm§Mr g§»`m 4,687 qH$dm

4,742 gwÕm Agoc. {ZamlrV cmoH$m§Mr g§»`m 76,839 qH$dm 84,372 Agy eHo$c.

1. EH$m Cƒ àmW{_H$ emio_Üòâ{dcoë`m {dkmZ àXe©Zmcm 4700{dÚmÏ`m©Zr oQ> {Xcr.

2. H$Zm©Q>H$m_Ü o Amcoë`m _hmnyam_wio3,500 cmoH$ _¥Ë`y_wIr nS>co.20,000 cmoH$ ~onÎmm AgyZ80,000 cmoH$ {ZamlrV ~Zco.

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C M Y K

2222

`m CXmhaUmdê$Zg_OyZ oVo H$s, CXmhaUmV gm§{JVcoë`m 4700, 20,000 d80,000 g§»¶mÀ¶m Odinmg g§»¶m BVHo$ AgVrc nU Zo_Š`m Ë`mM g§»¶o BVHo$McmoH$ VoWo ZgVrc. ¶m ZOrH$À¶m g§»`m AmhoV. A§XmOo g§»`m hr H$À`m nÕVrZoH$mT>cr OmVo m H$À`m nÕVrÀ`m AmH$S>o _moS>rcm "A§XmO ~m§YUo' Ago åhUVmV.

CnH«$‘ : Amnë`m X¡Z§{XZ OrdZmVrc Á`m àg§JmV AMyH$ AmH$S>odmarMr Amdí`H$Vm

AgVo. Aem àg§Jm§Mr Á`m {R>H$mUr A§XmOo AmH$S>odmarda mJVo Aem àg§Jm§erVwcZm H$am.

g§»`m§À`m g§~§YrV _yc^yV {H«$`m H$arV AgVmZm ~oarO, dOm~mH$s, JwUmH$ma d^mJmH$ma `mg§~§Yr AmnU A§XmO H$aVmo. CXm. 458 d 540 `m§À¶m ~oaOoMr A§XmOoqH$_V 1000 Aer Yacr OmVo.

AmVm AmnU A§XmO H$gm H$amdm d Ë`mMm Vmim H$gm nhmdm mg§~§Yr Aä`mgH$ê$.EImÚm g§»`oMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>Uo.

_wHy§$X d Jm¡ar ho 43 d 48 m§Mr ~oarO Imcrcà_mUo H$aVrc._wHw§$X gwQ>o ñWmZmVrc g§»`m§Mr ~oarO 3 + 8 = 11 ho EH$ XeH$mer 10 er

~amo~a åhUOoM 1 XeH$ åhUyZ YaVrc.Z§Va Vmo XeH$ ñWmZmVrc g§»`m§Mr ~oarO, 1 XeH$ + 4 XeH$ + 4 XeH$ = 9XeH$ åhUOoM 90 Aer H$aoc.Jm¡arMo CÎma 4 XeH$ + 5 XeH$ Ago XoB©c.= 40 + 50= 90XmoÝhr CÎmao ~amo~a AmhoV. Jm¡arZo CÎma H$go {Xco mg§~§Yr g_OmdyZ KoD$`m.43 d 48 ho 10 À`m H$moUË`m nQ>rV AmhoV?43 hr g§»`m 40 d 50 À`m _Ü o Amho. VgoM 48 hr g§»`m gwÕm 40 d 50 mg§»`m§À`m_Ü oM Amho.

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C M Y K

2323

Imcrc g§»`maofoMo {ZarjU H$am -

43 m g§»òÀ`m ñWmZmMr 40 d 50 m g§»`m§À`m ñWmZm§er VwcZm H$am.«43 hr g§»`m 40 nmgyZ 3 EH$H$ Odi Amho Va 50 nmgyZ 7 EH$Ho$ Xÿa Amho.

åhUyZ 43 ho Odinmg 40 er g_mZ AmhoV. Ago _mZco OmVo. åhUyZ 43 Mr XeH$ñWmZmn`ªVMr A§XmOo qH$_V 40 hmo`.

AmVm 48 m g§»òÀ`m ñWmZmMr 40 d 50 m g§»`m§À`m ñWmZm§er VwcZm H$am.48 hr g§»`m 50 nmgyZ XmoZ EH$H$ Odi Amho Va 40 nmgyZ 8 EH$Ho$ Xÿa Amho.

åhUyZ 48 ho A§XmOo 50 er g_mZ AmhoV Ago _mZco OmVo. åhUyZ 48 Mr XeH$ñWmZmVrc A§XmOo qH$_V 50 Aer Yacr OmVo.

åhUyZ Jm¡ar 40 d 50 m A§XmOo qH$_Vr {_idyZ darc g§»`m§À`m ~oaOoMr A§XmOoqH$_V H$mT>Vo.

‘wHy§$XZo A§XmOo qH$‘V gm§JVmZm 11 gwQ>o ¶mZm A§XmOo 1 XeH$ Ago ‘mZyZ XeH$m§À¶m~oaOo‘Ü¶o hm XeH$ {‘idyZ Ë¶m A§XmOo qH$‘V 90 Aer H$mT>br.

{Xcoë`m g§» oMr OdiÀ`m XeH$ ñWmZmn ªV A§XmOo qH$_V H$er H$mT>mdr?Oa {Xcoë`m g§»òVrc gwQ>o ñWmZMm A§H$ 1,2, 3 qH$dm 4 Agë`mg Ë`m gwQ>o

ñWmZmVrc A§H$mÀ`m {R>H$mUr Ë`m A§H$m§À`m EodOr 0 {chm. Oa gwQ>o ñWmZMm A§H$5,6,7,8 qH$dm 9 Agë`mg m A§H$mEodOr gwQ>o ñWmZr 0 {chm d XeH$ ñWmZmVrcA§H$m_Ü o 1 {_idm.

CXmhaU 1 …583 m g§»òMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>m.gwQ>o ñWmZr eyÝ` {chm

583

XeH$ ñWmZMm A§H$ Z ~XcVm VgmM R>odm. 583 `m g§» oMr XeH$ ñWmZmn ªVMr A§XmOo qH$_V 580 hmo .

40 41 42 43 44 45 46 47 48 49 50

XeH$ ñWmZmn ªVMrA§XmOo qH$_V 580

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C M Y K

2424

CXmhaU 2 …2,837 m g§»òMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>m.gwQ>o ñWmZr 0 {chm

2,837

XeH$ ñWmZÀ`m A§H$mV 1 {_idm. 2,837 m g§» oMr XeH$ ñWmZmn ªVMr A§XmOo qH$_V 2,840.

{Xcoë`m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>Uo.àXrncm 368 m g§» oMr eVH$ ñWmZmn ªVMr A§XmOo qH$_V H$mT>md`mMr Amho.368 hr g§»`m 100 À`m H$moUË`m nQ>tÀ`m _Üò Amho?368 hr g§»`m 300 d 400 `m g§»`m§À`m _Ü o Amho.Imcrc g§»`maofoMo {ZarjU H$am -

368 m g§»òÀ`m ñWmZmMo 300 d 400 m g§»`m§À`m ñWmZmer VwcZm H$am -368 hr 300 m g§» oÀ`m ñWmZmnmgyZ 68 EH$H$ Xÿa Amho Va 400 m g§» oÀ`m

ñWmZmnmgyZ 32 EH$H$ Odi Amho. åhUyZ 368 ho A§XmOo 400 m g§» oer g_ Ago_mZco OmVo. åhUyZ 368 Mr eVH$ ñWmZmn ªVMr A§XmOo qH$_V 400 hmo .

XeH$ ñWmZmn ªVMrA§XmOo qH$_V 2,840

300 310 320 330 340 350 360 370 380 390 400

368

EImÚm g§» oMr eVH$ ñWmZmn ªVMr A§XmOo qH$_V H$er H$mT>mdr?Oa {Xcoë`m g§» oVrc XeH$ ñWmZMm A§H$ 1,2,3 qH$dm 4 Agë`mgXeH$ ñWmZr 0 hm A§H$ {chmdm. Oa XeH$ ñWmZr 5,6,7,8, d 9`mn¡H$s H$moUVmhr A§H$ Agë`mg XeH$ ñWmZr 0 {chÿZ eVH$ñWmZmVrc A§H$m_Üò 1 {_idmdm.

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C M Y K

2525

CXmhaU 3 …3,548 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>m.`m A§H$m§À`m {R>H$mUr 0 {chm

3,548

eVH$ ñWmZMm A§H$ ~Xcy ZH$m 3,548 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V 3,500

CXmhaU 4 …5,764 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V H$mT>m.`m A§H$m§À`m {R>H$mUr 0 {chm

5,764

eVH$ ñWmZmV 1 {_idm 5,764 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V 5,800

{Xcoë`m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>Uo.Z\$sgmcm 1,897 `m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>md`mMr

Amho.1,897 hr g§»`m 1,000 À`m H$moUË`m nQ>rV _moSVo?1,897 hr g§»`m 1,000 d 2,000 `m XmoZ g§»`m§À`m_Ü o oVo.Imcrc g§»`maofoMo {ZarjU H$am -

eVH$ ñWmZMrA§XmOo qH$_V 3,500

eVH$ ñWmZmn ªVMrA§XmOo qH$‘V 5,800

1,897

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C M Y K

2626

1,897 m g§» oÀ`mS ñWmZmMr 1,000 d 2,000 m g§»`m§À`m ñWmZm~amo~a VwcZm H$am.1,897 hr g§»`m 2,000 nmgyZ 103 EH$Ho$ Odi Amho d 1,000 nmgyZ 897 EH$Ho$Xÿa Amho. åhUyZ 1,897 hr g§»`m 2,000 er g_mZ Amho, Ago _mZVmV. 1,897 m g§»`oMr ghó ñWmZmn`ªVMr A§XmOo qH$_V 2,000 oVo.

CXmhaU 5 …25,346 m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.`m {R>H$mUr 0 {chm

25,346

ghó ñWmZMm A§H$ ~Xcy ZH$m 25,346 m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V 25,000

CXmhaU 6 …35,756 m g§» oMr OdiÀ`m ghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.`m ñWmZmV 0 {chm

35,756

ghó ñWmZÀ¶m A§H$mV 1 {_idm 35,756 m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V 36,000

EImÚm g§» oMr ghó ñWmZm§n ªVMr A§XmOo qH$_V H$er H$mT>VmV?Oa {Xcoë`m g§» oVrc eVH$ ñWmZMm A§H$ 1,2,3 qH$dm 4 Agë`mg gwQ>o XeH$d eVH$ ñWmZÀ`m A§H$mEodOr Ë`m ñWmZmV 0 {chm. Oa eVH$ ñWmZMmA§H$5,6,7,8 d 9 Agë`mg Ë`m g§» oVrc gwQ>o, XeH$ d eVH$ ñWmZr eyÝ` (0){chm d ghó ñWmZmÀ`m A§H$m_Ü o 1 {_idm.

ghó ñWmZmn ªVMrA§XmOo qH$_V 25,000

ghó ñWmZmn ªVMrA§XmOo qH$_V 36,000

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2727

{Xcoë`m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>Uo.[aZmbm 16,382 ¶m g§»¶oMr Xeghó ñWmZmn¶ªVMr A§XmOo qH$‘V H$mT>md¶mMr Amho.16,382 hr g§»`m 10,000 À`m H$moUË`m nQtÀ`m_Ü o oVo?16,382 hr g§»`m 10,000 d 20,000 m§À`m_Ü o oVo.Imcrc g§»`maofoMo {ZarjU H$am -

16,382 m g§»òÀ`m ñWmZmMr 10,000 d 20,000 m§À`m ñWmZm§er VwcZm H$am.16,382 hr g§»`m 20,000 m g§» onmgyZ 3,618 EH$Ho$ Odi d 10,000 nmgyZ6,382 EH$H$ Xÿa Amho. åhUyZ 16,382 ho A§XmOo 20,000 er g_ Ago _mZco OmVo.åhUyZ 16,382 m g§» oÀ`m OdiÀ`m Xeghó ñWmZmn ªVMr A§XmOo qH$_V 20,000hmo .

CXmhaU 7 …12,654 m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.`m {R>H$mUr 0 {chm

12,654

10,000 ñWmZMm A§H$ Z ~XcVm VgmM R>odm. 12,654 m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V 10,000 Amho Ago _mZco OmVo.

{Xcoë`m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V H$er H$mT>VmV?Oa {Xcoë`m g§» oVrc ghó ñWmZMm A§H$ 1,2,3 qH$dm 4 Agë`mg Ë`m

g§»òVrc gwQ>o, XeH$, eVH$ d ghó ñWmZr eyÝ` {chm -Oa {Xcoë`m g§» oVrc ghó ñWmZMm A§H$ 5,6,7,8 qH$dm 9 Agë`mg,

Ë`m g§»òVrc gwQ>o, XeH$, eVH$ d ghó ñWmZr 0 {chm d XeghóñWmZmVrc A§H$m_Ü o 1 {_idm.

OdiÀ`m Xeghó ñWmZmn ªVMrA§XmOo qH$_V 10,000

16,382

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2828

CXmhaU 8 …25,748 m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.`m ñWmZmVrc A§H$mEodOr 0 {chm

25,748

Xeghó ñWmZÀ`m A§H$mV 1 {_idm 25,748 m g§» oMr OdiÀ`m Xeghó ñWmZmn ªVMr A§XmOo qH$_V 30,000 hmoVo.

~oarO d dOm~mH$sMm A§XmO ~m§YUo.CXmhaU 1 …2,462 d 3,487 m g§»`m§À`m ~oaOoMr OdiÀ`m XeH$ ñWmZmn ªVMr A§XmOo qH$_VH$mT>m.

2,462 m g§»`oMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V 2,4603,487 m g§»`oMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V + 3,490

A§XmOo ~oarO = 5,950àË`j ~oaOoZo Vmim nmhUo 2,462

+ 3,487 A§XmOo ~oarO hr OdiOdi àË`j ~oaOoBVH$s Amho. 5,949

Ü`mZmV R>odm -Ooìhm AmnUmg EImÚm g§» oMr {Xcoë`m ñWmZmn ªVMr A§XmOo qH$_V

H$mT>md`mMr AgVo, Voìhm Ë`m ñWmZmÀ`m COdrH$S>rc ñWmZm_Ü o AgUmè`m A§H$m§Mo{ZarjU H$am.* Oa Vmo A§H$ 5 nojm chmZ Agoc Va Amnë`mcm {Xcoë`m ñWmZmVrc A§H$

VgmM R>odm d Ë¶mÀ¶m COdrH$S>rb àË¶oH$ ñWmZm‘Ü¶o 0 hm A§H$ {bhm.* Oa Vmo A§H$ 5 BVH$m AWdm 5 nojm _moR>m Agoc Va {Xcoë`m ñWmZmVrc A§H$

1 Zo dmT>dm. d Ë¶mÀ¶m COdrH$S>rb àË¶oH$ ñWmZm‘Ü¶o 0 hm A§H$ {bhm dnwT>Mm A§H$ {chm.

Xeghó ñWmZmMrA§XmOo qH$_V 30,000

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2929

CXmhaU 2 …8,743 d 7,275 m g§»`m§Mr OdiÀ`m eVH$ñWmZm n ªVMr A§XmOo ~oarO H$am.8,743 m g§»`oMr OdiÀ`m eVH$ ñWmZmn`ªVMr A§XmOo qH$_V 8,7007.275 m g§» oMr OdiÀ`m eVH$ ñWmZmn ªVMr A§XmOo qH$_V+ 7,300

A§XmOo ~oarO = 16,000àË`j ~oarO H$ê$Z Vmim nmhUo 8,743

+ 7,27516,018

A§XmOo ~oarO hr OdiOdi àË`j ~oaOoBVH$s Amho.CXmhaU 3 …

24,316 d 34,861 m g§»`m§Mr OdiÀ`m ghó ñWmZmn ªVMr A§XmOo ~oarO H$mT>m.24,316 m g§» oMr OdiÀ`m ghó ñWmZmn ªVMr A§XmOo qH$_V 24,00034,861 m g§» oMr OdiÀ¶m ghó ñWmZmn ªVMr A§XmOo qH$_V+ 35,000

A§XmOo ~oarO = 59,000àË`j ~oarO H$éZ Vmim nmhUo 24,316

+ 34,86159,177

A§XmOo ~oarO hr OdiOdi àË`j ~oaOo BVH$s Amho.CXmhaU 4 …

38,527 d 32,596 m g§»`m§Mr OdiÀ`m Xeghó ñWmZmn ªVMr A§XmOo ~oarO H$mT>m.38,527 m g§» oMr OdiÀ¶m Xeghó ñWmZmn ªVMr A§XmOo qH$_V 40,00032,596 m g§» oMr OdiÀ¶m Xeghó ñWmZmn ªVMr A§XmOo qH$_V + 30,000

A§XmOo ~oarO = 70,000

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3030

àË`j ~oarO H$éZ Vmim nmhUo 38,527+ 32,596

71,123 A§XmOo ~oarO hr OdiOdi àË`j ~oaOo BVH$s Amho.

A§XmOo JwUmH$maCXmhaU 1 …

1,249 d 48 `m g§»`m§Mm gdm©V _moR>çm ñWmZmn`ªVMm A§XmOo JwUmH$ma H$am.

1,249 `m g§» oMr ghó ñWmZmn ªVMr A§XmOo qH$_V 1,000

48 `m g§»`oMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V x 50

A§XmOo JwUmH$ma = 50,000

àË`j JwUmH$mamZo Vmim nmhUo 1,249

x 48

59,952

A§XmOo JwUmH$ma hm àË`j JwUmH$mamnojm chmZ Amho.

CXmhaU 2 …19,426 d 4 `m g§»`m§Mm gdm©V _moR>çm ñWmZmn`ªVMm A§XmOo JwUmH$ma H$am.19,426 `m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V 20,000

x 4 A§XmOo JwUmH$ma = 80,000

àË`j JwUmH$mam_YyZ Vmim nmhUo 19,426x 4

77,704`oWo A§XmOo JwUmH$ma hm àË`j JwUmH$mamnojm _moR>m Amho.

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3131

CXmhaU 3 …EH$m {MÌnQ> J¥hm_Üò àËòH$s 88 AmgZo AgUmè`m 198 am§Jm AmhoV. Va Ë`m

{MÌnQ>J¥hm_Üò àËòH$ Ioim_Üò {dH«$s hmoUmè`m {VH$sQ>m§Mr A§XmOo g§»`m H$mT>m.198 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V 20088 `m g§»òMr XeH$ ñWmZmn`ªVMr A§XmOo qH$_V x 90

àËòH$ Ioim_Üò {dH«$s hmoUmè`m {VH$sQ>m§Mr A§XmOo g§»`m = 18,000àË`j JwUmH$mam_YyZ Vmim nmhUo 198

x 8817,424

òWo A§XmOo JwUmH$ma hm àË`j JwUmH$mamnojm _moR>m Amho.A§XmOo mJmH$maCXmhaU 1 …

44,238 ÷ 95 hm A§XmOo ^mJmH$ma H$am44,238 `m g§» oMr Xeghó ñWmZmn ªVMr A§XmOo qH$_V 40,00095 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V ÷ 100

A§XmOo ^mJmH$ma = 40000 ÷ 100= 400CXmhaU 2Mm°H$coQ>À`m 8 nm{H$Q>m_Üò EHy$U 768 Mm°H$coQ>g AmhoV. Va EH$m nm{H$Q>m_ÜòoAgUmè¶m Mm°H$coQ>gMr A§XmOo g§»`m H$mT>m.

768 `m g§»òMr eVH$ ñWmZmn`ªVMr A§XmOo qH$_V 800Mm°H$coQ> nm{H$Q>m§Mr g§»`m = 8 àËòH$ nm{H$Q>mV AgUmè`m Mm°H$coQ>Mr g§»`m = 800 ÷ 8 = 100 àËòH$ nmH$sQ>mV AgUmè`m Mm°H$coQ>Mr A§XmOo g§»`m = 100àË`j ^mJmH$mam_YyZ Vmim nmhUo. Q>

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3232

àË`oH$ nm{H$Q>mV àË`jnUo AgUmè`mMm°H$coQ>gMr g§»`m = 96.

ñdmÜ`m` 3.1I. Imcr {Xcoë`m g§»`m§Mr ghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.

1) 7>,5472) 3,4693) 15,2384) 32,658

II. Imcr {Xcoë`m g§»`m§Mr Xeghó ñWmZmn ªVMr A§XmOo qH$_V H$mT>m.1) 26,674

2) 32,464

3) 46,379

4) 53,668

III. Imcr {Xcoë`m g§»`mÀ¶m ghó ñWmZmn¶ªVÀ¶m A§XmOo qH$‘VrMr ~oarO H$am.1) 42,125 + 35,637

2) 54,837 + 41,354

3) 33,231 + 20,097

4) 47,463 + 41,541

gwMZm :{Xboë¶m g§»¶m§Mm A§XmOo mJmH$ma H$aVmZm mÁ¶ Am{U mOH$ ¶m§Mr

A§XmOo qH$‘V ¿`mdr.

8) 7 6 8 (967 2 80 4 8

4 80 0

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3333

IV. Imcr {Xcoë`m g§»`mÀ¶m Xeghó ñWmZmn ªVÀ¶m A§XmOo qH$‘VrMr ~oarO H$am.1) 56,256 + 24,872

2) 47,671 + 28,745

3) 32,184 + 45,138

4) 15,025 + 40,165

V.Imcrc g§»`mÀ¶m ghóñWmZmn ªVÀ¶m A§XmOo qH$‘VrMr dOm~mH$s H$am.1) 65,487 - 46,502

2) 45,630 - 32,148

3) 57,146 - 25,472

4) 60,046 - 15,247

VI. Imcrc g§»¶m§À¶m Xeghó ñWmZmn ªVÀ¶m A§XmOo qH$‘VtMr dOm~mH$s H$am.1) 51,689 - 34,6852) 86,853 - 47,8293) 80,808 - 55,0554) 77,777 - 44,444

VII. Imcrc g§»`m§Mm Ë`m§À`m ‘moR>çm ñWmZmn ªVÀ¶m A§XmOo qH$‘VtMm JwUmH$ma H$am.1) 428 x 542) 878 x 463) 5,476 x 114) 2,645 x 18

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3434

VIII. Imcr {Xcoë m g§» m§Mm Ë m§À m ‘moQ>çm> ñWmZmn ªVÀ¶m A§XmOo qH$‘VtMm mJmH$maH$am.1) 398 ÷ 822) 786 ÷ 223) 3,265 ÷ 584) 7,687 ÷ 43

Imbrb CXmhaUo gmoS>dm1) nmoemI V`ma H$amd`mÀ`m EH$m H|$Ðm_Ü o 16,783 eQ>©g d 12,438 n±Q>g EH$m

_{hÝ`mÀ`m H$mcmdYr_Üò {edco AmhoV. Va {edboë¶m nmoemIm§Mr Xeghó

ñWmZmn`ªVMrA§XmOo g§»`m H$mT>m.

2) EH$ d¥ÎmnÌ{dH«o$Vm n{hë`m _{hÝ`m_Üò 36,721 dV©_mZnÌo d Xþgè`m _{hÝ`mV24,172 dV©_mZnÌo {dH$Vmo. Xþgè`m _{hÝ`mV Amcoë`m dV©_mZ nÌmÀ`m {dH«$sÀ`mg§» oVrc KQ> Xe©{dUmè¶m g§»¶oMr Xeghó ñWmZmn ªVMr A§XmOo g§»`m H$mT>m.

3) EH$ aoëdoJmS>r 225 {H$._r. / Vmg doJmZo YmdV Agë`mg EH$m {Xdgm_Üò Ë`maoëdoJmS>rZo AmH«${_coco ghóñWmZmn`ªVMo A§XmOo A§Va H$mT>m.

4) EH$m gwVmamcm Zmoìh|~a _{hÝ`m_Üò ` 18,634 d {S>g|~a _{hÝ`m_Üò` 32,645 BVH$r _Owar {_imcr. {S>g|~a _{hÝ`mV Ë`mcm {_imcoë`m OmXm_OyarMr Xeghó ñWmZmn ªVMr A§XmOo g§»`m H$mT>m.

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35

àH$aU 4Xem§e AnyUmªH$

`m àH$aUmÀ`m AÜ``ZmZ§Va Vwåhr ho {eH$mb - dñVyMr cm§~r Xem§e AnyUmªH$mV gm§JUo. g|{Q>_rQ>a_Ü o cm§~r gm§JÊ`mg Xem§e AnyUmªH$mMm Cn`moJ. _rQ>a_Üò cm§~r gm§JÊ`mg Xem§e AnyUmªH$mMm Cn`moJ. qH$_Vr énò_Üò gm§JÊ`mg Xem§e AnyUmªH$mMm Cn`moJ. AnyUmªH$mMr g§»¶m Xem§e ñdénmV ì¶º$ H$aUo. Xem§e AnyUmªH$mMo AnyUmªH$mV énm§Va H$aUo.

_mJrc B`ÎmoV Vwåhr 0.1, 0.2 ....B. `m gma»`m Xem§e AnyUmªH$mMm Aä`mgHo$cm AmhmV. AmVm AmnU Aem Xem§e AnyUmªH$m§Mm Cn`moJ dñVy§Mr cm§~r d qH$_Vgm§JÊ`mg H$gm H$aVmV mMm Aä`mg H$ê$.

CXmhaU 1 …Imcrc {MÌmMo {ZarjU H$am.nopÝgcMr cm§~r _moOÊ`mg ‘moOnÅ>rMm Cn`moJ Ho$bobm Amho.

nopÝgcMr cm§~r {H$Vr Amho?Vr 3 g|Q>r_rQ>anojm OmñV, na§Vy 4 g|Q>r_rQ>anojm H$_r Amho.

nopÝgcMr cm§~r dmMm.......

1 2 3 4 5 6 7 8

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nyUmªH$m_Ü`o Zgcocr _moO_mno H$er dmMVmV, H$moUVr nyUmªH$ g§»`m Zmhr. hoAmnU nmhÿ_moOnÅ>rMo {ZarjU H$am. Ë`mda 1 g|Q>r_rQ>a _Ü o g_mZ 10 mJ AmhoV. åhUyZ àË oH$ mJ hm g|Q>r_rQ>aMm

EH$ Xem§e Amho. AmnU EH$ Xem§e hm 0.1 g|Q>r_rQ>a Ago gwÕm {c{hVmo. hoM AmnU ""q~Xÿ EH$ g|Q>r_rQ>a'' (Point one centimetre) qH$dm ""eyÝ` q~Xÿ

EH$ g|Q>r_rQ>a'' Ago dmMVmo.AmVm nopÝgcMr AMyH$ cm§~r gm§Jm.Vr 3 g|Q>r_rQ>a Am{U AmR> Xem§e g|Q>r_rQ>a Amho. åhUOoM 3.8 g|Q>r_rQ>a qH$dm3.8 g|._r.g|Q>r_rQ>a = g|._r.AmnU hoM ""VrZ q~Xÿ AmR> g|Q>r_rQ>a'' qH$dm VrZ nyUmªH$ AmR> Xem§e g|Q>r_rQ>aAgo dmMVmo.

CXmhaU 2 …{MÌmVrc ImoS>a~aMr cm§~r _moOm.

ImoS>a~aMr cm§~r {H$Vr Amho?Vr 2 g|Q>r_rQ>a d VrZ Xem§e g|Q>r_rQ>a Amho. hoM AmnU 2.3 g|. ‘r. Ago

{c{hVmo.2.3 hm Xem§e AnyUmªH$ qH$dm Xem§e g§»`m Amho.

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CXmhaU 3 …

{MÌmV XmI{dë`mà_mUo H¥$îUmZo Amnë`m XmoZ eoVm_Ü o amonm§Mr cmJdS> Ho$cr Amho.AmnUmg Ago {XgVo H$s, Ë`mZo EH$ nyU© eoV Am{U Xþgè`m eoVmMm VrZ Xem§e

^mJ cmJdS> Ho$cr Amho.3AnyUmªH$m_Üò ho AmnU 1 — Ago {c{hVmo.10

Xem§eMm Cn`moJ H$ê$Z ho 1.3 Ago {c{hVmo.Xem§em§V {c{hUo d dmMUo.

Xem§e {MÝhmMm Cn¶moJ H$éZ Xem§e H$go {bhmdoV ho nmhÿ.1EH$ Xem§e = — = 0.1, ho eyÝ` q~Xÿ 1 Ago dmMVmV.102

XmoZ Xem§e = — = 0.2, ho eyÝ` q~Xÿ 2 Ago dmMVmV.106XmoZ nyUmªH$ ghm Xem§e = 2 — = 2.6 åhUOo XmoZ q~Xÿ ghm.10

darc CXmhaUmdê$Z AmnU Ago gm§Jy eH$Vmo H$s, q~XÿÀ`m S>mì`m ~mOyMo A§H$ nyUmªH$ qH$dm nyU© mJ AgVmV. q~XÿÀ`m COì`m ~mOyMo A§H$ Xem§e mJ qH$dm AnyUmªH$ mJ AgVmV. Xem§e mJ hm EH$ nyUmªH$mnojm chmZ AgVmo.

8.6 _Üò 8 hm nyUmªH$ ^mJ d 6 hm Xem§e ^mJ.13.7 _Üò 13 hm nyUmªH$ ^mJ d 7 hm Xem§e ^mJ.

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CXmhaU 4 …

+ +

AmH¥$VrV a§J{dcocm EHy$U mJ 2.4 Agm Xe©{dVmV.

nyUmªH$ ^mJ 2 ● 4 Xem§e ^mJ

Xem§e {MÝh (q~Xÿ)1darc {MÌmVrc àËòH$ ^mJ hm EH$ Xem§e, — qH$dm 0.1 Amho.10

AmVm AmnU EH$ Xem§e hm nwÝhm Xhm g_mZ mJmV {d^mJcm Va H$m` hmoB©c ho nmhÿ.

òWo 100 g_mZ ^mJ AmhoV. `m 100^mJmn¡H$s EH$ mJ a§J{dcocm Amho.

1òWo àËòH$ mJmcm EH$ eVm§e qH$dm –– qH$dm 0.01 åhUVmV.100EH$ eVm§eMo Xem§e ê$n 0.01 Amho.

+ +

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CXmhaU 5 …Imcr {Xcoë`m EH$ _rQ>a bm§~r _moOÊ`mÀ`m Q>onMo {ZarjU H$am.

Q>on {H$Vr g_mZ ^mJmV {d^mJcocm Amho?

100 g_mZ mJmV.

åhUyZ àË`oH$ ^mJ hm EH$ _rQ>aMm EH$ eVm§e ^mJ Amho.1— _r., AmnU ho 0.01 _r. Ago {c{hVmo.100

AmVm {MÌmVrc noZMr cm§~r _rQ>a_Ü`o gm§Jy eH$mc H$m§?

Vr 0.08 _r. åhUOo EH$m _rQ>aMm AmR> eVm§e.

Imcrc CXmhaUo nmhm Am{U dmMm.

Xem§e g§»`m nÕVrV, A§H$mMo ñWmZ_yë` Oa Vo COdrH$Sy>Z S>mdrH$S>o EH$ ñWmZgaH$co Va, ñWmZ_yë` XhmÀ`m nQ>rV AgVo. Oa Vo COdrH$Sy>Z S>mdrH$S>o XmoZ A§H$gaH$co Va Ë`mMo ñWmZ_yë` 100 À`m nQ>rV AgVo.

AnyUmªH$ Xem§e AnyUmªH$ Ago dmMm5— 0.05 eyÝ` q~Xÿ eyÝ` nmM qH$dm nmM eVm§e10013— 0.13 eyÝ` q~Xÿ EH$ VrZ qH$dm Voam eVm§e10046 nñVrg q~Xÿ Mma ghm qH$dm 35— 35.46100 nñVrg nyUmªH$ gohoMmirg eVm§e

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40

Xe ghó ghó eVH$ XeH$ gwQ>o A§H$mMo ñWmZ_yë`

Imcrc ñWmZ_yë` VŠË`mMo {ZarjU H$am Am{U Ooìhm A§H$ S>mdrH$Sy>Z COdrH$Sy>ZgaH$Vmo V|ìhm H$m¶ KS>Vo Vo nmhm.Xe ghó ghó eVH$ XeH$ gwQ>o A§H$mMo ñWmZ_yë`

Imcrc VŠË`mV 4 Mr qH$_V H$er ~XcVo. Vo nmhm.

8 3 6 5 4 4 Mo ñWmZ_yë` gwQ>o = 4

6 8 5 4 3 4 Mo ñWmZ_yë` 4 XeH$= 4 x 10 = 40.

3 6 4 8 5 4 Mo ñWmZ_yë` 4 eVH$= 4 x 100 = 400

8 4 5 3 6 4 Mo ñWmZ_yë` 4 ghó= 4 x 1,000 = 4,000

4 5 8 6 3 4 Mo ñWmZ_yë` 4 XeghñÌ= 4 x 1,0000 = 40,000

4 5 3 2 9 4 Mo ñWmZ_yë` 40,000 Amho.4 x 10,000 = 40,000

9 4 5 3 2 4 Mo ñWmZ_yë` 4,000 Amho4,000 = 40,000 ÷ 10.

2 3 4 5 9 4 Mo ñWmZ_yë` 400 Amho= 4,000 ÷ 10

3 5 2 4 9 4 Mo ñWmZ_yë` 40 Amho.= 400 ÷ 10

2 3 5 9 4 4 Mo ñWmZ_yë` 4 Amho.= 40 ÷ 10

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åhUyZ, A§H$ S>mdrH$Sy>Z COdrH$S>o EH$ ñWmZ gaH$cm Va A§H$mMo ñWmZ_yë` 10nQ>rZo H$_r hmoVo.

Ooìhm gwQ>o ñWmZmVrc 4 hm A§H$ S>mdrH$Sy>Z COdrH$S>o AmUIr EH$ ñWmZgaH$VVmo Voìhm Ë`mMo ñWmZ _wë` {H$Vr hmoB©c?

44 ÷ 10 = — ho Mma Xem§e Ago dmMm.10åhUyZ 4 Mo ñWmZ_yë` Mma Xem§e hmo`. Ooìhm gwQ>o ñWmZmVrc A§H$ S>mdrH$Sy>Z COdrH$S>o gaH$Vmo. Ë`mdoir Ë¶m A§H$mMo

ñWmZ_yë` Xem§e hmoB©c.`mà_mUo A§H$mMr ñWmZ_yë` EH$ eVm§e hmoÊ¶mgmR>r Vmo A§H$ S>mdrH$Sy>Z COdrH$S>o

XmoZ ñWmZ gaH$cm nm{hOo.åhUyZ A§H$mMo ñWmZ_yë` nwT>o EH$ Xem§e, EH$ eVm§e ................... Ago

hmoV OmB©c.1 1hoM Ago {c{hVm oVo — , — ,.............................10 100

qH$dm 0.1, 0.01, ..............................

Imbrb ñWmZ‘yë¶ V³Ë¶mMo {ZarjU H$am.

gwQ>o ñWmZ d Xem§e m§À`m_Ü o R>odcoë`m q~Xÿcm Xem§e {MÝh (q~Xÿ) åhUVmV. hm q~XÿXem§e g§»¶oVrb nyUmªH$s mJmcm AnyUmªH$s mJmnmgyZ doJim H$aVmo.

ghó eVH$ XeH$ gwQ>o Xem§e eVm§e1000 100 10 1 0.1 0.01

nyUmªH$s ^mJ Xem§e {MÝh Xem§e AnyUmªH$(q~Xÿ)

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Xem§e {MÝh KmcyZ {c{hcoë`m g§»`m§Zm Xem§e AnyUmªH$ qH$dm Xem§eg§»`m åhUVmV.

AnyUmªH$ {c{hÊ`mMr Xþgar nÕV åhUOo Xem§e g§»`m hmo`. 10,100,1000 ...... N>oX AgUmao AnyUmªH$ åhUOo Xem§e AnyUmªH$ hmoV.

cm§~rMr _moOUr H$aÊ`mg Xem§emMm Cn`moJ1. Amåhmg _mhrV Amho 10 {‘ _r. = 1 g|._r.

åhUyZ 1 {_._r. hm g|._r. Mm EH$ Xem§e ^mJ11 {_._r. = — g|._r. = 0.1 g|._r.1077 {_._r. = — g|._r. = 0.7 g|._r.10717{_._r. = 1— g|._r. = 1.7 g|._r.10

2. Amåhmg _mhrV Amho 100 g|._r. = 1 _r.

åhUyZ 1 g|._r. hm _rQ>aMm EH$ eVm§e (e§^amdm) ^mJ11 g|._r. = — _r. = 0.01 _r.100

55 g|._r. = — _r. = 0.05 _r.100

8989 g|._r. =— _r. = 0.89 _r.1003åhUyZ 7 _r. 3 g|._r. ho 7 _r. — _r.= 7.03 _r. Ago AmnU {c{hVmo.100

`mà_mUo 18 _r. 27 g|._r. åhUOoM 18.27 _r.

{_cr_rQ>a = {_._r.

g|Q>r_rQ>a = g|._r.

_rQ>a = _r.

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n¡em_Ü o Xem§emMm Cn`moJAmåhmg _mhrV Amho H$s,100 n¡go = 1 én`m én¶m Xe©{dUmao {MÝh = åhUyZ EH$ n¡gm hm EH$ én`mMm EH$ eVm§e

11 n¡gm = ` — = 0.0110025VgoM 25 n¡go = ` — = ` 0.25100

åhUyZ AmnU Ago {c{hVmo.2 én o 15 n¡go ho ` 2.1518 én o 60 n¡go ho ` 18.609 én`o 5 n¡go ho ` 9.05640 n¡go ho ` 6.40850 én o 50 n¡go ho ` 850.50

ñdmÜ`m` 4.1I. Imcrc AnyUmªH$ dmMm Am{U AjamV {chm.

1) 0.5 2) 0.13 3) 1.7 4) 5.21II. Imcrc Ajar g§»`m A§H$mV {chm.

1) eyÝ` q~Xÿ EH$-XmoZ 4) Mma q~Xÿ eyÝ` XmoZ2) ghm q~Xÿ AmR> 5) ghm q~Xÿ AmR> Mma3) Xhm q~Xÿ nmM 6) EH$eoho AmR> q~Xÿ eyÝ` ghm.

III. _moH$ù`m OmJm am.1) 8 {_._r. = ......................... g|._r.2) 75 {_._r. = ......................... g|._r.3) 8 g|._r. 5 {_._r. = ......................... g|._r.4) 525 {_._r. = ......................... g|._r.

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IV. _moH$ù`m OmJm am.

1) 8 g|._r. = ......................... _r.

2) 72 g|._r. = ......................... _r.

3) 375 g|._r. = ......................... _r.

4) 4 _r. 80 g|._r. = ......................... _r.

5) 15 _r. 6 g|._r. = ......................... _r.

V. Xem§e AnyUmªH$mV {chm.

1) 75 n¡go = ......................

2) 10 é. Am{U 25 n¡go = ......................

3) 870 n¡go = ......................

4) 782 én o Am{U 10 n¡go = ......................

5) 2050 n¡go = ......................

AnyUmªH$mMo Xem§e AnyUmªH$mV énm§VaVwåhr AnyUmªH$s g§»`m d Xem§e g§»`m `m§Mr _m{hVr H$ê$Z KoVcr Amho.

amOyZo 50 n¡H$s 41 JwU {_i{dco AmhoV.

41ho AmnU AnyUmªH$mV — Ago {bhÿ eH$Vmo.50

hr AnyUmªH$s g§»`m Xem§e énmV H$er ~XcVm oB©c?

AmVm AmnU AnyUmªH$ g§»`m Xem§emV H$er ~XcVm oVo ho nmhÿ.

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CXmhaU 1 …`m {MÌmMo {ZarjU H$am.

a§JrV M|Sy>gmR>r AnyUmªH$ {chm3Vmo Amho —10

hoM Xem§e AnyUmªH$mV VrZ Xem§e qH$dm 0.3

3åhUyZ AmnUmg Ago g_OVo H$s = –– = 0.310CXmhaU 2 …

Imcrc {MÌmMo {Z[ajU H$am.

a§J{dcoë`m mJmgmR>r AnyUmªH$ {chm.7Vmo Amho —10

a§J{dcocm mJ Xem§e AnyUmªH$mV {chm.

gmV Xem§e qH$dm 0.77åhUyZ, — = 0.710

Imcrc VŠË`mMo {ZarjU H$am.

N>oXmVrcAnyUmªH$ N>oX Xem§e ê$neyÝ`m§Mr g§»`m4a) — 10 1 0.41017b) — 10 1 1.710523c) —– 10 1 52.310

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`mdê$Z Amåhmg Ago g_OVo H$s, Oa AnyUmªH$mMm N>oX 10 Agoc VaXem§e_Üò {c{hVmZm g§»òÀ`m A§em_Üò COdrH$Sy>Z EH$ A§H$ gmoSy>Zq~Xÿ R>odmdm.

Imcrc AnyUmªH$m§Mo {ZarjU H$am.2 3 1– , – , –5 5 2

òWo> N>oX 10 Zmhr na§Vy Vmo 10 _Üò ghO ~XcVm òVmo.

2– hm AnyUmªH$ N>oX 10 _Üò énm§VarV H$am5

2 2 x 2 4 2– = ––— = — = 0.4 – = 0.45 5 x 2 10 5

3 3 x 2 6 3Ë`mM à_mUo, – = ––— = —= 0.6 – = 0.65 5 x 2 10 5

1 1 x 5 5 1– = ––— = —= 0.5 – = 0.52 2 x 5 10 2

CXmhaU 3 …

a§J{dcoë`m mJmgmR>r AnyUmªH$ {chm13Vmo Amho —100

a§J{dcocm mJ Xem§e AnyUmªH$mV {chm.

Vmo Amho, Voam eVm§e qH$dm 0.1313åhUyZ, — = 0.13100

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Imcrc VŠË`mMo {ZarjU H$am.

`mdê$Z Amåhmg Ago g_OVo H$s, Oa AnyUmªH$mMm N>oX 100 Agoc VaXem§e_Üò {c{hVmZm g§»òÀ`m A§em_Üò COdrH$Sy>Z XmoZ A§H$ gmoSy>Z q~Xÿ R>odmdm.

ho AnyUmªH$ nmhm.3 7 6 41– , — , — , —4 20 25 50

`m AnyUmªH$m§Mm N>oX 100 Zmhr.

na§Vw A§e d N>oX `m§Zm EH$m g_mZ g§»òZo JwUyZ N>oX 100 H$ê$Z KoVm òVmo.

3 3 x 25 75 3– = —— = — = 0.75 – = 0.754 4 x 25 100 4

7 7 x 5 35 7— = —— = — = 0.35 — = 0.3520 20 x 5 100 20

6 6 x 4 24 6— = —— = — = 0.24 — = 0.2425 25 x 4 100 25

41 41 x 2 82 41— = —— = — = 0.82 — = 0.8250 50 x 2 100 50

N>oXm_YrcAnyUmªH$ N>oX Xem§e ê$neyÝ`m§Mr g§»`m

24a) — 100 2 0.241008b) — 100 2 0.08100

153c) — 100 2 1.53100

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Xem§e AnyUmªH$m§Mo AnyUmªH$mV énm§VaCXmhaU 1 …

{MÌmMo {ZarjU H$am.a§J{dcoë`m mJmgmR>r Xem§e AnyUmªH$ {chmVmo Amho, 0.7 (gmV Xem§e)

7hoM AnyUmªH$mV —107 0.7 = —10

CXmhaU 2 …ÌoMmirg eVm§egmR>r Xem§e AnyUmªH$ {chm. Vmo Amho. 0.43

43AnyUmªH$mV ––10043 0.43 = —100

Imcrc VŠË`mV {Xcoë`m CXmhaUm§Mm Aä`mg H$am.

40.4 04 = 4 1 10 —1090.9 09 = 9 1 10 —10

181.8 18 = 18 1 10 —1040.04 004 = 4 2 100 –—100

780.78 078 = 78 2 100 –—1001671.67 167 = 167 2 100 –—100

AnyUmªH$Xem§eAnyUmªH$

Xem§e {MÝhZgVmZm g§»`m

Xem§e ñWmZm§Mrg§» m N>oX

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CXmhaU 3 …1.42 hm Xem§e AnyUmªH$ AnyUmªH$mV {chm.

1) g§»`m Xem§e {MÝh H$mTy>Z {chm åhUOo A§e hmoVmo. 142

2) Xem§e AnyUmªH$mVrc Xem§e ñWmZo _moOm. Vr 2 AmhoV.

3) N>oXm_Ü`o 1À`m nwT>o XmoZ eyÝ` {chm 100142 1.42 = —100

ñdmÜ`m` 4.2I. Imcrc AnyUmªH$ Xem§e AnyUmªH$mV {chm.

8 7 61) — 2) — 3) —10 10 10

16 42 834) — 5) —– 6) —10 10 10

7 72 8617) —– 8) —– 9) –—100 100 100

162 141 146110) —– 11) —– 12) ——10 100 100

VŠË`mdê$Z, Xem§e AnyUmªH$mMo AnyUmªH$mV énm§Va H$aVmZm Imcrc nm`è`mcjmV R>odmì`mV.

1) {Xcoco Xem§e AnyUmªH$mMo A§H$ Xem§e {MÝh ZgVmZm {chm. Ë`m_wio A§e{_iVmo.

2) {Xcoë`m Xem§e AnyUmªH$mVrc Xem§e ñWmZo _moOm.3) àË¶oH$ Xem§e ñWmZmgmR>r N>oXmV 1À`m nwT>o EH$ eyÝ` R>odm.

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1 3 213) — 14) — 15) —2 4 5

7 38 1716) — 17) — 18) —20 50 25

13 819) — 20) —20 25

II. Imcrc Xem§e AnyUmªH$ AnyUmªH$mV {chm.

1) 0.7 4) 14.5 7) 14.57 10) 8.5

2) 0.02 5) 0.56 8) 85.4 11) 85.61

3) 3.8 6) 8.03 9) 147.5 12) 6.84

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àH$aU 5Am{W©H$ ì¶dhma

`m àH$aUmÀ¶m AÜ``ZmZ§Va Vwåhr ho {eH$mb ê$n¶o Am{U n¡go Xem§e AnyUmªH$mÀ¶m ñdê$nmV {b{hUo.

Am{W©H$ ì¶dhmamda AmYmarV J{UVmÀ¶m Mmahr ‘yb^yV {H«$¶m H$aUo.

n¡gm {‘i{dUo, Ë¶mMr ~MV H$aUo ¶m§Mo ‘hËd AmoiIUo Am{U Ë¶mMmAmdí¶H$VoZwgma dmna H$ê$Z IM© H$aUo Ë¶m§Mo ‘hËd AmoiIUo.

dñVy IaoXr Ho$ë¶mda Ë¶m dñVy§Mr ¶mXr VnmgUo.

~mOmamVrb dñVy§Mr qH$‘V g‘OmdyZ KoD$Z Ë¶mbm AZwgê$Z dñVy IaoXr H$aUo.

IaoXr Ho$boë¶m dñVy§À¶m nmdVrMo ‘hËd OmUyZ KoUo.

nmdVr ({~b) V¶ma H$aUo.

nmdVrM| dmMZ d Ë¶mdê$Z Ë¶mVrb ‘m{hVr OmUyZ KoUo.

Am{W©H$ ì¶dhmamer g§~§YrV g‘ñ¶m‘mJrb B¶ÎmoV Vwåhr ê$n¶o Am{U n¡go ¶m§À¶m ñdê$nmV {Xboë¶m a¸$‘oMr

~oarO Am{U dOm~mH$s, H$aUo, EHy$U qH$‘V Am{U EH$H$ qH$‘V emoYyZ H$mT>UoAm{U Xa’$bH$ Am{U {~b ¶mMr ‘m{hVr {ddaU H$aUo ho {eH$bmV. AmVmAmnU AmUIr H$mhr CXmhaUm§Mm Aä¶mg H$ê$.

CXmhaU 1 :aOZrZo ` 12.50 bm EH$ nwñVH$, ` 28.75 bm EH$ noZ d ` 3.25

bm EH$ nopÝgb IaoXr Ho$br. Va {VZo {dH$V KoVboë¶m gd© dñVy§Mr EHy$UqH$‘V {H$Vr ?

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dñVy§À¶m {H$‘Vr Imbrb à‘mUo AmhoV.nwñVH$ ............................. ` 12.50noZ ................................. + ` 28.75nopÝgb ............................. + ` 3.25dñVy§Mr EHy$U qH$‘V : ` 44.50

gyMZm : EHy$U a¸$‘ H$mT>Vm§Zm ê$n¶o d n¡go EH$m Imbr EH$ H«$‘~Õ[aVrZo{bhmdoV d q~Xÿ Imbr q~Xÿ Agmdm.

CXmhaU 2 :‘mohZbm ` 38.75 qH$‘V Agboë¶m EH$ M|Sy> {dH$V ¿¶md¶mMm Amho.

Ë¶mÀ¶m H$S>o ’$º$ ` 25 AmhoV. Va Ë¶mbm AOyZ {H$Vr a¸$‘oMr JaO Amho?

EH$m M|Sy>Mr qH$‘V = ` 38.75

‘mohZH$S>rb a¸$‘ = - ` 25.00

‘mohZbm nm{hOo Agbobr a¸$‘ = 13.75

‘mohZbm M|Sy> IaoXr H$aÊ¶mgmR>r JaO Agbobr OmñVrMr a¸$‘ = 13.75

gyMZm : ¶m CXmhaUmV XoIrb AmnU nmhÿ eH$Vmo H$s a¸$‘ H«$‘~Õ[aVrZo {b{hbr AgyZ q~XÿImbr q~Xÿ AmhoV.

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AmVm AmnU Am{W©H$ ì¶dhmamVrb ‘yb^yV {H«$¶m§darb Cn¶moJmMrAmUIr H$mhr CXmhaUo nmhÿ.

CXmhaU 3 :EH$m nwñVH$mMr qH$‘V ` 24.25 Amho. Va 6 nwñVH$m§Mr qH$‘V {H$Vr?

ghm nwñVH$m§À¶m qH$‘Vr~m~V Vwåhr H$m¶ {dMma H$amb ?

Ë¶m§Mr qH$‘V EH$m nwñVH$mÀ¶m qH$‘Vrnojm OmñV hmoB©b H$s H$‘r ?

Voìhm§ EHy$U qH$‘V H$mT>Ê¶mgmR>r J{UVmVrb H$moUVr {H«$¶m H$amdr bmJob ?

6 nwñVH$m§Mr EHy$U qH$‘V OmñV hmoUma åhUyZ EH$m nwñVH$m§À¶m qH$‘VrbmEHy$U nwñVH$m§À¶m g§»¶oZo JwUbo AgVm åhUOo 6 Zo JwUbo AgVm EHy$UqH$‘V {‘iVo.

EH$m nwñVH$mMr qH$‘V = ` 24.75

6 nwñVH$m§Mr qH$‘V = ` 24.75 c 6

= ` 148.50

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CXmhaU 4 …8 ~mhþë¶m§Mr EHy$U qH$‘V ` 128.00 Amho; Va EH$m ~mhþbrMr qH$‘V{H$Vr?

EH$m ~mhþbrMr qH$‘V 8 ~mhþë¶m§À¶m qH$‘Vrer VwbZm Ho$ë¶mg OmñV AgobH$s H$‘r Agob ? ho emoYÊ¶mH$arVm J{UVmVrb H$moUVr {H«$¶m Cn¶moJ H$amdr?

EH$m ~mhþbrMr qH$‘V H$‘r AgVo.

Ë¶mH$arVm ~mhþë¶m§À¶m EHy$U qH$‘Vrbm ~mhþë¶m§À¶m g§»¶oZo ^mJm.

` 128 D 88) 1 2 8 ( 16 - 8

4 8 - 4 8

0 0 àË¶oH$ ~mhþbrMr qH$‘V = ` 16

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ñdmÜ¶m¶ 5.1I. gyMZo à‘mUo {H«$¶m H$ê$Z CÎmao emoYm.

1) ` 13.25, ` 6.30 ` 10.40 ¶m§Mr ~oarO =

2) ` 78.45 Am{U ` 69.70 ¶mVrb ’$aH$ =

3) ` 147.25 Am{U 17 ¶m§Mm JwUmH$ma =

4) ` 4,960 bm ` 8 Zo ^mJyZ ¶oUmam ^mJmH$ma =

II. Imbrb CXmhaUo gmoS>dm.

1) ` 279.05 d ` 103.25 ¶m§À¶m ~oaOoVyZ ` 95.80 dOm H$am.

2) ` 32 ho n¡í¶m‘Ü¶o {bhm.

3) ` 19.75 ho n¡í¶m‘Ü¶o {bhm.

4) 4,705 n¡go ho ê$n¶mV {bhm.

Am{W©H$ ì¶dhmamVrb ~oaOoMr CXmhaUo.III. gmoS>dm :1) ‘mÂ¶m Odi ` 625 AmhoV. ‘mÂ¶m d{SbmZr ‘bm ` 450.75 {Xbo Va

‘mÂ¶m Odi AmVm EHy$U {H$Vr a¸$‘ Pmbr ?

2) ‘hoeZo ` 18.5 bm EH$ noZ, ` 10.75 bm EH$ nwñVH$ Am{U ` 125bm EH$ Xáa {dH$V KoVbo. Va Ë¶mZo {dH$V KoVboë¶m gd© dñVy§Mr EHy$UqH$‘V {H$Vr ?

3) {J[aOmZo ^mOrÀ¶m XþH$mZmVyZ ` 36.50 bm XmoZ {H$.J«°. H$m§Xo, ` 12.25bm EH$ {H$.J«°. Q>mo‘°Q>mo Am{U ` 14.75 bm EH$ {H$.J«°. ~Q>mQ>o IaoXrHo$bo. Va {VZo XþH$mZXmambm EHy$U {H$Vr a¸$‘ Úmdr ?

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Am{W©H$ ì¶dhmamVrb dOm~mH$sMr CXmhaUo.IV. gmoS>dm :1) ` 500 ‘YyZ ` 348.25 dOm H$am.

2) dê$UZo ` 475.5 Mr {‘R>mB© {dH$V KoVbr. Ë¶mZo XþH$mZXmambm ` 500Mr ZmoQ> {Xbr Va XþH$mZXma dê$Ubm {H$Vr a¸$‘ naV H$aob ?

3) a{P¶mOdi ` 345 AmhoV. Ë¶mn¡H$s ` 245.75 qH$‘VrMo H$nS>o IaoXrHo$bo Va {VÀ¶mOdi {e„H$ am{hbobr a¸$‘ {H$Vr ?

4) nm¡{U©‘mOdi ` 3425 hmoVo. {VZo Amnë¶m ‘¡{Ì{Ubm gmS>r {dH$V KoÊ¶mgmR>r` 2745.75 {Xbo Va {VÀ¶m Odi {e„H$ am{hbobr a¸$‘ {H$Vr ?

5) Omogo’$À¶m ~±H$ ImË¶mV ` 2,500 {e„H$ hmoVr. Ë¶mn¡H$s ` 1,800.75BVH$s a¸$‘ ñdVçÀ¶m IMm©gmR>r Ë¶mZo H$mTy>Z KoVbr Va, Ë¶mÀ¶m ~±H$ImË¶mV {H$Vr a¸$‘ {e„H$ am{hbr?

Am{W©H$ ì¶dhmamVrb JwUmH$mamMr CXmhaUo.

V. gmoS>dm :1) EH$m A§S>çmMr qH$‘V `4 Amho. Va EH$ S>PZ A§S>¶m§Mr qH$‘V {H$Vr?

2) ñdmVrZo H$mnS> XþH$mZmVyZ EH$ ‘rQ>abm ` 75 XamZo 8 ‘rQ>a H$mnS> IaoXrHo$bo Va {VZo XþH$mZXmambm {H$Vr a¸$‘ Úmdr ?

3) EH$m N>ÌrMr qH$‘V ` 225 Amho Va 15 N>Í¶m§Mr qH$‘V {H$Vr ?

4) EH$ ‘Oya {Xdgmbm ` 525 H$‘{dVmo. EH$ AmR>dS>çmV Vmo {H$Vr a¸$‘H$‘dob ?

5) EH$m Q>o~bMr qH$‘V ` 4,320 Amho Va 16 Q>o~bm§Mr qH$‘V {H$Vr ?

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Am{W©H$ ì¶dhmamVrb ^mJmH$mamMr CXmhaUo.VI. gmoS>dm :1) EH$m gaH$mar Cƒ àmW{‘H$ emioVrb 10 {dÚmÏ¶m©gmR>r 4,000 BVHo$ {eî¶doVZ

‘§Oya Pmbo Va, àË¶oH$ {dÚmÏ¶m©bm {‘iUmar {eî¶doVZmMr a¸$‘ {H$Vr ?2) ‘mohZZo 9 eQ>© {dH$V KoÊ¶mgmR>r ` 1,422 {Xbo Va àË¶oH$ eQ>m©Mr qH$‘V

{H$Vr ?3) ` 4,425 hr a¸$‘ A‘a, AH$~a Am{U A±WZr ¶m§À¶mV g‘mZ dmQ>br Va

àË¶oH$mbm {‘iUmar a¸$‘ {H$Vr ?4) EH$ S>PZ g’$aM§XmMr qH$‘V ` 96 BVH$s Amho Va EH$ g’$aM§XmMr

qH$‘V {H$Vr?5) {dZmoX gwVmaH$m‘ H$ê$Z 6 {XdgmV ` 9,666 {‘i{dVmo Va Ë¶mMr EH$

{XdgmMr H$‘mB© {H$Vr ?

Xa’$bH$ Am{U nmdË¶m‘m{Jb B¶ÎmoV Vwåhr Xa’$bH$ Am{U nmdVr ¶m§Mo {ddaU H$go H$amdo ho {eH$bmAmhmV. Ë¶mÀ¶mer g§~YrV BVa AmUIr H$m§hr CXmhaUm§Mm Aä¶mg H$ê$.

CXmhaU 1…Am¶oem H$m§hr H$nS>o IaoXr H$aÊ¶mgmR>r A§{~H$m Q>o³gQ>mB©ëg ¶m XþH$mZmVJobr {VZo EH$ n±Q>, EH$ eQ>©, ñH$Q>© d ãbmD$O d gbdma gyQ> IaoXrHo$bm H$nS>o n°H$s¨J H$ê$Z XoUmè¶m ì¶³VrZo {Vbm {VZo IaoXr Ho$boë¶mH$nS>¶m§Mr a¸$‘ XþH$mZXmambm XoD$Z Vo H$nS>o KoD$Z OmÊ¶mg gm§{JVbo. n¡goÚmd¶mÀ¶m {R>H$mUr, Am¶oemZo IaoXr Ho$boë¶m H$nS>çmMo dU©Z AgUmar nmdVr{Vbm XoÊ¶mV Ambr Vr nmdVr Imbrb à‘mUo hmoVr.

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CXmhaU 2…

Om°Z EH$m nwñVH$mbm ` 12 à‘mUo 4 nwñVHo$, EH$m noZbm ` 15 à‘mUo6 noZ, EH$m nopÝgbbm ` 3 à‘mUo 6 nopÝgëg Am{U ` 45 qH$‘VrÀ¶mH§$nmg ~m°³g ""pìhOZ ñQ>oeZarO'' Zm§dmÀ¶m XþH$mZmVyZ {dH$V KoVmo.

{dH$V KoVboë¶m dñVy§Mo {ddaU Agbobr nmdVr Om°Zbm {Xbr Amho. {VMo{Z[ajU H$am.

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pìhOZ ñQ>oeZarOO¶ZJa, ~|Jcmoa

nmdVr H«$‘m§H$ 840 {XZm§H$ 22-10-2011J«mhH$mMo Zm§d : Om°ZA.Z§. Vnerb ZJ Xa( `) EHy$U qH$‘V (`)

1. nwñVH$ 4 12.00 48.00

2. noZ 6 15.00 90.00

3. nopÝgb 6 3.00 18.00

4. H§$nmg ~m°³g 1 45.00 45.00

EHy$U ` 201.00AjamV : XmoZeo EH$ ê$n¶o ’$³V.

ghr.CXmhaU 1 d CXmhaU 2 ‘Yrb nmdË¶m§Mr VwbZm H$am.CXmhaU 1 ‘Ü¶o dñVy doJdoJù¶m AmhoV na§Vy àË¶oH$mMo à‘mU "EH$' Amho.CXmhaU 2 ‘Ü¶o ZJm§Mo à‘mU EH$ qH$dm Ë¶mnojm OmñV Amho åhUyZ XamZo

Ë¶m§Zm JwUyZ EHy$U qH$‘V H$mT>br Amho.

XþH$mZmVyZ dñVy IaoXr Ho$ë¶mZ§Va Ë¶m dñVy~m~V d qH$‘Vr~m~V {bhÿZ XþH$mZXmaJ«mhH$mbm Or {MÇ>r XoVmo. Ë¶mbmM "nmdVr' qH$dm "{~b' Ago åhUVmV.

da {Xboë¶m XmoZ CXmhaUmV nmdVr‘Ü¶o Amåhmbm Imbrb JmoîQ>tMr Zm|XHo$br Amho ho {XgyZ ¶oVo.

* XþH$mZmMo Zmd Am{U nÎmm

* IaoXr KoVbobr VmarI

* J«mhH$mMo Zm§d

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* {dH$V KoVboë¶m dñVy§Mr Zmdo

* {dH$V KoVboë¶m dñVy§Mr g§»¶m

* àË¶oH$ dñVyMm Xa

* J«mhH$mZo Úmd¶mMr EHy$U a¸$‘

* XþH$mZXmamMr ghr.

gyMZm : nmdVr hr dñVy IaoXr Ho$ë¶mMm nwamdm AgVmo. J«mhH$ nmdVrXmIdyZ EImXr dñVy ~XbyZ KoD$ eH$Vmo qH$dm Ë¶m dñVy EodOr n¡gonaV KoD$ eH$Vmo åhUyZ J«mhH$mZr XþH$mZXmamH$Sy>Z nmdVr ‘mJyZ ¿¶mdr.

AmUIr H$m§hr nmdVr~m~V OmñV ‘m{hVr OmUyZ KoD$. Imbr EH$ nmdVrMmZ‘wZm {Xbm Amho. Vmo dmMyZ Ë¶mImbr {dMmaboë¶m àým§Mr CÎmao Úm.

CXmhaU 3…

M§ÐH$m§VZo ""ì¶§H$Q>oe àmopìhOZ ñQ>moAg©'' ¶m XþH$mZmVyZ {X. 24-11-2011amoOr Imbr Z‘yX Ho$bobo nXmW© {dH$V KoVbo.

gmIa - ` 37 {H$. J«°. à‘mUo 3 {H$. J«°.

Vm§Xÿi - ` 25 {H$. J«°. à‘mUo 5 {H$. J«°.

Jhÿ - ` 18 {H$. J«°. à‘mUo 4 {H$. J«°.

Vya S>mi - ` 72 {H$. J«°. à‘mUo 2 {H$. J«°.

e|JmVob - ` 92 {H$. J«°. à‘mUo 2 {H$. J«°.

¶m nXmWmªMo {~b² V¶ma H$aÊ¶mV Ambo Amho Ë¶mMo {Z[ajU H$am.

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ì¶§H$Q>oe àmopìhOZ ñQ>moAg©H«$‘m§H$ 17 {XZm§H$ 24-11-2011J«mhH$mMo Zm§d : M§ÐH$m§V

A.Z§. Vnerb ZJ Xa(`) a¸$‘ (`)

1. gmIa 3 {H$.J«°. 37.00 111.00

2. Vm§Xÿi 5 {H$.J«°. 25.00 125.00

3. Jhÿ 4 {H$.J«°. 18.00 72.00

4. VyaS>mi 2 {H$.J«°. 72.00 144.00

5. e|JmVob 2 {H$.J«°. 92.00 184.00

EHy$U a¸$‘ 636-00

AjamV : ê$n¶o ghmeo N>Îmrg ’$³V.ghr.

Imbrb àûZm§Mr CÎmao Úm. 3 {H$.J«°. gmIaoMr qH$‘V = 2 {H$.J«°. e|JmVobmMr qH$‘V = 4 {H$.J«°. JìhmMr qH$‘V = 5 {H$.J«°. Vm§XimMr qH$‘V= 2 {H$.J«°. VyaS>mirMr qH$‘V =

XþH$mZmMo Zm§d :

J«mhH$ H$moU ? :

{dH$V KoVboë¶m nXmWm©Mr g§»¶m {H$Vr ?

nmdVrMr EHy$U a¸$‘ `

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21

2

11

2

11

4

CXmhaU 4…Jm¶ÌrZo {X. 25-11-2011 amoOr "A¶w~ ’y«$Q> ñQ>m°b' ‘YyZ ’$im§Mr IaoXr Ho$br.

g’$aM§X : {H$.J°«. bm ` 35 à‘mUo {H$.J«°.

g§Ìr : {H$.J°«. bm ` 28 à‘mUo {H$.J«°.

Am§~o : {H$.J°«. bm ` 40 à‘mUo 3 {H$.J«°.

Ho$ir : {H$.J°«. bm ` 17 à‘mUo {H$.J«°.

A¶w~ ’«w$Q> ñQ>m°bZ§. : 24 {XZm§H$ 25-11-2011J«mhH$mMo Zm§d : Jm¶Ìr

A.Z§. Vnerb ZJ Xa (`) a¸$‘ (`)

1. g’$aM§X {H$.J«°. 35.00 87.50

2. g§Ìr {H$.J«°. 28.00 42.00

3. Am§~o 3 {H$.J«°. 40.00 120.00

4. Ho$ir {H$.J«°. 17.00 21.25

EHy$U a¸$‘ 270.75AjamV : ê$n¶o XmoZeo gÎma Am{U n¡go n§À¶mhÎma ’$³V.

ghr.Imbrb àým§Mr CÎmao {bhm : ’$im§À¶m XþH$mZmMo Zm§d :

J«mhH$mMo Zm§d :

IaoXr VmarI :

21

2

11

2

11

4

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21

2

11

2

11

4

IaoXr Ho$bobo EHy$U nXmW© :

3 {H$.J«°. Am§ã¶m§Mr qH$‘V :

{H$.J«°. Ho$itMr qH$‘V :

{H$.J«°. g’$aM§Xm§Mr qH$‘V :

{H$.J«°. g§Í¶m§Mr qH$‘V :

gd© ’$im§Mr EHy$U qH$‘V :

CXmhaU 5…

Imbr {Xboë¶m nmdVrMo {Z[ajU H$am Am{U MyH$ Agë¶mg Xþê$ñV H$am.

‘{h‘m aoS>r‘oS> Jm‘}Qg²E‘.Or. amoS>, ‘¡gya.

nmdVr H«$.: 246 {XZm§H$ 26-11-2011J«mhH$mMo Zm§d : lr‘Vr Cfm


1. ~{Z¶Ýg 10 53.00 153.00

2. hmVê$‘mb 08 12.50 100.00

3. gm°³g 12 OmoS> 25.00 300.00

4. ñdoQ>a 02 285.00 285.00

EHy$U a¸$‘ 838.00

AjamV : ê$n¶o AmR>eo AS>Vrg ’$³V.ghr.

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nS>Vmim :~{Z¶ZMr qH$‘V = ` 53 10 ~{Z¶ÝgMr qH$‘V = 53 C 10 = ` 530.00hmVê$‘mbmMr qH$‘V = ` 12.50 8 hmVê$‘mbmMr qH$‘V = 12.50 C 8 = ` 100.00OmoS> gm°³gMr qH$‘V = ` 25 12 OmoS> gm°³gMr qH$‘V = 25 C 12 = ` 300.00ñdoQ>aMr qH$‘V = ` 285 2 ñdoQ>aMr qH$‘V = 285 C 2 = ` 570.00

EHy$U = ` 1500.00

Imbr {Xboë¶m MwH$m Xþê$ñV H$am¶bm hì¶mV. 10 ~{Z¶ÝgMr {H$‘V ` 530 2 ñdoQ>g©Mr qH$‘V ` 570 nmdVrMr EHy$U a¸$‘ ` 1500

ñdmÜ¶m¶ 5.2I. Imbr {Xboë¶m nmdË¶m§Mo {Z[ajU H$ê$Z Ë¶mVrb MwH$m Xþê$ñV H$am.

A‘a Ho$H$ n°bog²{MH$noQ>, hþã~ùir.

H«$.: 350 {XZm§H$ 26-11-2011Zm§d : Hw$‘mar gwYm

A.Z§. Vnerb ZJ Xa (`) a¸$‘ ( `)1. Om‘Mr ~mQ>br 8 65.00 520.002. Ho$H$ 15 8.00 115.003. Mm°H$boQ²>g 12 15.00 156.004. ’«w$Q> ~Ýg 10 5.00 52.00

EHy$U a¸$‘ 853.00AjamV : ê$n¶o AmR>eo ÌonÞ ’$³V.

ghr.

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amoPr ’°$Ýgr ñQ>moAg©217/~r-2, ~|Jiyé.

H«$‘m§H$ : 178 {XZm§H$ 26-11-2011

Zm§d : Hw$‘mar J§Jm


1. ~m§JS>çm 12 4.00 48.002. H$mZmVrb [a§½O 18 9.00 175.003. {Q>H$ë¶m 24 3.00 70.004. A§JR>çm 10 16.00 150.00

EHy$U a¸$‘ 350.00AjamV : ê$n¶o VrZeo nÞmg ’$³V.

ghr.II. Imbr {Xboë¶m ‘m{hVr dê$Z nmdË¶m V¶ma H$am. àË¶oH$ dñVyMrqH$‘V d gd© dñVy§Mr EHy$U qH$‘V H$mT>m.1) [aVmZo Amnë¶m emioÀ¶m dm{f©H$moËgdmgmR>r "‘oKm ñQ>oeZarO' ¶m XþH$mZmVyZImbrb dñVy IaoXr Ho$ë¶m.

` 9 bm EH$ à‘mUo 25 a§JrV H$mJX` 19 bm EH$ à‘mUo 18 gmoZoar a§JmMo H$mJX` 18 bm EH$ à‘mUo 12 Mm§XrÀ¶m a§JmMo H$mJX` 30 bm EH$ à‘mUo 2 qS>H$mÀ¶m ~mQ>ë¶m

2) aU{daqgJZo "hZw‘mZ hmS>©doAa ñQ>moAg©' ‘YyZ Imbrb dñVy IaoXr Ho$ë¶m.` 85 bm EH$ à‘mUo 2 hmVmoS>çm` 25 bm EH$ à‘mUo 6 ~m°³g ‘moio` 30 bm EH$ à‘mUo 8 ~m°³g ñH«y$` 175 bm EH$ à‘mUo 2 ñn°Zg©

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àH$aU 6dOZ Am{U KZ’$i

¶m àH$aUmÀ¶m AÜ¶¶ZmZ§Va Vwåhr ho {eH$mb - X¡Z§{XZ OrdZmV dmnaë¶m OmUmè¶m hb³¶m§ d OS> dñVy§Mo dOZ H$aÊ¶mgmR>r

dmnaë¶m OmUmè¶m EH$H$m§Mr AmoiI. hb³¶m d OS> dOZm§er g§~§YrV EH$H$m§Mr VwbZm H$ê$Z Ë¶m§Mm g§~§Y

ñnîQ> H$aUo. dOZmer g§~§YrV CXmhaUm§Mo {díbofU H$ê$Z J{UVr {H«$¶m§À¶m ghmæ¶mZo

Vr CXmhaUo gmoS>{dUo.

dOZ__Vm, ê$nm, Á¶ybr Am{U a{P¶m ¶m Mm¡KrZr g‘mZ a¸$‘ KmbyZ EH$m

KmD$H$ ì¶mnmè¶mH$Sy>Z EH$ nmoVo Vm§Xÿi IaoXr Ho$bm. ¶m EH$m nmoË¶mVrb Vm§XÿiË¶m Mm¡Kr g‘mZ [aVrZo dmQy>Z KoUma AmhoV.

nmoË¶mVrb Vm§Xÿi g‘mZ dmQy>Z ¿¶md¶mMm Pmë¶mg àW‘ Ë¶m Vm§XimÀ¶mnmoË¶mMo dOZ ‘m{hV AgUo Amdí¶H$ Amho.

dOZmMo à_m{UV EH$H$ ""J«°_'' hmo .

OmñV dOZmÀ`m dñVy§Mo dOZ _moOÊ`mgmR>r S>oH$mJ«°_, hoŠQ>moJ«°_, {H$cmoJ«°_{³d§Q>b Am{U Q>Z hr à_m{UV EH$Ho$ AmhoV.

H$_r dOZmÀ`m dñVy§Mo dOZ _moOÊ`mgmR>r S>ogrJ«°_, g|Q>rJ«°_ Am{U {_{cJ«°_hr à_m{UV EH$Ho$ dmnaVmV.

AmVm à_m{UV EH$H$m~Ôc A{YH$ _m{hVr {_idy.

S>oH$m, hoŠQ>mo, {H$cmo, S>ogr, g|Q>r Am{U {_cr ho eãX "J«°_' ¶m EH$H$mÀ¶mAJmoXa cmdco OmVmV.

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1—21—4

3—4

darc EH$Ho$ J«°_Mm {H$Vdm mJ AmhoV ho nmhÿ VgoM Ë`m§Mm AW© nmhÿ-_moR>r à_m{UV EH$Ho$ chmZ à_m{UV EH$Ho$

1 J«°_ 1 J«°_

1S>oH$m = 10 nQ> S>ogr = — ^mJ 101hoŠQ>mo = 100 nQ> g|Q>r = — ^mJ100 1{H$cmo = 1000 nQ> {_cr = —– ^mJ 1000

1 J«°_er dOZmÀ¶m _moR>çm à_m{UV EH$H$m§Mr VwcZm -

1 J«°_Mo 10 nQ> = 10 J«°_ = 1 S>oH$mJ«°_

1 J«°_Mo 100 nQ> = 100 J«°_ = 1 hoŠQ>moJ«°_

1 J«°_Mo 1000 nQ> = 1000 J«°_ = 1 {H$cmoJ«°_

1 J«°_er dOZmÀ¶m chmZ à_m{UV EH$H$m§Mr VwcZm -

1 11 J«°_Mo — = — J«°_ = 1 S>ogrJ«°_10 101 11 J«°_Mo — = — J«°_ = 1 g|Q>rJ«°_100 1001 11 J«°_Mo —–> = —– J«°_ = 1 {_crJ«°_1000 1000

X¡Z§{XZ OrdZmV dmnaÊ`mV oUmar dOZmMr à_m{UV EH$Ho$ -

1 Q>Z² = 1000 {H$. J«° 1 q¹$Q>c = 100 {H$cmoJ«°_

1 {H$. J«° = 1000 J«°. {H$. J«° = 750 J«°.

{H$. J«° = 500 J°«. {H$. J«° = 250 J«°.

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dOZmÀ¶m EH$H$m§Mo ê$nm§VadOZmer g§~§YrV ‘moR>çm EH$H$mMo bhmZ EH$H$mV ê$nm§Va H$aVm§ZmMo {Z¶‘-{H$cmoJ«°_Mo J«°__Üò ê$nm§Va H$aVmZm 1000 Zo JwUmdo.hoŠQ>moJ«°_Mo J«°__Ü o énm§Va H$aVmZm 100 Zo JwUmdo.S>oH$mJ«°_Mo J«°__Üò énm§Va H$aVmZm 10 Zo JwUmdo.

dOZm§À¶m _moR>çm à_m{UV EH$H$mMo chmZ à_m{UVEH$H$mV énm§Va H$aVmZm JwUmH$ma H$amdm.

AmVm, dOZmÀ¶m EH$H$m§Mo énm§Va H$go H$aVmV Vo nmhÿ -CXmhaU 1 … 3 {H$cmoJ«°_ åhUOo {H$Vr J«°_?

1 {H$cmoJ«°_ =1000 J«°_ 3 {H$cmoJ«°_ = 1000 X 3 = 3000 J«°_g²

CXmhaU 2 … 4 hoŠQ>moJ«°_ åhUOo {H$Vr J«°_?1 hoŠQ>moJ«°_ = 100 J«°_ 4 hoŠQ>moJ«°_g² = 100 X 4 = 400 J«°_g²

CXmhaU 3 … 15 S>oH$mJ«°_g² åhUOo {H$Vr J«°_?1 S>oH$mJ«°_ = 10 J«°_ 15 S>oH$mJ«°_g² = 10 X 15 = 150 J«°_g²

CXmhaU 4 … 5 q¹$Q>c åhUOo {H$Vr {H$bmo J«°_ ?1 q¹$Q>c = 100 {H$cmoJ«°_5 q¹$Q>c = 100 X 5 = 500 {H$cmoJ«°_

dOZmer g§~§YrV bhmZ EH$H$m§Mo ‘moR>çm EH$H$m ‘Ü¶o ê$nm§Va H$aUo {df¶r {Z¶‘.

J«°_Mo {H$cmoJ«°__Üò énm§Va H$aVmZm 1000 Zo mJmdo. {_cr J«°_Mo J«°__Üò énm§Va H$aVmZm 1000 Zo mJmdo. {H$cmoJ«°_Mo q¹$Q>c_Ü o énm§Va H$aVmZm 100 Zo mJmdo.

dOZm§À¶m chmZ à_m{UV EH$H$mMo _moR>çm à_m{UV EH$H$mV énm§VaH$aVmZm ^mJmH$ma H$amdm.

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Imcrc CXmhaUm§Mm Aä`mg H$ê$.

CXmhaU 5 … 500 {_crJ«°_ åhUOo {H$Vr J«°_?1000 {_crJ«°_ = 1 J«°_

500 1 500 {_crJ«°_ = —– = – J«°_1000 2

CXmhaU 6 … 1600 g|Q>rJ«°_ åhUOo {H$Vr J«°_?100 g|Q>rJ«°_ = 1 J«°_

1600 1600 g|Q>rJ«°_ = —– = 16 J«°_100

CXmhaU 7 … 280 S>ogrJ«°_ åhUOo {H$Vr J«°_?10 S>ogrJ«°_ = 1 J«°_

280 280 S>ogrJ«°_ = —– = 28 J«°_10

CXmhaU 8 … 750 J«°_ åhUOo {H$Vr [H$cmo J«°_?1000 J«°_ = 1 {H$cmo J«°_

750 3 750 J«°_ = —– = – {H$cmoJ«°_ 1000 4

CXmhaU 9 … 850 {H$cmoJ«°_ åhUOo {H$Vr q¹$Q>c?100 {H$cmoJ«°_ = 1 q¹$Q>c

850 1 850 {H$cmoJ«°_ = — = 8– q¹$Q>c100 2

H¥$Vr 1 …emioVrc dOZ H$mQ>çmda Vw_Mo dOZ nmhm.

H¥$Vr 2 …OdiÀ`m {H$amUm XþH$mZmV OmD$Z 50 J«°_, 100 J«°_, 200 J«°_. 500 J«°_,

1 {H$cmoJ«°_, 2 {H$cmoJ«°_, 5 {H$cmoJ«°_ Am{U 10 {H$cmoJ«°_ dOZmMo {ZarjUH$ê$Z Ë`m§Mr AmoiI H$ê$Z ¿`m.

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H¥$Vr 3 …gmoZmaÀ`m XþH$mZmcm oQ> XoD$Z 50 {_crJ«°_, 100 {_crJ«°_, 200 {_crJ«°_,

500 {_crJ«°_, 1 J«°_, 2 J«°_, 5 J«°_ Am{U 10 J«°_ dOZmMo {ZarjU H$am.

dOZÀ¶m ‘moO‘mnmda AmYmarV CXmhaUo -CXmhaU 1 … Imcrc ~oarO H$am.

15 {H$cmoJ«°_, 750 J«°_, 13 {H$cmoJ«°_ Am{U 227 J«°_

{H$cmoJ«°_ J«°_15 00000 75013 00000 22728 97728 {H$cmoJ«°_ 977 J«°_.

CXmhaU 2 …EH$m XþH$mZXmamH$S>o 100 {H$cmo J«°_ Vm§XimMo nrR> Amho. Oa Ë`mZo Ë`mVrc

45 {H$cmo J«°_ nrR> {dH$co. Va XþH$mZmV {e„H$ Agcoco nrR> {H$Vr?XþH$mZmV Agcoco Vm§XimMo nrR> 100 {H$cmoJ«°_{dH$coco Vm§XimMo nrR> - 45 {H$cmoJ«°_{e„H$ Agcoco Vm§XimMo nrR> = 55 {H$cmoJ«°_ XþH$mZmV {e„H$ Agcoco Vm§XimMo nrR> = 55 {H$cmo J«°_.

CXmhaU 3 …am_æ`mÀ`m Hw$Qw>§~mV Mma _mUgo AmhoV. àË`oH$ _mUgmbm aoeZ XþH$mZXma

12 {H$cmoJ«°_ Vm§Xÿi XoVmo. Va am‘æ¶mÀ¶m Hw$Qw>§~mcm EHy$U {H$Vr Vm§Xÿi {_imcm?àË oH$ _mUgmcm {_imcobm Vm§Xþi= 12 {H$cmoJ«°_ 4 _mUgm§Zm {_imcocm Vm§Xÿi= 12 {H$cmoJ«°_ X 4 = 48 {H$cmoJ«°_

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CXmhaU $4 …

am_y, A{Zc, aV d {W_æ`m ho Mma eoVH$ar {_iyZ 50 {H$cmoJ«°_ gy ©\w$cmMo ~rIaoXr H$ê$Z Ë`mMo n¡go gwÕm Ë¶m gdmªZr gma»¶mM a¸$‘oZo {Xbo. gy`m©\w$cmMo ~r Vogdm©_Üò g_mZ dmQy>Z KoVmV.Va àËòH$ eoVH$è`mcm {H$Vr {H$cmoJ«°_ ~r {_imco?

gy`©\w$cmÀ`m ~r Mo EHy$U dOZ= 50 {H$cmoJ«°_

EHy$U eoVH$è`m§Mr g§»¶m = 4 50

àËòH$ eoVH$è`mcm {_imcoco ~r = — 4

= 12.5 {H$cmoJ«°_

= 12 {H$cmoJ«°_ 500 J«°_.

ñdmÜ`m` 6.1I) Vm|S>r CÎmao Úm …

1) Aë~Q>© 16 {H$cmoJ«°_ Ádmar Am{U 15 {H$cmoJ«°_ Vm§Xyi XþH$mZmVyZ {dH$V

KoVmo. Vmo XmoÝhr nmH$sQ>o EH$m {nedrV R>odVmo. Va Ë`m {nedrMo EHy$U

dOZ {H$Vr?

2) EH$m emiocm Aja Xmgmoh `moOZoVyZ 62 {H$cmoJ«°_ Vm§Xÿi {_imcm. Oa 15

{H$cmoJ«°_ Vm§Xÿi OodUmgmR>r dmnacm Va {e„H$ am{hcocm Vm§Xÿi {H$Vr ?

3) EH$m {nedrV 20 {H$cmoJ«°_ adm ‘mdVmo. Va 140 {H$cmoJ«°_ adm

{neì`m_Ü o âÊ`mg {H$Vr {neì`m cmJVrc?

4) EH$m ì`mnmè`mH$S>o gmIaoMr 5 nm{H$Q>o AgyZ Ë¶m àË oH$ nm{H$Q>mV 15 {H$cmoJ«°_

gmIa Amho. Va 5 nmH$sQ>m ‘Yrb gmIaoMo EHy$U dOZ {H$Vr ?

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II) énm§Va H$am1) 7 {H$cmo J«°_ = .................. J«°_2) 16 J«°_ = .................. {_crJ«°_3) 6000 J«°_ = .................. {H$cmoJ«°_4) 750 {_crJ«°_ = .................. J«°_5) 12 q¹$Q>c = .................. {H$cmoJ«°_6) 1500 {H$cmoJ«°_ = .................. q¹$Q>c

III) ~oarO H$am.

1) 4 {H$cmoJ«°_ 250 J«°_ Am{U 12 {H$cmoJ«°_ 355 J«°_.




5) 6 {H$cmoJ«°_ 250 J«°_, 8 {H$cmoJ«°_ 430 J«°_, 7 {H$cmoJ«°_ 220 J«°_ Am{U430 J«°_.

IV) dOm~mH$s H$am.

1) 28 {H$cmoJ«°_ 250 J«°_ _YyZ 13 {H$cmoJ«°_ 250 J«°_





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V) Imcrc CXmhaUo gmoS>dm…

1) ^mOrÀ¶m XþH$mZmVyZ amYmZo 2 {H$cmoJ«°_ 500 J«°_ JmOa, 2 {H$cmoJ«°_

500 J«°_ dm§Jr Am{U 3 {H$cmoJ«°_ 250 J«°_ Q>mo_°Q>mo {dH$V KoVco.

Va {VZo KoVboë¶m ^mOrnmë¶mMo EHy$U dOZ {H$Vr ?

2) EH$m ì`mnmè`mOdi 68 {H$cmoJ«°_ 250 J«°_ dOZmMo Jhÿ AmhoV.

Ë`mZo EH$m {JèhmB©H$mcm 15 {H$cmoJ«°_ 250 J«°_ d Xþgè`m {JèhmB©H$mcm

13 {H$cmoJ«°_ 500 J«°_ Jhÿ {dH$co. Va am{hcoë`m JìhmMo dOZ

{H$Vr ?

3) EH$ EH$a eoVmV 29 q¹$Q>c 50 {H$. J«°_ ^mV {nH$Vo amMßnmMo

30 EH$a eoV Amho Va Vmo Ë`mV {H$Vr ^mV {nH$dy eHo$c?

4) 18 {H$cmoJ«°_ 400 J«°_ gmIa Mma {neì¶mV g‘mZ dOZ hmoB©b Aem

[aVrZo ^acr Amho. Va àË oH$ {nedrMo dOZ {H$Vr hmoB©b ?

5) EH$ eoVH$ar EH$m eoVmVyZ 60 {H$cmoJ«°_ 400 J«°_ Va Xþgè`m eoVmVyZ

56 {H$cmoJ«°_ 800 J«°_ H$m§Xo {nH${dVmo. Ë`m_Yrc 98 {H$cmoJ«°_ 200

J«°_ H$m§Xo Vmo {dH$Vmo. Va am{hcoë`m H$m§ÚmMo dOZ {H$Vr?

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KZ’$i¶m KQ>H$m§Mm Aä¶mg Ho$ë¶mZ§Va Vwåhr ho {eH$mb. bhmZ Z ‘moR>çm KZ’$imer g§~§YrV EH$H$mMr ‘m{hVr. KZ’$im§er g§~§YrV ‘moR>çm EH$H$mMr bhmZ EH$H$mer VwbZm d Ë¶m‘Yrb

g§~§Y. KZ’$imda AmYm[aV Agcocr CXmhaUo gmoS>dyZ Ë¶m§Mo {díbofU H$aVm oVo.

AmH¥$Vr (1) d (2) _Yrb XmoÝhr m§S>r XÿYmZo abocr AmhoV.

Vwåhr gm§Jy eH$mb H$m§, H$moUË`m ^m§S>çmV OmñV XÿY Amho?

àË`oH$ m§S>çmV {H$Vr XÿY Amho ho A§XmOo Vwåhr gm§Jy eH$mb H$m§ ? ho gm§JVm`oV Zmhr hmo¶ Zm§ ?

àË oH$ m§S>çmVrb XÿY {H$Vr Amho, ho gm§JÊ`mgmR>r àË oH$ m§S>çmVrc XþYmÀ¶mKZ’$imMo ‘mnZ Ho$bo nm{hOo.

^m§S>çm_Ü o Agcoë`m EHy$U Ðdmcm KZ’$i Ago åhUVmV.

KZ’$i ho KZ EH$H$mV gm§JrVbo OmVo.

KZ’$i _moOÊ`mMo à_m{UV EH$H$ ""{cQ>a'' ho Amho.

S>oH$m {cQ>a, hoŠQ>mo {cQ>a Am{U {H$cmo{bQ>a hr ÐdmMo _moOÊ`mMr _moR>o KZ’$ià_m{UV EH$Ho$ AmhoV.

AmH¥$Vr (1) AmH¥$Vr (2)

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S>ogr{cQ>a, g|Q>r {bQ>a Am{U {_cr {bQ>a hr ÐdmMo bhmZ _moOÊ`mMr KZ’$ibhmZ à_m{UV EH$Ho$ AmhoV.

AmVm `m à_m{UV EH$H$m~Ôc OmñV _m{hVr {_idy.S>oH$m, hoŠQ>mo, {H$cmo, S>ogr, g|Q>r Am{U {_cr ho eãX "{cQ>a'À`m AJmoXa

{c{hco OmVmV.hr EH$Ho$ {cQ>aÀ`m {H$Vr nQ> Ë¶m‘Ü¶o gm‘mdbobo AmhoV ho XmI{dVmV.

åhUyZ àW_ darc eãXm§Mo AW© {eHy$,

‘moR>çm KZ’$imer g§~§YrV EH$Ho$ bhmZ KZ’$imer g§~§YrVEH$ {bQ>a EH$ {bQ>a

1S>oH$m = 10 nQ> S>ogr = —– ^mJ 101hoŠQ>mo = 100 nQ> g|Q>r = —– ^mJ100

1{H$cmo = 1000 nQ> {_cr = —— ^mJ 1,000

EH$ {cQ>aMr _moR>çm EH$H$m~amo~a VwcZm -

1 {cQ>aMo 10 nQ> = 10 {cQ>a = 1 S>oH$m{cQ>a1 {cQ>aMo 100 nQ> = 100 {cQ>a = 1 hoŠQ>mo{cQ>a1 {cQ>aMo 1000 nQ> = 1000 {cQ>a = 1 {H$cmo{cQ>a

EH$ {cQ>aMr chmZ EH$H$m~amo~a VwcZm -

1 11 {cQ>aMm — ^mJ = — {cQ>a = 1 S>ogr{cQ>a10 10 1 11 {cQ>aMm —— ^mJ = —— {cQ>a = 1 g|Q>r{cQ>a 100 100 1 11 {cQ>aMm —— ^mJ = —— {cQ>a = 1 {_cr{cQ>a 1,000 1,000

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1—2

1—4

KZ’$imer g§~§YrV X¡Z§{XZ dmnamV Agcocr à_m{UV EH$Ho$ -

1 {cQ>a = 1000 {_cr{cQ>a

{cQ>a = 500 {_cr{cQ>a

{cQ>a = 250 {_cr{cQ>a

1 {H$cmo {cQ>a = 1,000 {cQ>a

{cQ>a 'l', {_cr {cQ>a 'ml' Am{U {H$cmobrQ>a 'kl' ¶m Ajam§Zo Xe©{dVmV.KZ’$imÀ¶m EH$m EH$H$mMo Xþgè`m EH$H$mV énm§Va H$go H$aVmV

KZ’$imÀ¶m ‘moR>çm EH$H$mMo bhmZ EH$H$mV ê$nm§Va H$aUo.{Z¶‘ :

{H$cmo{cQ>aMo {cQ>a _Ü o ê$nm§Va H$aVmZm 1,000 Zo JwUmdo.hoŠQ>mo{cQ>aMo {cQ>a _Ü o énm§Va H$aVmZm 100 Zo JwUmdo.S>oH$m{cQ>aMo {cQ>a _Ü`o énm§Va H$aVmZm 10 Zo JwUmdo.

KZ’$iÀ¶m ‘moR>çm EH$H$mMo chmZ EH$H$mV énm§Va H$aVmZmJwUmH$ma H$amdm.

CXmhaU 1 … 4 {H$cmo{cQ>a åhUOo {H$Vr {cQ>a?1 {H$cmo{cQ>a = 1,000 {cQ>a 4 {H$cmo{cQ>a = 1,000 X 4 = 4,000 {cQ>a

CXmhaU 2 … 5 hoŠQ>mo{cQ>a åhUOo {H$Vr {cQ>a?1 hoŠQ>mo{cQ>a = 100 {cQ>a 5 hoŠQ>mo{cQ>a = 100 X 5 = 500 {cQ>a

CXmhaU 3 … 17 S>oH$m{cQ>a åhUOo {H$Vr {cQ>a?1 S>oH$m{cQ>a = 10 {cQ>a 17 S>oH$m{cQ>a = 10 X 17 = 170 {cQ>a

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KZ’$imÀ¶m bhmZ EH$H$mMo KZ’$imÀ¶m ‘moR>çm EH$H$mV ê$nm§Va H$aUo.{Z¶‘ :

{cQ>aMo {H$bmo {cQ>a_Ü o énm§Va H$aVmZm 1,000 Zo ^mJmdo.{cQ>aMo hoŠQ>mo {cQ>a_Ü o énm§Va H$aVmZm 100 Zo ^mJmdo.{cQ>aMo S>oH$m {cQ>a_Ü o énm§Va H$aVmZm 10 Zo ^mJmdo.{‘br {cQ>aMo {cQ>a_Ü o énm§Va H$aVmZm 1,000 Zo ^mJmdo.

KZ’$imÀ¶m bhmZ EH$H$m§Mo KZ’$imÀ¶m ‘moR>çm EH$H$mV énm§VaH$aVmZm ^mJmH$ma H$amdm.

CXmhaU 4 … 7,000 {cQ>a åhUOo {H$Vr {cQ>a?1,000 {cQ>a = 1 {H$cmo{cQ>a 7,000 {cQ>a = 7,000 1,000 = 7 {H$cmo[cQ>a

CXmhaU 5 … 1,200 {cQ>a åhUOo {H$Vr hoŠQ>mo{cQ>a?100 {cQ>a = 1 hoŠQ>mo {cQ>a 1,200 {cQ>a = 1,200 100 = 12 hoŠQ>mo{cQ>a

CXmhaU 6 … 900 {cQ>a åhUOo {H$Vr S>oH$m{cQ>a?10 {cQ>a = 1 S>oH$m{cQ>a 900 {cQ>a = 900 10 = 90 S>oH$m{cQ>a

CXmhaU 7 … 15,000 {_cr{cQ>a åhUOo {H$Vr {cQ>a?1,000 {_cr{cQ>a = 1 {cQ>a 15,000 {_cr{cQ>a =15,000 1,000 = 15 {cQ>a

H¥$Vr 1 …XÿY S>oAar qH$dm Voc XþH$mZmcm oQ> XoD$Z 50 {_cr{cQ>a, 100 {_cr{cQ>a,

200 {_cr{cQ>a, 1 {cQ>a, 2 {cQ>a, 5 {cQ>a Am{U 10 {cQ>a _moOnmÌm§Mo{ZarjU H$am.

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H¥$Vr 2 …

5 {cQ>a nmUr ‘mdob Ago ^m§S>o KoD$Z Ë¶mV 2 {cQ>a j_Vm Agcoco^m§S>o nmÊ¶mZo ^ê$Z n{hë`m ^m§S>çmV 2 doim AmoVm. Z§Va 1 {cQ>a nmUrKoD$Z n{hë`mM ^m§S>çmV AmoVm. ^m§S>o nmÊ¶mZo nyU© âco Amho Vo nhm.

H¥$Vr 3 …

EH$ {Xdgmcm gamgar AmnU 2 Vo 3 {cQ>a nmUr {nVmo. AmnU nwaogonmUr {nVmo ho g‘OÊ¶mgmR>r ~mQ>crda {d{eîQ> IyU H$ê$Z ‘mnZmMr ~mQ>brR>odm.

CXmhaUmW© … g_Om Vw_À`mH$S>o 500 {_cr{cQ>a _mnmMr ~mQ>cr Amho.Ë`mV àËòH$doir nmUr âm d Z§Va Vo ß`m.

Vwåhr nmUr {nD$Z Vr ~mQ>cr {H$Vr doim [aH$m_r Ho$cr Vo _moOm.

Oa Vwåhr ~mQ>cr_Yrc nmUr 6 doim nyU© {nV Agmc Va Vwåhr nwaogonmUr {nVm ho g‘OVo.

ÐdmÀ`m KZ’$imdarc CXmhaUo -

CXmhaU 1 … Imcrc ~oarO H$am.

12 {cQ>a 500 {_cr{cQ>a, 8 {cQ>a 300 {_cr{cQ>a, 9 {cQ>a600 {_cr{cQ>a.

{cQ>a {_cr{cQ>a12 500

08 300

09 600

30 {b. 400 {‘.{b.

30 {cQ>a 400 {_cr{cQ>a.

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CXmhaU 2 …18 {cQ>a 500 {_cr{cQ>a_YyZ 6 {cQ>a 750 {_cr{cQ>a dOm H$am.

{cQ>a {_cr{cQ>a18 500

- 0611 750

11 {cQ>a 750 {_cr{cQ>a.

CXmhaU 3 …EH$ _mUyg {Xdgmcm 2 {cQ>a 300 {_cr{cQ>a nmUr {nVmo.Va Vmo 10

{XdgmV {H$Vr nmUr {nVmo?2 {cQ>a 300 {_cr {cQ>a X 10= 23 {cQ>a

2 {cQ>a X 10 = 20 {cQ>a300 {_cr {cQ>a X 10 = 3,000 {_cr{cQ>a =3 {c. 20 {cQ>a + 3 {cQ>a = 23 {cQ>a

10 {XdgmV 23 {cQ>a nmUr {nVmo.

CXmhaU 4 …g‘mZ KZ’$i AgUmao 8 ½bmg nmÊ¶mZo ^ê$Z EH$m$ ^m§S>¶mV AmoVë¶mg

Vo ^m§S>o ^aVo.Oa ^m§S>çmMr j_Vm 5 {cQ>a 600 {_cr{cQ>a Agoc Va ½bmgMr j_Vm

{H$Vr?1 {cQ>a = 1,000 {_cr{cQ>a5 {cQ>a 600 {_cr{cQ>a = 5 X 1,000 + 600

= 5,600 {_cr{cQ>a 8 ½bmgMr j_Vm = 5600 {_cr{cQ>a

5,600 1 ½bmgMr j_Vm —– = 700 {_cr{cQ>a8

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ñdmÜ`m` 6.2I. Vm|S>r CÎmao Úm …

1) EH$m ½cmg ‘Ü¶o 300 {‘br{cQ>a nmUr Amho. d Xþgè`m ½cmg ‘Ü¶o 250{_cr{cQ>a nmUr Amho. XmoÝhr ½cmg nmÊ`mMo ê$Z EH$m OJ_Ü o AmoVco. VaOJ_Yrc nmÊ`mMo EHy$U _mn {H$Vr?

2) EH$m Jdù`mH$S>o 5 {cQ>a 700 {_cr{cQ>a XÿY Amho. Ë`mZo EH$m _mUgmcm1 {cQ>a 350 {_cr{cQ>a d Xþgè`m _mUgmcm 2 {cQ>a 250 {_cr{cQ>a XÿY{dH$co. Va Jdù`mH$S>o {H$Vr XÿY {e„H$ am{hco?

3) EH$m ~mQ>crV 200 {_cr{cQ>a XÿY Amho. Va Aem 5 ~mQ>ë¶mV {H$Vr XÿYAgob?

4) 4 {_Ìm_Ü o 100 {_cr {cQ>a D$gmMm ag g_mZ dmQ>cm. Va àË oH$mcmD$gmMm {H$Vr ag {‘ioc?

II. énm§Va H$am1) 5 {cQ>a = .................. {_cr{cQ>a2) 6 {H$cmo{cQ>a = .................. {cQ>a3) 500 {_cr{cQ>a = .................. {cQ>a4) 8,000 {cQ>a = .................. {H$cmo {cQ>a

III. ~oarO H$am.1) 3 {cQ>a 250 {_cr{cQ>a, 750 {_cr {cQ>a Am{U 6 {cQ>a 500 {_cr{cQ>a.

2) 15 {cQ>a 450 {_cr{cQ>a, 5 {cQ>a 350 {_cr{cQ>a Am{U 21 {cQ>a 750 {‘br{bQ>a.

3) 12 {cQ>a 550 {_cr{cQ>a, 14 {cQ>a 450 {_cr{cQ>a Am{U 12 {cQ>a 650 {_cr{cQ>a.

4) 8 {H$cmo{cQ>a 250 {cQ>a, 3 {H$cmo{cQ>a 350 [bQ>a Am{U 4 {H$cmo{cQ>a 550

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{cQ>a.

IV. dOm~mH$s H$am.1) 25 {cQ>a 350 {_cr{cQ>a _YyZ 15 {cQ>a 750 {_cr{cQ>a

2) 64 {cQ>a 450 {_cr{cQ>a _YyZ 24 {cQ>a 550 {_cr{cQ>a

3) 75 {cQ>a 750 {_cr{cQ>a _YyZ 45 {cQ>a 800 {_cr{cQ>a

4) 55 {H$cmo{cQ>a _YyZ 34 {H$cmo{cQ>a 750 {cQ>a.

V. Imcrc CXmhaUo gmoS>dm…1) Am°\$sg _YyZ naV oVmZm {dUmZo 3 {cQ>a 250 {_cr{cQ>a e|JmVoc

{dH$V KoVco. Ë`mM{Xder {VÀ`m AmB©Zo gwÕm 1 {cQ>a 500 {_cr{cQ>ae|JmVoc {dH$V AmUco. Va Ë`mZr EHy$U {H$Vr e|JmVoc {dH$VAmUco?

2) EH$m Jdù`mOdi 25 {cQ>a XÿY Amho. Ë`mZo 16 {cQ>a 750{_cr{cQ>a XÿY {dH$co. Va Jdù`mOdi {H$Vr XÿY {e„H$ am{hco?

3) EH$m ~mQ>crV 1 {cQ>a 500 {_cr{cQ>a M§XZ Voc Amho. ho Voc250 {_cr{cQ>a j_Vm Agcoë`m ~mQ>ë`mVyZ âÊ¶mg EHy$U {H$Vr~mQ>ë`m cmJVrc?

4) EH$m H°$Z_Ü o 15 {cQ>a gy ©\w$cmMo Voc Amho. Ë`m_Yrc ñZohcZo 3{cQ>a 600 {_cr{cQ>a n{hë`m _{hÝ`mV d 5 {cQ>a 300 {_cr{cQ>aXþgè`m _{hÝ`mV dmnaco. Va H°$Z _Üò EHy$U gy`©\y$cmMo Voc {H$Vr{e„H$ am{hco?

5) EH$m ^m§S>çmV 1 {cQ>a 800 {_cr{cQ>a Mhm Amho. Vmo 12 ½cmg_Ü og_mZ âcm Va àËòH$ ½cmg_Üò {H$Vr Mhm Agoc?

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àH$aU 7doi (H$mb)

`m àH$aUmÀ¶m AÜ``ZmZ§Va ho {eH$mb. 24 VmgmÀ¶m KS>çmimVrb doi 12 VmgmÀ¶m KS>çmimVrb doioV n[adVuV

H$aUo. X¡Z§{XZ OrdZmV ¶oUmè¶m, doioer g§~§YrV Agboë¶m ~oarO Am{U dOm~mH$s ¶m§Mm

g‘mdoe AgUmar CXmhaUo gmoS>{dUo. EH$ H$m‘ nyU© H$aÊ¶mgmR>r bmJUmam doi J{UVmÀ¶m ghmæ¶mZo H$mT>Uo.

24 VmgmÀ¶m KS>çmimVrb doi 12 VmgmÀ¶m KS>çmimVrb doioV ~XbUo.

gamo{OZr Jmdmbm OmÊ¶mgmR>r Amnë¶m ^mdmgmo~V aoëdo ñQ>oeZda Ambr.aoëdoÀ¶m doimnÌH$ ’$bH$mda JmS>r gwQ>Ê¶mMr doi 22:05 Aer {b{hbr hmoVr.Vr aoëdoV ~gbr. aoëdo {ZKmbr. gamo{OZrZo Amnë¶m ^mdmÀ¶m KS>çmimV doin{hbm Ë¶mV 10:05 BVHo$ {Xgbo. ho Ago H$go ? doimnÌH$m§V aoëdo {ZKm¶Mrdoi 22:05 Ago {Xbr Amho. KS>çmimV ‘mÌ 10:05 dmObo AmhoV. KS>çmimVVa 1 Vo 12 n¶ªVMo A§H$ AgVmV. 22.05 hr doi H$er OmUyZ ¿¶m¶Mr ?Ago AZoH$ àý {VÀ¶m ‘ZmV {Z‘m©U Pmbo.

EH$m {XdgmMo 24 Vmg AgVmV. Ë¶mZwgma aoëdo Am{U {d‘mZ ¶m§Mo doimnÌH$00 Vo 24 Vmg ¶m à‘mUo V¶ma Ho$bobo AgVo. ho AmnU 00 Vo 24 VmgAgboë¶m KS>çmimV Xe©dy eH$Vmo.

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24 VmgmÀ¶m KS>çmimMo {Z[ajU H$am.

¶m KS>çmimV {XdgmMo 24 Vmg Xe©{dbo AmhoV. BWo {XdgmMo 24 Vmg XmoZg‘mZ ^mJmV {d^mJbo AmhoV. amÌr 00 Vo XþnmaMo 12 n¶ªV EH$ g‘ ^mJAm{U Xþnmar 12 Vo amÌr 00 (24) Mm Xþgam g‘^mJ. ‘Ü¶amÌr 00 Vo Xþnmar12 n¶ªVÀ¶m H$mbmdYrbm "nydm©Ýh' (Anti Meridian) Ago åhUVmV. ho am.øm g§{já ñdê$nmV Xe©{dVmV.

Xþnmar 12 Vo ‘Ü¶mamÌr 00 (24) n¶ªVÀ¶m H$mbmdYrbm "AnamÝh' (PostMeridian) Ago åhUVmV. ho pm. øm g§{jßV ñdê$nmV Xe©{dVmV.

24 VmgmÀ¶m KS>çmimVrb doi 12 VmgmÀ¶m KSmi¶mVrb doioV ê$nm§VarV H$aUo.CXmhaU 1…

aoëdoÀ¶m doimnÌH$mV aoëdo {ZKÊ¶mMr doi 22.05 Aer Xe©{dbr Amho.12 VmgmÀ¶m KS>çmimZwgma aoëdo {ZKmÊ¶mMr doi {H$Vr ?

aoëdo {ZKÊ¶mMr doi = 22.05 - 12.00 = 10.05 pm. (amÌrMo 10.05)

gyMZm : {Xbobr doi 12 nojm OmñV Agob Va Ë¶mVyZ 12 dOm H$amdoVAm{U Ambobo CÎma {b{hVmZm doio Z§Va pm. {bhmdo.

{Xbobr doi 12 nojm H$‘r Agob Va VrM doi {bhÿZ Ë¶mZ§Va a.m.{bhmdo.

‘Ü¶amÌ

Xþnma

nwdm©ÝhA

namÝh

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CXmhaU 2…

{d‘mZ ¶oÊ¶mMr doi 13:50 Amho. hr doi 12 VmgmÀ¶m KS>çmimÀ¶mdoioÀ¶m ñdê$nmV ~Xb H$am.

{d‘mZ ¶oÊ¶mMr doi = 13:50 - 12:00

= 1.50 pm. (XþnmaMo 1:50)CXmhaU 3…

Imbr {Xbobr doi a.m. AWdm pm. À¶m ñdê$nmV Zm|X H$am.

i) 20:20 ii) 10:45

i) 20:20 ho 12 Vmgm nojm OmñV AmhoV. 20:20-12:00 = 8:20 pm.

ii) 10:45 ho 12 Vmgmnojm H$‘r AmhoV. 10:45 = 10:45 am.

H¥$Vr 1 : nopÝgb, H§$nmg Am{U H$moZ‘mnH$ ¶m§À¶m ghmæ¶mZo 24 VmgmÀ¶mKS>çmimMo {MÌ H$mT>m.

H¥$Vr 2 : nopÝgb, H§$nmg Am{U H$moZ‘mnH$ ¶m§À¶m ghmæ¶mZo 12 VmgmÀ¶mKS>çmimMo {MÌ H$mTy>Z Ë¶mV Vmg, {‘{ZQ> Am{U goH§$X H$mQ>m XmIdm.

H¥$Vr 3 : 02 : 36 : 15

hr {S>{OQ>b KS>çmi Xe©{dV Agbobr doi Amho. Vr Vmg, {‘ZrQ> Am{UgoH§$X ho hr Xe©[dVo. Aer doi Xe©{dUmè¶m AZoH$ nÅ>¶m V¶ma H$am. {S>{OQ>bKS>çmimMm Z‘wZm V¶ma H$ê$Z Ë¶mV EH$ {IS>H$s H$ê$Z Ë¶mV Ë¶m nÅ>m§À¶mghmæ¶mZo doi Xe©dm.

Imbr {Xboë¶m V³Ë¶mMm Aä¶mg H$am. Ë¶mdê$Z Vwåhmbm nydm©Ýh (am.)d AnamÝhMr (pm.) H$ënZm ¶oB©b.

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24 VmgmÀ¶m KS>çmimVrb doi 12 VmgmÀ¶m KS>çmimVrb doi 00:00 VmgmnmgyZ 24 Vmgm n¶ªV 00:00 VmgmnmgyZ 12 Vmgm n¶ªV

01:00 dmOVm 1 a.m.

02:00 dmOVm 2 a.m.

11:00 dmOVm 11 a.m.

12:00 dmOVm 12 (XþnmaMo)13:00 dmOVm 1 p.m.

14:00 dmOVm 2 p.m.

23:00 dmOVm 11 p.m.

00.00 AWdm 24.00 dmOVm 12 (‘Ü¶amÌrMo)

ñdmÜ¶m¶ 7.1I. Vm|S>r CÎmao Úm :

1) gH$mir Vy {H$Vr dmOVm CR>Vmog ?

2) Vy {H$Vr dmOVm emiobm OmVmog ?

3) Vy Ioim¶bm {H$Vr dmOVm OmVmog ?

4) Vy amoO amÌr {H$Vr dmOë¶mnmgyZ Vo {H$Vr dmOon¶ªV Aä¶mg H$aVmog?

5) Vy amÌr {H$Vr dmOVm OodVmog ?

6) Vy amÌr {H$Vr dmOVm PmonVmog ?

II. Imbr {Xbobr doi am. Am{U .m. ‘Ü¶o Z‘yX H$am :

1) gH$miMo 10:15 2) amÌrMo 8:10 3) XþnmaMo 1:45

4) gH$miMo 4:30 5) amÌrMo 9:45 4) gm¶§H$miMo 5:35

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III. Imbr {Xbobr doi 12 VmgmÀ¶m KS>çmimÀ¶m doioV ~Xb H$ê$Z{bhm Am{U Vr am. AWdm pm. ‘Ü¶o Xe©dm.

1) 23:25 2) 12:35 3) 14:45

4) 18:40 5) 08:30 6) 11:55

Amåhmbm ‘m{hV Amho H$s goH§$X, {‘{ZQ> Am{U Vmg ho H$mb‘mnZmMo {d{dYà‘mU AmhoV. Ë¶m§Mm EH$_oH$mer Agboë¶m g§~§YmMm Aä¶mg H$ê$.

60 goH§$X = 1 {‘{ZQ>

60 {‘{ZQ>o = 1 Vmg

24 Vmg = 1 {Xdg

7 {Xdg = 1 AmR>dS>m

30 AWdm 31 {Xdg = 1 ‘{hZm (’«o$~w«dmar ‘{hZm gmoSy>Z)

12 ‘{hZo = 1 df©

365 {Xdg = 1 df©

’o$~«wdmar ‘{hÝ¶mV 28 {Xdg AgVmV. Xa 4 dfm©Z§Va ’o$~«wdmar ‘{hÝ¶mV29 {Xdg AgVmV. 29 {Xdg Agbobm ’o$~«wdmar ‘{hZm Á¶mdfu¶oVmo Ë¶m dfm©bm ""brn df©'' Ago åhUVmV

H$mb‘mnZmda AmYmarV ~oarOCXmhaU 1 : 2 Vmg 20 {‘ZrQ>o Am{U 3 Vmg 30 {‘{ZQ>o ¶m§Mr ~oarO.

2 Vm. 20 {‘.

+ 3 Vm. 30 {‘.

5 Vm. 50 {‘.

gyMZm : H$mb‘mnZmda AmYmarV ~oarOH$aVmZm goH§$Xm‘Ü¶o goH§$X, {‘{ZQ>m‘Ü¶o{‘{ZQ>o d Vmgm‘Ü¶o Vmg {‘idmdoV.

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CXmhaU 2 : 3 Vmg 50 {‘ZrQ>o 30 goH§$X Am{U 2 Vmg 15 {‘{ZQ>o 50goH§$X ¶m§Mr ~oarO H$am.

3 Vm. 50 {‘. 30 go.+ 2 Vm. 15 {‘. 50 go.

6 Vm. 06 {‘. 20 go.(30 go + 50 go = 80 go - 60 go = 20 goH§$X.)20 goH§$X ho goH§$XmÀ¶m OmJoV {b{hUo.60 goH§$X = 1 {‘ZrQ> hm 1 {‘ZrQ>, {‘{ZQ>m‘Ü¶o {‘idrbo.1 {‘. + 50 {‘ + 15 {‘ = 66 {‘. - 60 {‘ = 06 {‘ZrQ>o ho06 {‘{ZQ>o, {‘{ZQ>mÀ¶m OmJoV {b{hUo.60 {‘{ZQ>o = 1 Vmg hm EH$ Vmg Vmgm‘Ü¶o {‘i{dbm.1 Vm. + 3 Vm. + 2 Vm. = 6 Vm.

CXmhaU 3 : 3 df© 8 ‘{hÝ¶mV, 2 df© 7 ‘{hZo {‘idm.3 d. 8 ‘.

+ 2 d. 7 ‘.6 d. 3 ‘.

gyMZm : 8 ‘. + 7 ‘. = 15 ‘. - 12 ‘. = 3 ‘.

12 ‘. = 1 df©

ho 1 df© dfm©‘Ü¶o {‘i{dbo.

1 d. + 3 d. + 2 d. = 6 df}

H¥$Vr 1 : gmo‘dma Vo e{Zdma n¶ªV amoO Vwåhmbm J{UVmMr 40 {‘{ZQ>mMr EH$Vm{gH$m AgVo. AmR>dS>çmVyZ J{UVmÀ¶m {H$Vr Vm{gH$m AgVmV?Ë¶mMo {H$Vr Vmg hmoVmV ?

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H¥$Vr 2 : H¥$Vr 1 ‘Ü¶o gm§{JVë¶m à‘mUo àË¶oH$ {df¶mÀ¶m EHy$U Vm{gH$m{H$Vr ? d Ë¶m§Mo {H$Vr Vmg hmoVmV ?


1) EH$m {‘ZrQ>mV {H$Vr goH§$X AgVmV ?

2) {H$Vr {‘ZrQ>m§Mm EH$ Vmg hmoVmo ?

3) EH$ {XdgmV {H$Vr Vmg AgVmV ?

4) EH$m AmR>dS>çmV {H$Vr {Xdg AgVmV ?

5) EH$m dfm©V {H$Vr ‘{hZo AgVmV ?

6) {H$Vr {Xdgm§Mo EH$ df© ~ZVo ?

7) EH$m ‘{hÝ¶mV {H$Vr {Xdg AgVmV ?

8) ’o$~w«dmar ‘{hÝ¶mV {H$Vr {Xdg AgVmV ?

9) brn df© åhUOo H$m¶ ?

10) 3 Vmg 20 {‘ZrQ>o Am{U 4 Vmg 30 {‘ZrQ>o ¶m§Mr ~oarO {H$Vr ?

II. ~oarO H$am :

1) 4 Vm. 40 {‘. Am{U 6 Vm. 10 {‘.

2) 3 Vm. 30 {‘. Am{U 2 Vm. 20 {‘.

3) 2 Vm. 50 {‘. Am{U 4 Vm 40 {‘.

4) 5 Vm. 30 {‘. Am{U 2 Vm. 50 {‘.

5) 3 Vm. 15 {‘. 18 go. Am{U 1 Vm. 19 {‘. 17 go.

6) 2 Vm. 30 {‘. 40 go. Am{U 4 Vm. 50 {‘. 30 go.

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7) 5 Vm. 45 {‘. 30 go. Am{U 3 Vm. 25 {‘. 40 go.

8) 3 d. 8 ‘. Am{U 2 d. 7 ‘.

9) 5 d. 6 ‘. Am{U 4 d. 9 ‘.

H$mb‘mnZmda AmYmarV dOm~mH$s

CXmhaU 1 : 5 Vmg 30 {‘{ZQ>mVyZ 2 Vmg 20 {‘ZrQ>o dOm H$am.

5 Vm. 30 {‘.

- 2 Vm. 20 {‘.

3 Vm. 10 {‘.

CXmhaU 2 : 6 Vmg 15 {‘{ZQ>mVyZ 3 Vmg 45 {‘ZrQ>o dOm H$am.

6 Vm. 15 {‘.

- 3 Vm. 45 {‘.

2 Vm. 30 {‘.

(gyMZm : 15 {‘{ZQ>mVyZ 45 {‘{ZQ>o dOm H$aUo e³¶ Zmhr. Ë¶mH$arVm 6

VmgmVyZ 1 Vmg CgZm KoVbm.

1 Vmg = 60 {‘{ZQ>o

60 + 15 = 75 {‘{ZQ>o

75 - 45 = 30 {‘{ZQ>o

VmgmÀ¶m ñWmZmV 5 Vm. - 3 Vm. = 2 Vmg)

gyMZm : H$mb‘mnZmda AmYmarVdOm~mH$s H$aVmZm goH§$Xm‘YyZ goH§$X,{‘{ZQ>m‘YyZ {‘{ZQ d Vmgm‘YyZ Vmg dOmH$amdoV.

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CXmhaU 3 : 7 df© 7 ‘{hÝ¶mVyZ 4 df© 9 ‘{hZo dOm H$am.

7 d. 7 ‘.

- 4 d. 9 ‘.

2 d. 10 ‘.

(gyMZm : 7 ‘{hÝ¶mVyZ 9 ‘{hZo dOm H$aVm ¶oV ZmhrV Ë¶m H$arVm 7 dfm©H$Sy>Z EH$ df© ‘{hÝ¶mÀ¶m ñWmZmda CgZo KoVbo.1 df© = 12 ‘{hZo12 ‘ + 7 ‘ = 19 ‘.19 ‘ - 9 ‘ = 10 ‘.

dfm©À¶m ñWmZmda 6 d. - 4 d. = 2 df©)

H¥$Vr 1 : emim gwê$ hmoÊ¶mMr doi Am{U emim gwQ>Ê¶mMr doi nmhm. emioÀ¶mH$m‘mMo {H$Vr Vmg hmoVmV ¶mMo {Z[ajU H$am. Ë¶m‘YyZ ‘Yë¶mgwÅ>rMrdoi dOm H$am. emioV {eH${dÊ¶mMo H$m‘ {H$Vr Vmg MmbVo ho emoYyZH$mT>m.

H¥$Vr 2 : Q>r. ìhr. À¶m nS>Úmda ~mVå¶m àgm[aV H$aÊ¶mnydu doiXe©{dVmV. Vmg, {‘{ZQ> Am{U goH§$XmMo AmH$S>o H$go ~XbVmV ¶mMo{Z[ajU H$am. EH$m {XdgmV "XþaXe©Z-I' da àgmarV hmoUmè¶m~mVå¶m§À¶m doim§Mr ¶mXr H$am.

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1) 5 {‘ZrQ>mMo goH§$X {H$Vr ?

2) 10 VmgmMr {H$Vr {‘{ZQ>o hmoVmV ?

3) EH$ VmgmV {H$Vr goH§$X AgVmV ?

4) 9.30 am. Vo Xþnmar 12 n¶ªV {H$Vr Vmg d {‘ZrQ>o hmoVmV ?

5) 5.30 pm. hr doi aoëdoÀ¶m doimnÌH$mZwgma gm§Jm.

II. dOm~mH$s H$am :

1) 7 Vmg 30 {‘{ZQ>mVyZ 5 Vmg 10 {‘{ZQ>o.

2) 4 Vmg 40 {‘{ZQ>o 50 goH§$XmVyZ 3 Vmg 20 {‘{ZQ>o 25 goH§$X.



5) 6 df} 4 ‘{hZo ¶mVyZ 3 df} 8 ‘{hZo.

6) 5 df} 6 ‘{hZo ¶mVyZ 2 df} 9 ‘{hZo.

7) 7 df} 5 ‘{hZo ¶mVyZ 4 df} 11 ‘{hZo.

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EImXo H$m‘ nyU© H$aÊ¶mg bmJUmam H$mbmdYr H$gm H$mT>mdm.

CXmhaU 1 : em{bZr emiobm OmÊ¶mgmR>r 7.30 am. bm KamVyZ {ZKVo Am{U

9.00 am. bm emioV nmohmoMVo ; Va {Vbm emiobm nmohmoMÊ¶mg {H$Vr doi

bmJbm.

em{bZr KamVyZ {ZKÊ¶mMr doi = 7:30 am.

emioV nmohmoMÊ¶mMr doi = 9:00 am.9:00 am. ‘YyZ 7:30 am. dOm H$am.

Vm. {‘. 9 Vmgm n¡H$s 1 Vmg CgZm (hmVMm) KoVbm.9 : 00 1 Vmg = 60 {‘{ZQ>o

- 7 : 30 60 {‘ - 30 {‘. = 30 {‘.1 : 30 8 Vm. - 7 Vm. = 1 Vm.

CXmhaU 2 : CÝhmù¶mÀ¶m gwÅ>rgmR>r 11 Eàrb amoOr emim ~§X Pmë¶m.CÝhmi¶mMr gwÅ>r g§ndyZ emim nwÝhm 31 ‘o amoOr gwê$ Pmë¶m VaCÝhmù¶mÀ¶m gwÅ>rMo {Xdg {H$Vr ?

Eàrb 11 Vo Eàrb 30 n¶ªVMo {Xdg = 20

‘o 1 Vo ‘o 30 n¶ªVMo {Xdg = 30

CÝhmù¶mÀ¶m gwÅ>rMo EHy$U {Xdg = 50

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ñdmÜ¶m¶ 7.4Imbrb CXmhaUo gmoS>dm :

1) EH$ H$m‘Jma H$m‘mgmR>r H$maImÝ¶mV 6:15 am. bm ¶oVmo. VmoH$m‘ g§ndyZ 2:15 pm. dmOVm H$maImÝ¶mVyZ ~mhoa nS>Vmo. VaVmo {H$Vr doi H$m‘ H$aVmo ?

2) EH$m emiobm 3 Am³Q>mo~a Vo 31 Am°³Q>mo~a n¶ªV gwÅ>r Agë¶mg.Ë¶m gwÅ>rMo {Xdg {H$Vr ?

3) EH$ emim e{Zdmar 8:00 am. bm gwê$ hmoVo Am{U 12:30pm. bm gwQ>Vo, Va emim Mmbbobm H$mbmdYr {H$Vr ?

4) lo¶g Amnë¶m H$m¶m©b¶mV 9:00 am. bm ¶oVmo. H$m¶m©b¶mV Vmo 8Vmg H$m‘ H$aVmo. Va Vmo H$m¶m©b¶mVyZ {H$Vr dmOVm ~mhoa nS>Vmo?

5) ’$m{V‘m emioV 5 Vmg 10 {‘{ZQ>o Aä¶mg H$aVo Am{U Kar 2Vmg 50 {‘{ZQ>o Aä¶mg H$aVo. Va {VZo EH$ {XdgmV EHy$U {H$VrVmg Aä¶mg Ho$bm?

6) ¶moJoe {XZm§H$ 09-03-2017 nmgyZ 15 {XdgmgmR>r Amnë¶m ‘m‘mH$S>ogwÅ>rgmR>r Jobm. gwÅ>r g§ndyZ Vmo H$moUË¶m VmaIobm ‘m‘mÀ¶m KamVyZnaV {ZKob?

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àH$aU 8g‘{‘{V¶ AmH¥$Ë¶m

`m àH$aUmÀ¶m AÜ``Zm Z§Va Vwåhr ho {eH$mb. H$mJXmbm KS>r KmbyZ, H$mJX H$mnyZ qH$dm {Q>n H$mJXmda emB© Q>mHy$Z Ë¶mnmgyZ

V¶ma hmoUmè¶m {d{dY AmH¥$Ë¶m AmoiIUo. gmÜ¶m m¡{‘VrH$ AmH¥$Ë¶mÀ¶m à{V‘m AmoiIUo. {Û{‘Vr Am{U {Ì{‘Vr¶ AmH¥$VtMr gê$nVm AmoiIUo. dVw©i, H$mQ>H$moZ {ÌH$moU Am{U Am¶V ¶m gma»¶m d {Û{‘Vr¶ AmH¥$Ë¶m Jmob

{’$a{dë¶mZo hmoUmè¶m AmH¥$Ë¶m AmoiIUo.

g‘{‘Vr¶ AmH¥$Ë¶m :’w$bnmIamÀ¶m {MÌmMo {Z[ajU H$am. Ë¶m {MÌmdaEH$ gaiaofm AmIbr Amho. ¶m gaiaofoda KS>rKmVë¶mg {MÌmMm EH$ ^mJ Xþgè¶m ^mJmer ~amo~aOwiVmo. Aem aMZobm g‘{‘Vr¶ AmH¥$Vr AgoåhUVmV. Am{U gai aofobm g‘{‘Vr Aj åhUVmV.{MÌ (a) ‘Yrb g‘{‘Vr d AmH¥$Ë¶mnmhm Ë¶m AmH¥$Ë¶m§Zm XmoZ g‘{‘Vr AjAmhoV.{MÌ (b) ‘Yrb g‘{‘Vr d AmH¥$Ë¶m§ZmAZoH$ g‘{‘Vr Aj AmhoV. na§Vy H$m§hrAj Ë¶mV XmI{dbo AmhoV.{MÌ (c) ‘Yrb AmH¥$Ë¶m g‘{‘VrZoZmhrV. H$maU Ooìhm§ AmnU H$mJXmMr KS>rKmbVmo Voìhm§ Ë¶m KS>rdarb {MÌmMm ^mJmX þgè¶m ^mJmer O wiV Zmhr. Ë¶mg‘{‘Vr¶ AmH¥$Ë¶m ZmhrV.

a)

b)

c)

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g‘{‘{V¶ AmH¥$VtMr CXmhaUo. a) b) c) d)

Ag‘{‘Vr¶ AmH¥$VtMr CXmhaUo.

g‘{‘Vr¶ KZmH¥$VtMr {MÌog‘W© Am{U gmW©H$ ¶m§Zr doJdoJù¶m AmH$mamMo Ho$H$ IaoXr Ho$bo. {MÌmV

XmI{dë¶mà‘mUo Ë¶mZr Ë¶m§Mo XmoZ g‘mZ ^mJ Ho$bo àË¶oH$mÀ¶m XmoZ ^mJmMo {Z[ajU H$am.

g‘{‘Vr¶ KZmH¥$VrMr {MÌm§Mr CXmhaUo.

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a)

b)

c)

{dMma H$am : H$ma, {d‘mZ, ‘mo~mB©b goQ>, H$m±ß¶wQ>a, ‘mUyg ho g‘{‘Vr¶ KZmH¥$Vr AmhoV H$m§ ?

à{Vq~~ :H¥$Vr 1 : doJdoJir {MÌo Amaí¶mg‘moaYê$Z Ë¶m§Mo à{Vq~~ nmhm. ¶mV dñVyMmCOdm ^mJ S>mdrH$S>o Am{U S>mdm ^mJCOdrH$S>o {XgVmo.H¥$Vr 2 : EH$ nm§T>am H$mJX ¿¶m Ë¶mdaemB©Mo EH$ AWdm XmoZ W|~ Q>mH$m. H$mJXmMrKS>r Kmbm. Ë¶mda hiydma hmV {’$adm.H$mJXmMr KS>r CbJS>m. KS>rÀ¶m XmoÝhr~mOybm C‘Q>bobo {MÌ Am{U Ë¶m§Mo à{Vq~~nhm.

a) b) c) d)

H¥$Vr 3 : EH$ Am¶VmH$ma a§JrV H$mJX ¿¶m {MÌmV XmI{dë¶mà‘mUo Ë¶mÀ¶m‘Ü¶mda KS>r Kmbm. Ë¶mda Vwåhmbm ¶mo½¶ dmQ>ob Aer AmH¥$Vr H$mnm. AmVmKS>r CbJS>m. AmH¥$VrMr COdr ~mOy S>mdr ~mOy EH$ gmaIrM {XgVo H$m§ ?

¶m gd© H¥$Vr‘YyZ EH$m AmH¥$VrMo à{Vq~~ {‘iVo.

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CXmhaUo 1 :

1) {Xboë¶m AmH¥$Ë¶m g‘{‘Vr¶ AmhoV H$m ? Ë¶mMo n[ajU H$am. Oa Ë¶mAmH¥$Ë¶m g‘{‘Vr` AgVrb Va Ë¶mV {H$Vr g‘{‘Vr Aj H$mT>Vm ¶oVrb.

a) b) c)

a) hr g‘{‘Vr¶ AmH¥$Vr Amho. H$maUË¶mbm EH$ g‘{‘Vr Aj Amho.

b) hr g‘{‘Vr¶ AmH¥$Vr Zmhr. åhUyZ{Vbm g‘{‘Vr Aj Zmhr.

c) hr g‘{‘Vr¶ AmH¥$Vr Amho. H$maUË¶mbm XmoZ g‘{‘Vr Aj AmhoV.

a)

b)

c)

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(1)

(2)(3)

CXmhaUo 2 :{Xboë¶m AmH¥$VrV AZoH$ gaiaofm H$mT>boë¶m AmhoV.Ë¶mn¡H$s H$moUË¶m§ aofm g‘{‘Vr Aj AmhoV? gaiaofm(1) Am{U (2) ¶m g‘{‘Vr Aj AmhoV na§Vygaiaofm (3) hr g‘{‘Vr Aj Zmhr.

CXmhaUo 3 :~mOyÀ¶m {MÌmV {Xbobo Aja Am{U g§»¶oMoà{Vq~~ ho ‘yi Aja AWdm g§»¶oer OwiVo H$m¶mMo {Z[ajU H$am.a) 'A' ¶m AjamMo à{Vq~~ ho ‘yi

AjamgmaIoM Amho.b) '6' ¶m g§»¶oMo à{Vq~~ ho ‘yi A§H$m gmaIo Zmhr.

ñdmÜ¶m¶ 8.11) Imbr {Xboë¶m {MÌmVrb g‘{‘Vr¶ AmH¥$Vr g‘moa "' d Ag‘{‘Vr¶

AmH¥$Vr g‘moa "' hr IyU H$am.

2) Imbrb {MÌmV H$mhr gaiaofm H$mTy>Z Ë¶mZm H«$‘m§H$ {Xbo AmhoV. Ë¶m aofm§n¡H$s g‘{‘V Aj Agboë¶m aofmMr H«$‘m§H$ {bhm.

a) b) c) d)

b) c)(1)

(2)

(3)

(1)(2)

(3)

a) (1)

(2)

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3) Imbrb g‘{‘Vr¶ AmH¥$Ë¶m§Mo g‘{‘Vr Aj H$mT>m.

4) Imbrb {MÌmV g‘{‘Vr¶ AmH¥$Ë¶m§Mm AYm© ^mJ Xe©{dbm Amho. am{hboë¶mAÜ¶m© ^mJmMo MÌ H$mTy>Z Vr g‘{‘Vr¶ AmH¥$Vr nyU© H$am.

5) Imbr H$mhr {MÌm§À¶m OmoS>çm {Xë¶m AmhoV. Ë¶mn¡H$s H$moUVo {MÌ ho n{hë¶mMo

à{Vq~~ Amho Ë¶m g‘moa () IyU H$am. d Zgë¶mg () Aem IyU H$am.

6) Imbr H$mhr {MÌo {Xbr AmhoV. {Xboë¶m [aH$må¶m OmJoV Ë¶mMo à{Vq~~ H$mT>m.

a) b) c)

a) b) c) d)

a) b) c) d)

BOX

a) b) c) d)

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7) Imbr H$mhr g§»¶m Am{U H$mhr eãX {Xbo AmhoV. Ë¶mVrb H$m§hr g§»¶m

Am{U eãX ¶m§Mo à{Vq~~ ‘yi eãX AWdm ‘yi {Xboë¶m g§»¶o gmaIoM

{XgVo. Ë¶m§Mr ¶mXr H$am.

a) 818 b) 310 c) 18081 d) 80888

e) DAD f) MAM g) EVE h) THAT

8) g^modVmbr Vwåhr nm{hboë¶m g‘{‘Vr¶ dñVy§À¶m Zmdm§Mr ¶mXr H$am.

H¥$Vr : EH$ H$mS>©~moS>© KoD$Z Ë¶mVyZ Am¶V, H$mQ>H$moZ {ÌH$moU Am{U dVy©i¶m§À¶m AmH¥$Ë¶m H$mnyZ ¿¶m. Ë¶mZm EH$m {MÌmV XmI{dë¶m à‘mUoH$mS>rbm {MH$Q>dm. XmoÝhr hmVmÀ¶m Viì`m_Ü¶o Yê$Z Vr H$mS>r {’$adm.V¶ma hmoUmè¶m KZmH¥$VrMo {Z[ajU H$am Am{U Ë¶mMo Zmd {MÌm g‘moa{Xboë¶m [aH$må¶m OmJoV {bhm.

{d{eîQ Ajmda R>odyZ Ooìhm§ AmnU Am¶V {ÌH$moU Am{U dVw©i {’$a{dVmo Ë¶mnmgyZ

AmnUmbm AZwH«$‘o X§S>Jmob (d¥Îm{MVr), e§Hy$ Am{U Jmob V¶ma Pmbobo AmT>iVmV.

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AmH¥$Ë¶m§Mo n[a^«‘UOmohamZo Amnë¶m ImobrÀ¶m q^Vrda H$mhr {MÌo {MH$Q>{dbr AmhoV.

Ooìhm§ Vr ~mhoa Jobr hmoVr. Voìhm§ {VÀ¶m ‘¡{ÌUrZr {MÌmMm daMm mJ Imbr åhUOoM mJ

{’$adyZ R>odbm. Omoham naV Amë¶mZ§Va {Vbm XmoZ {MÌo CbQ>r H ê$Z bmdbobr AmT>ibr.‘¡{ÌUrZr Va Mmahr {MÌo {’$a{dbr hmoVr. na§Vy {Vbm BVa XmoZ {MÌo ¶mo½¶ dmQ>br. Ago H$m?

AmnU ho {MÌ nyU© {’$a{dVmo Voìhm§ Ë¶mMo ñdê$n ‘yi AmH¥$Vr qH$dm

{MÌmgmaIoM {‘iVo.

ho {MÌ AmnU AY} {’$a{dë¶mg Amåhmbm Ago {MÌ {‘iVo.

ho {MÌ {’$a{dë¶mg Amåhmbm Ago {MÌ AmT>iVo.



ho {MÌ , , , , {’$a{dë¶mg ‘yi {MÌmer Z {‘iUmao {MÌ {‘iVo.

Imbr {Xboë¶m AmH¥$Ë¶m§Mr ’o$ar nyU© Ho$ë¶mg Ë¶m AmH¥$Ë¶m ‘yi

AmH¥$Ë¶mgma»¶mM AmT>iVmV.

a) b) c) d)

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AmUIr H$mhr CXmhaUo Imbr {Xbr AmhoV Ë¶m§Mo {Z[ajU H$am.

Ooìhm§ ho {MÌ åhUOoM 900 BVHo$

{’$a{dë¶mg Vo nydugmaIoM {XgVo.

Ooìhm ho {MÌ åhUOoM 1200 BVHo$

{’$a{dë¶mg Vo ‘yi {MÌmgmaIoM {XgVo.

Ooìhm§ ho {MÌ åhUOoM 600 BVHo$

{’$a{dë¶mg ‘yi {MÌmgmaIoM {XgVo.

ho {MÌ nyU© EH$ ’o$ar, ’o$ar d ’o$ar

BVHo$ {’$a{dë¶mg Vo ‘yi {MÌmgmaIoM {XgVo.

bjmV R>odm : H$mhr AmH¥$Ë¶m BV³¶m, {’$a{dë¶mg ‘yi AmH¥$Vr gma»¶m {XgV

AgVrb Va Ë¶m BV³¶m {’$a{dë¶m Var À¶m ‘yi AmH¥$Vr gma»¶mM {XgVmV.

H$mhr AmH¥$Ë¶m EH$ ’o$ar nyU© hmoB©b BV³¶m {’$a{dë¶mg ‘yi AmH¥$Vr gma»¶m {XgVmV.

1)

2)

3)

4)

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Imbrb AmH¥$Vr , , , , JmobmH$ma {’$a{dë¶mg Vr ‘yi AmH¥$VrgmaIrM {XgVo H$m ? ¶mMo {Z[ajU H$am.

ho {MÌ ’o$ar d ’o$ar BVHo$ {’$a{dë¶mg ‘yi{MÌ AmT>iVo : na§Vy ’o$ar, ’o$ar BVHo${’$a{dë¶mg ‘yi {MÌmMo ñdê$n {‘iV Zmhr.

bjmV R>odm : Oa EImXr AmH¥$Vr {’$a{dë¶mg Ë¶mMr ‘yi AmH¥$Vr {‘iVAgob Va Vr {’$a{dë¶mg XoIrb Ë¶mMr ‘yi AmH¥$Vr {‘iVo.

H¥$Vr : AemoH$ MH«$mMo {MÌ , , , ’o$ar hmoB©bBVHo$ {’$a{dë¶mg Ë¶mVrb H$moUË¶m H¥$VrV ‘yi {MÌ {‘iVoH$m ? Vo nmhm.

ñdmÜ¶m¶ 8.21) Imbrb VH²$Ë¶mÀ¶m darb ^mJmV H$mhr {MÌo {Xbobr AmhoV Am{U Cä¶m^mJmV Vo {MÌ {’$a{dÊ¶mMo à‘mU {Xbo Amho. {Xboë¶m à‘mUmZwgma Vo {MÌ{’$a{dë¶mg ‘yi {MÌ AmT>iV Agob Va Ë¶m g‘mo[ab [aH$må¶m OmJoV "'IyU H$am Am{U ‘yi {MÌmgmaIo AmT>iV Zgob Va "' Aer IyU H$am.

’o$ar

’o$ar

’o$ar

’o$ar

AmH¥$Vr

’o$arW

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2) Imbr {Xboë¶m AmH¥$Ë¶m ’o$ar {’$a{dë¶mg Ë¶m ‘yi AmH¥$Vr à‘mUo {XgV

ZmhrV. Voìhm ’o$ar nyU© Ho$ë¶mZ§Va ‘yi AmH¥$Vr {‘imdr ¶m H$arVm Ë¶m

AmH¥$Ë¶m‘Ü¶o ¶mo½¶ Vmo ~Xb H$am.

CXmhaUo

3) a) ’o$ar {’$a{dë¶mg B§½bre n{hë¶m {bnrVrb H$moUVr Ajao ‘yi ñdê$nmV AmT>iVmV Vr {bhm.

b) B§½bre n{hë¶m {bnrVrb H$moUVo Aja ’o$ar {’$a{dë¶mg Xþgao Aja V¶ma hmoVo?

c) ’o$ar {’$a{dë¶mZo B§½bre n{hë¶m {bnrVrb Xþgao H$moUVo Aja V¶ma hmoVo ?

4) ’o$ar {’$a{dë¶mg ‘yi {MÌ {Xgob Ago {MÌ H$mT>m.

5) ’o$ar {’$a{dë¶mg ‘yi {MÌ {Xgob Ago {MÌ H$mT>m.

MMm© H$am :EH$ ‘wbJm gai C^m amhÿZ ~moS>© nhmVmo,Am{U Xþgam ‘ybJm {efm©gZ H$ê$Z VmoM ~moS>©nhmVmo. Ë¶mZm Ë¶m ~moS>©da OmUdUmam ’$aH$

H$moUVm.

a) b) c)

108

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àH$aU 9{Ì{_Vr¶ AmH¥$Ë`m

`m àH$aUmÀ`m AÜ``ZmZ§Va Vwåhr ho {eH$mc {Ì{_Vr¶ AmH¥$Ë`mdéZ {Û{_Vr¶ AmH¥$Ë`m H$mT>Uo. {Ì{_Vr¶ m¡{_VrH$ AmH¥$Ë`m§Mm g_moarc AmamIS>m d ~mOyÀ¶m mJm§Mo {MÌ H$mT>Uo. R>am{dH$ OmbmÀ¶m gmhmæ¶mZo KZ, d¥Îm{MVr d e§Hy$ ¶m§Mr m¡{‘VrH$ {MÌaMZm H$aUo.

Amnë`m g^modVmcr Agcoë`m AZoH$ {Ì{_Vr¶ dñVy§Mo AmnU {ZarjU H$aVmo.Ë`mn¡H$s H$mhr Imcr {Xë`m AmhoV.

darb AmH¥$VrVrb dñVy§Zm KZm`V, d¥Îmm{MVr, KZ d e§Hy$ `m dñVy {Ì{_Vr¶^m¡{_{VH$ AmH$mamgma»`m {XgVmV. Vwåhr _mJrc B`ÎmoV m AmH¥$Ë`m§Mo JwUY_© {eH$cmAmhmV. Imcrc VŠË`mMm Aä`mg H$am.

{Ì{_Vr¶AmH¥$VrMo

Zm§d

EHy$Un¥ð> mJAmH¥$Vr JwUY_©

EHy$UH$S>m§Mrg§»¶m

EHy$U{eamoq~XÿMr

g§»¶m

KZ 6 6 Mm¡agmH¥$Vr n¥ð>^mJ 12 8

KZm`V 6 6 n¥ð>^mJ 12 8

(Mm¡ag qH$dm Am`V)

a) b) c) d)

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3 n¥ð>^mJd¥Îm{MÎmr 3 (2 dVw©imH$ma n¥ð> mJ) - -

(1 dH«$mH$ma n¥ð>^mJ)

e§Hy$ 2 1 dVw©imH$ma n¥ð>^mJ - 11 dH«$mH$ma n¥ð>^mJ

H$mhr {dÚmWu KZm`V ¶m EH$mM dñVyMo {MÌ Imbrb à‘mUo H$mT>VmV. oWo H$mhrAmH¥$Ë m H$mT>ë m AmhoV

Oar {dÚmÏ¶mªZr EH$mM dñVyÀ`m AmH¥$Ë`m H$mT>ë¶m Agë¶m Var àË`oH$ AmH¥$VrdoJ-doJir Amho. H$maU àË`oH$ OU Vr dñVy doJdoJù`m {XeoZo nmhVmo.

doJdoJù¶m m¡{‘{VH$ AmH$mamÀ¶m H$m§hr dñVy§À¶m {MÌm§Mo {ZarjU H$am.

darc gd© AmH¥$Ë`§m‘Ü¶o AmnU EH$mMdoir gd© n¥ð>^mJ d gd© H$S>m nmhÿ eH$VZmhr. AmnU H$S>m§ gaiaofmZo (———— ) Xe©{dVmo d Ooìhm H$S>m {XgV ZmhrVVoìhm Ë`m q~Xþ¶wº$ aofmZo (.........) Xe©{dVmo.

Imcrc AmH¥$Ë`m‘Ü¶o ¶mMo {ZarjU H$am.

a) b) c) d) e)

a) b) c) d)

a) b) c) d)

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Ooìhm AmnU EImXr dñVy qH$dm KZmH¥$Îmr doJdoJù`m {Xem§_YyZ nmhVmo, Voìhm Ë`mAmnUmbm doJdoJù`m {XgVmV. CXmhaU … Ooìhm AmnU ~g doJdoJù`m ~mOyZo nmhVmoVoìhm Amnë¶mbm Imcrc à_mUo AmH¥$Ë`m {_iVmV.

`m doJdoJù`m Ñí¶mVrb 3 Ñí¶mMm g§~§Yr g‘OmdyZ KoD$ -

1) g_moéZ {XgUmao Ñí¶ - Ooìhm dñVy AmnU g_moê$Z nmhVmo.2) ~mOyZo {XgUmao Ñí¶ - Ooìhm dñVy AmnU S>mì`m qH$dm COì`m ~mOyZo nmhVmo.3) déZ {XgUmao Ñí¶ - Ooìhm dñVy AmnU dê$Z nmhVmo.

Imcrc aH$mÝ`mVrc AmH¥$Ë`m§Mo {ZarjU H$am.

AmH$mamMoZmd

déZ {XgUmaoÑí¶

{Ì{_Vr¶ AmH¥$VrMr{Û{_Vr¶ AmH¥$Vr

g‘moéZ {XgUmaoÑí¶

~mOyZo {XgUmaoÑí¶

KZ

KZm`V

d¥Îm{MÎmr

e§Hy$

a) b) c) d) e)

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OmUyZ ¿¶m … Ka qH$dm B_maV ~m§YÊ`m AJmoXa B§{O{ZAa Ë`m KamMm qH$dmB_maVrMm ßc°Z (AmamIS>m), g_moarc ^mJ d ~mOyMm ^mJ H$mT>Vmo. Vo {MÌB_maVrMo joÌ\$i, C§Mr, AmH$ma, Imoë¶m§Mr g§»¶m, XadmOm§Mr g§»¶m d {IS>Š`m§Mrg§»¶m m§Mr _m{hVr XoVo.

CXmhaU …

`m KamV XmoZ Imoë`m, EH$ XadmOm d VrZ {IS>Š`m AgyZ Ë`m KamMo N>ßna CVaVo Amho.

AmUIr H$mhr CXmhaUo Imcr {Xcr AmhoV -1) gw_Z, {nQ>a d Bem©X m§Zr H$mS>çmnoQ>rnmgyZ nwcmMm Z_wZm ~Z{dcm Amho -

A) {nQ>aZo nwbmÀ¶m Xe©Zr mJmMo {MÌ H$mT>co.

~) gw_ZZo nwbmÀ¶m ~mOyÀ`m mJmMo {MÌ H$mT>co.

H$) Bem©XZo nwbmMo (AmamIS>m) {MÌ H$mT>co.

2) nm¶è¶m§À¶m doJdoJù¶m Ñí¶m§Mo {ZarjU H$am.

a) b) c)

a)

b)

c)

a) b) c)

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ñdmÜ`m` 9.1I. `mo½` eãX ê$Z [aH$må`m OmJm am …

a) YZmÀ¶m àË¶oH$ n¥ð> mJmMm AmH$ma H$gm AgVmo?b) d¥Îm{MÎmrbm {H$Vr dV¥imH$ma n¥ð>^mJ AgVmV?c) e§Hy$bm AgUmè¶m gnmQ> d dH«$n¥ð>r mJm§Mr g§»¶m {H$Vr?

II. Imcrc aH$mÝ`m§Mo {ZarjU H$am. àË oH$ KZmH¥$VrÀ`m AmH$mamÀ¶m g‘moa H$m§hr{MÌo {Xcobr AmhoV. {Xbobo {MÌ Ë`m AmH$mamÀ`m AmH¥$VrMo CXmhaU Agoc VaË¶m {MÌm g‘moa "' Aer IyU H$am Am{U CXmhaU Zgë¶mg "x' Aer IyUH$am.

III. doJdoJù¶m KZmH¥$Vr dmnéZ amo~moQ> V¶maHo$bobm Amho. ¶m‘Ü¶o dmnaboë¶mKZmH¥$VrMo AmH$ma H$moUVo ho AmoiIyZVo {H$Vr doim dmnabo AmhoV Vo {bhm.

KZ

d¥Îm{MVr

e§Hy$

KZm`V

a) b) c) d)

e) f ) g) h)

i) j) k) l )

m) n) o) p)

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IV. Q>o~cmÀ¶m doJdoJù¶m Ñí¶m§Mr {MÌo {Xbobr AmhoV. Ë¶m§Zm Zm§do Úm.a) b) c)

V.1) doJdoJù`m _mnmÀ`m KZ, d¥Îm{MÎmr d e§Hy$ m§À`m {Û{_Vr¶ AmH¥$Ë¶m H$mT>m.2) Vw‘À¶m emioMo g‘moéZ {XgUmao Ñí¶, ~mOyZo {XgUmao Ñí¶ d emioÀ¶m B‘maVrMm

AmamIS>m (ßb°Z) H$mT>m.3) Vw_À`m KamVrc doJdoJù`m dñVy§Mo g_moéZ {XgUmao Ñí¶, ~mOyZo {XgUmao

Ñí¶ d AmamIS>m Xe©{dUmar {MÌo H$mT>m.

OmbmÀ¶m gmhmæ¶mZo KZmH¥$VrMr aMZm H$aUo -EH$ KZmH¥$Vr noQ>r KoD$Z {VÀ¶m H$S>m a§JrV aofm§Zr H$mT>m Am{U Ë¶m H$mnm. O|ìhm

Vr noQ>r CKS>mc V|ìhm Vwåhmcm gnmQ> AmH¥$Vr {_ioc. a) b)

`m gnmQ> AmH¥$Vrc«m KZmMo "Omc' åhUVmV. ¶m Omcmbm H$S>m§daVr KS>r (fold)KmVë¶mg KZmH¥$Vr V¶ma hmoVo.

a) b)

KZmMo Omc KZ

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a) b)

d¥Îm{MVrMo Omc d¥Îm{MVra) b)

KZm`VmMo Omc KZm`Va) b) c)

e§Hy$Mo Omc e§Hy$

ñdmÜ`m` 9.21. Imcrc Omc H$mS>©{eQ>da N>mnm. H$S>mdê$Z Vo H$mnm. (H$S>m^modVrÀ`m nonaÀ¶m

VwH$S¶mgh) Omc KS>r Kmcm, VwH$S>o OmoS>m Am{U KZmH¥$Vr ~Zdm.

a) b) c)

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àH$aU 10AmH¥$Vr~§Y (Patterns)

`m àH$aUmÀ`m AÜ``ZmZ§Va Vwåhr ho {eH$mc - AmH¥$Vr~§Y _Yrc {Z`_ g_OmdyZ KoUo. {Z`_m§Mm dmna H$ê$Z AmH¥$Vr~§Y nyU© H$aUo. {d{dY aMZm H$aUo g§»`m§Mr AmH¥$Vr~§Y aMZm H$aVm oVo ho OmUyZ KoUo. g§»`m AmH¥$Vr~§Y AmoiIUo. AmH¥$Vr~§YmVyZ {ÌH$moUmH$ma Am{U Mm¡agmH$ma g§»`m aMZm H$aUo. g§»`m AmH¥$Vr~§Y AmoiIUo Am{U Ë`mdarc CXmhaUo gmoS>{dUo. {df_ g§»`m m H«$_ d H«$_mJV dJ© g§»`m m§À`mVrc H«$_ g§~§Y Xe©{dUo. {H$Zmam (border) Mo d cmXr qH$dm H$m¡cm§ (tiles) Mo AmH¥$Vr~§Y V`ma

H$aUo. {H$Zmam§Mo d cmXrÀ`m {d{dY AmH¥$Vr~§Ym§À`m aMZm OmUyZ KoUo.

_mJrc B`ÎmoV Vwåhr g§»`m aMZ|À`m ~§Ym§Mr _m{hVr KoVcr Amho.Imcrc CXmhaUo nhmCXmhaU 1 …

5, 10, 15, 20, 25, 30, 35, 40 .......................................`m g§»`m 5 À`m nQ>rVrc AmhoV. Ë`m§Mr aMZm Aer Amho.5, 5+5, 10+5, 15+5, 20+5 .......................................

CXmhaU 2 …2, 3, 6, 7, 10, 11, 14, 15 ........................................`m CXmhaUmV 2 d 3 _Yrc \$aH$ EH$ Amho Am{U 3 d 6 _Yrc \$aH$ 3

Amho.

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`m g§»`m Imcrc ñdê$nmV Xe©{dVm oVrc.

åhUOoM, : 2, 2+1, 3+3, 6+1, 7+3, 10+1, 11+3 ..............Imcrc g§»`m§Mm AmH¥$Vr~§Y Z_wZm nmhm Am{U Ë`m nwT>rc VrZ g§»`m {chm.

20, 40, 60, 80, .............., .............., ..............,8, 16, 24, 32, .............., .............., ..............,1, 4, 7, 10, .............., .............., ..............,19, 18, 17, 16, .............., .............., ..............,

AmVm AmnU AmUIr H$mhr _Ooera g§»`m aMZm {eHy$`m.dJ©g§»`m

Imcr {Xcoë`m {R>nŠ`m§À`m {MÌmH$S>o nhm. àË oH$ {MÌmV V`ma PmcocrAmH¥$Vr AmoiIm

AmnUmg oWo Ago {XgyZ oVo H$s EH$mM {XeoV Agcoco AZoH$ q~Xÿ ({R>nHo$)OmoSy>Z gai aofmI§S> V`ma hmoVmo.

AmVm AmnU gai aofoV Zgcoë`m q~Xÿ g§~§Yr nmhÿ.AmVm Ü`mZmV KoVcoë`m q~Xÿ§Mr g§»`m d OmoSy>Z V`ma Pmcoë`m AmH¥$VrÀ`m

AmH$mamH$S>o cj Úm.

3 q~Xÿ - {ÌH$moU

4 q~Xÿ = Mm¡ag

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Imcrc AmH¥$Vr nmhm. mV {H$Vr q~Xÿ AmhoV.

- 4 q~Xÿ

- 9 q~Xÿ

- 16 q~Xÿ

- 25 q~Xÿ

oWo V`ma Pmcocr àË oH$ AmH¥$Vr hr Mm¡ag H¥$Vr ~Zcr Amho.

4, 9, 16. 25 q~Xÿ OmoS>ë`mg Mm¡agm V`ma hmoVmo ho cjmV ¿`m. Mm¡agmVyZ V`mahmoUmè`m m g§»`m§Zm dJ©g§»`m Ago åhUVmV.

Imcr {Xcoë`m q~Xÿ§Mr aMZm nmhm Am{U dJ© g§»`m AmoiIm.

a) b)

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nwT>rc dJ© g§» ogmR>r q~Xÿ§Mr aMZm H¥$Vr {chm.

JwUmH$mamMo H$moï>H$ nmhm

JwUmH$mamMo H$moï>H$

`m Mm¡agmVrc n{hë`m Cä`m am§JoVrc g§»`m Am{U gdm©V Imcr Agcoë`mAmS>ì`m am§JoVrc g§»`m `m§Mm JwUmH$ma H$ê$Z `m VŠË`mVrc g§»`m {c{hë`mAmhoV. Xþæ`_ H$Um©darc darc g§»`m dJ© g§»`m AmhoV.

1

2

3

4

5

6

7

8

9

10

3

6

9

5

10

15

20

25

2

4

4

8

12

16

6

12

18

24

30

36

7

14

21

28

35

42

49

8

16

24

32

40

48

56

64

9

18

27

36

45

54

63

72

81

10

20

30

40

50

60

70

80

90

100

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{ÌH$moUmH¥$Vr g§»`m

{R>nHo$ OmoSy>Z V`ma Pmcoë`m Imcrc AmH¥$Ë`m nmhm.

3 {R>nHo$

6 {R>nHo$

10 {R>nHo$

15 {R>nHo$

{ÌH$moU V`ma H$aUmè`m g§»`m Agcoë`m 3,6,10 Am{U 15 `m gma»`mg§»`m§Zm {ÌH$moUr g§»`m åhUVmV.

gd© g§»`m {ÌH$moUr g§»`m AgV ZmhrV.

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{ÌH$moUmH¥$Vr g§»`mloUr AmnU ñdm^m{dH$ g§» onmgyZ AmnU {_idy eH$Vmo.Imcrc aMZoMo {ZarjU H$am.

1

1+2 = 3

(1+2)+3 = 6

(1+2+3)+4 = 10

(1+2+3+4)+5 = 15

Imcrc {MÌmÀ`m gmhmæ`mZo {ÌH$moUmH¥$Vr g§»`m Xe©{dVm oVmV.

Imcrc {R>nŠ`m§À`m {MÌm§Mo {ZarjU H$am. Ë`mVrc {ÌH$moUmH¥$Vr g§»`mAmoiIyZ {chm.

a) b)

{ÌH$moUmH¥$Vr g§»`m AmoiIyZ [aH$må`m OmJoV {chm

AmH¥$Vr (a) AmH¥$Vr (b)

1 3 6 10 15 21 28 36 45

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{df_ g§»`m Am{U H«$_dma dJ© g§»`mImcrc {R>nŠ`m§Mr aMZm nhm Am{U g§»`m§Mo {ZarjU H$am.

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

EH$ nmgyZ àma§ H$ê$Z H«$_dma {df_ g§»`m§Mr ~oarO Ho$ë`mg AmnUmgnyU© dJ©g§»`m {_iVmV.

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Imcr {Xcoë`m H«$_dma {df_ g§»`m nhm. Ë`m§Mr ~oarO H$am. H$moUË`màH$maÀ`m g§»`m V`ma hmoVmV Ë`mMo {ZarjU H$am.

1 + 3 + 5 + 7 + 9 + 11 = 36

1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

1 + 3 + 5 + 7 + 9 + 11 + 13 +15 = 64

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

36, 49, 64, 81 Am{U 100 m nyU© dJ©g§»`m AmhoV

H¥$Vr …

Imcrc VŠË`mVrc H«$_dma {df_ g§»`m {ZdS>m Am{U Ë`mnmgyZ dJ© g§»`mV`ma H$am.

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

CXmhaU …1 + 3 = 41 + 3 +5 = 9

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120120

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ñdmÜ`m` 10.1I) Imcrc CXmhaUo gmoS>dm.

1) 1 Vo 50 n`ªVÀ`m g§»`m Imcrc VŠË`mV {chm.Ë`mn¡H$s dJ© g§»`m cmc a§JmZo d {ÌH$moUr g§»`m {Zù`m a§JmZo a§Jdm.

A)dJ©g§»`m {chm.

Am){ÌH$moUmH¥$Vr g§»`m {chm.

B)1 Vo 50 n ªVÀ`m g§»`m_Ü o {H$Vr dJ© g§»`m AmhoV?

B©)1 Vo 50 n ªVÀ`m g§»`m_Ü o nmhm Am{U [aH$må`m OmJm ^am

2) Imcrc g§»`mMr aMZm nmhm Am{U [aH$må`m OmJm ^am

1 + 2 + 1 = 4

1 + 2 + 3 + 2 + 1 = 9

1+ 2 + 3 + 4 + 3 + 2 + 1 =16

=

=

=

1 2

50

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3) Imcr {Xcoë`m dJ© g§»`m, H«$_dma {df_ g§»`m§À`m ~oaOoÀ`m ñdê$nmV ì`º$ H$am.16, 36, 81, 100, 121, 144, 169, 225CXm. : 9 = 1 + 3 + 5

4) [aH$må`m Mm¡H$moZr OmJoV Jmicocr {df_ g§»`m {chm Am{U dVw©imV dJ©g§»`m {chm.

A) Am)

5) n{hë`m Mma dJ© g§»`m Am{U {ÌH$moUr g§»`m {R>nŠ`m§À`m {MÌmÀ`m ghmæ`mZoXe©dm.

6) àW_ {ÌH$moUr g§»`m§Mr `mXr nyU© H$am Am{U Imcr {Xcoë`m VŠË`mVXe©{dë`m à_mUo {chm.1, 3, 6, 10, _______, _______, _______, 36, 45.

Vw_À`m dhrV Imcr {Xcocm Vº$m H$mT>m Am{U Ë`mV [aH$må`m OmJm am.

AmVm EH$m Imcr EH$ Amcoë`m g§»`mMr ~oarO H$am d Amcocr ~oarO gdm©VImcrc {Vgè`m aH$mÝ`mV {chm. m aH$mÝ`mV V`ma Pmcoë`m g§»`mZm Vwåhr H$m`åhUmc? Vw_Mm {ZîH$f© dmŠ`mV {chm.

1 3 6 10 36

1 3 6 10 36

7

3

9

1 5

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7) Imcrc VŠË`mMo {ZarjU H$am.

3 Mm nmT>m {ÌH$moUr g§»`m dJ©g§»`m

3 1 = 3 3, 6, 15, 9

3 2 = 6 21

3 3 = 9

3 4 = 12

3 5 = 15

3 6 = 18

3 7 = 21

3 8 = 24

3 9 = 27

3 10 = 30

`m CXmhaUmà_mUo 4,5 Am{U 6 À`m nmT>çmMm Vº$m V`ma H$am Ë`m àË oH$VŠË`mV darc VŠË`mV XmI{dë`mà_mUo {ÌH$moUmH¥$Vr g§» o modVr Jmoc H$amAm{U dJ© g§» o modVr Mm¡H$moZ H$am Am{U Ë`m§Zm Ë`m g§»`m nwT>rc g§~§YrVaH$mÝ`mV {chm.

51 Vo 100 n ªVÀ`m g§»`m {chm Ë`mVrc {ÌH$moUmH¥$Vr g§»`m Am{U dJ©g§»`mAmoiIm.

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{H$Zmam§Mr d cmXr qH$dm H$m¡cm§Mr AmH¥$Vr~§Y aMZm_mJrc B`ÎmoV g_{_V m¡{_VrH$ aMZoda AmYmarV aoImH¥$Vr Vwåhr {eH$cm

AmhmV.Imcr {Xcoë`m H$mhr aMZm nhm.

g_{_Vrda AmYmarV H$mhr aMZm§Mr H$ënZm H$ê$Z Ë`m§Mr {MÌo H$mT>m.Ë`mM nÕVrZo H$mhr aMZm qH$dm AmH¥$Vr~§Y dmnê$Z AmnU {H$Zmam§Mr aMZm

H$ê$ eH$Vmo.{Xcoë`m H$mhr {H$Zmam§Mo {ZarjU H$am.

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da Xe©{dcoë`m H$mhr {H$Zmam§À`m aMZoV d AmH¥$Vr _Yrc _moH$ù`mOmJo_Ü o g_mZVm {XgyZ oVo.

AmVm AmnU KamVrc O{_Zrda ~g{dë`m OmUmè`m cmXrÀ`m qH$dm Q>mBëgÀ`maMZm nmhÿ.

BWo Q>mBëg OmoS>Ur A{Ve` gma»`m nÕVrZo Pmcr Amho. Q>mB©ëg OmoS>VmZm`m_Yo A§Va gmoS>coco Zmhr qH$dm Ë`m EH$_oH$m§da OmoS>coë`m ZmhrV.

AmUIr H$mhr Q>mB©ëgÀ`m aMZm nmhÿ.

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125125

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KamVrc d Xodmc`mVrc O{_Zrda VgoM aoëdo ßc°Q>\$m°_©da, ehamVrcañË`mÀ`m ~mOyZo nXnWmda EH$mM VèhoÀ`m g_mZ AmH$mamÀ`m Q>mB©ëgaMZmË_H$ [aVrZo ~g{dcoë`m {XgVmV.

Q>mB©ëg qH$dm cmXr OmoS>VmZm A§Va Z gmoS>Vm; Ë`m EH$_oH$mda oD$ Z XoVmì`dpñWVnUo OmoS>Ê`mÀ`m H$cocm "cmXr OmoS>Ur' (tiling) Ago åhUVmV.

ñdmÜ`m` 10.2I) Imcr {Xcoë`m {H$ZmamMr aMZm nyU© H$am.

a)

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b)

II) Imcr {Xcoë`m H$mhr {H$Zmam§À`m aMZm nhm; Am{U Vw_À`mAmdS>rÀ`m Aem AmUIr H$mhr aMZm H$mT>m.

..........., ..........

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III) Imcr {Xcoë`m {d{dY Q>mBëg/cmÚm§À`m AmUIr H$mhr aMZm nhm.

A B

C D

E F

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128128

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H$m`m©Zw d …1) Imcr {Xcoë`m EH$ cmXr (Q>mB©c) darc aMZm nhm. Vw_À`m {ZdS>rMr

AerM EH$ aMZm H$am.

2) Imcr {Xcoë`m AmH$mam§Mo H$miOrnyd©H$ {ZarjU H$am.

`mVrc H$moUVm AmH$ma cmXrÀ`m OmoS>Urcm mo½` Amho. ([aH$m_r OmJmZ gmoS>Vm)

`m AmH¥$Ë`m§Mm dmna H$ê$Z cmXr/Q>mBëgMr aMZm H$am. Mm¡agmÀ`m AmH$mamMm dmna H$ê$Z cmXrMr EH$ ZdrZ aMZm H$am. VrM

aMZm {ÌH$moUr AmH$mamZo H$aVm oUo eŠ` Amho H$m? à`ËZ H$ê$Z nhm.

3) Imcr {Xcocr O{_Zrdarc cmXrMr aMZm nyU© H$am Am{U a§Jdm.

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4) {R>nŠ`m§Mm dmna H$ê$Z Vw_À`m AmdS>rÀ`m EH$m cmXrMr aMZm H$ê$Z Vr a§Jdm.

5) {ÌH$moU d Mm¡agmMm dmna H$ê$Z cmXrMr Am{U {H$ZmamMr aMZm H$am.

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130

CÎmaoàH$aU-1

ñdmÜ`m` 1.1I 1) 25,258 2) 25,276 3) 21,842 4) 38,064 5) 16,0506) 52,576 7) 31,600 8) 52,300II 1) 25,749 2) 27,639 3) 43,524 4) 30,205 5) 64,224

6) 39,555III. 1) 90250 2) 50,980 3) 86,158 4) 90,364 5) 75,609

6) 16,354 7) 38,036 8) 38,000IV. 1) 64,491 2) 78,730 3) 77,336 4) 90,351V. 1) 37,296 2) 17,280 3) ` 55,809 4) ` 44,505

àH$aU-2ñdmÜ`m` 2.1I. 1) ^mJmH$ma = 8, ~mH$s = 0, 2) ^mJmH$ma = 12, ~mH$s = 0

3) ^mJmH$ma= 13, ~mH$s = 3, 4) ^mJmH$ma = 10, ~mH$s = 2II. 1) ^mJmH$ma = 58, ~mH$s = 0, 2) ^mJmH$ma = 79, ~mH$s = 03) ^mJmH$ma= 23, ~mH$s = 2, 4) ^mJmH$ma= 43, ~mH$s = 11III. 1) ^mJmH$ma= 206, ~mH$s =5, 2) ^mJmH$ma = 662, ~mH$s = 13) ^mJmH$ma = 95, ~mH$s =10, 4) ^mJmH$ma = 203, ~mH$s = 8IV. 1) ^mJmH$ma = 12,329, ~mH$s = 0 2) ^mJmH$ma = 2000, ~mH$s = 53) ^mJmH$ma = 3274, ~mH$s = 5 4) ^mJmH$ma = 1004, ~mH$s = 8V. 1) 2 _rQ>a 2) 48 {H$._r. 3) 1,786 4) ` 86

5) ` 7,576

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ñdmÜ`m` 2.2I. 1) 410 2) ` 195 3) ` 1,080àH$aU-3

ñdmÜ`m` 3.1I. 1) 8,000 2) 3,000 3) 15,000 4) 33,000II. 1) 30,000 2) 30,000 3) 50,000 4) 50,000III. 1) 78,000 2) 96,000 3) 53,000 4) 89,000IV. 1) 80,000 2) 80,000 3) 80,000 4) 60,000V. 1) 18,000 2) 14,000 3) 32,000 4) 45,000VI. 1) 20,000 2) 40,000 3) 30,000 4) 30,000VII. 1) 20,000 2) 45,000 3) 50,000 4) 60,000VIII. 1) 5 2) 40 3) 50 4) 200IX. 1) 30,000 2) 20,000 3) 4,000 {H$._r. 4) ` 10,000àH$aU-4

ñdmÜ`m` 4.1II. 1) 0.12 2) 6.8 3) 10.5 4) 4.02 5) 6.84 6) 108.06III. 1) 0.8 2) 7.5 3) 8.5 4) 52.5IV. 1) 0.08 2) 0.72 3) 3.75 4) 4.80 5) 15.06V. 1) 0.75 2) 10.25 3) 8.70 4) 782.10 5) 20.50

ñdmÜ`m` 4.2I. 1) 0.8 2) 0.7 3) 0.6 4) 1.6 5) 4.26) 8.3 7) 0.07 8) 0.72 9) 8.61 10) 16.211) 1.41 12) 14.61 13) 0.5 14) 0.75 15) 0.416) 0.35 17) 0.76 18) 0.68 19) 0.65 20) 0.32

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II. 1) 2) 3) 4) 5)

6) 7) 8) 9) 10)

11) 12)

àH$aU-5ñdmÜ`m` 5.1I. 1) ` 29.95 2) ` 8.75 3) ` 2,503.25 4) ` 620II. 1) ` 286.5 2) 3,200 n¡go 3) 1,975 n¡go 4) ` 47.05III. 1) 1075.75 2) ` 154.25 3) ` 63.50

4) 1003.60 5) ` 19806IV. 1) ` 151.75 2) ` 24.50 3) ` 99.254) ` 679.25 5) ` 699.25V. 1) ` 48 2) ` 600 3) ` 33754) ` 3,675 5) ` 69,120VI. 1) 400 2) ` 158 3) ` 1,4754) ` 8 5) ` 1,611

ñdmÜ`m 5.2I 1) 843 2) 910àH$aU-6

ñdmÜ`m` 6.1II. 1) 7,000 J«°_ 2) 16,000 {_.J«°. 3) 6 {H$.J«°.4) 7.5 J«°_ 5) 1,200 {H$.J«°. 6) 15 q¹$Q>cIII. 1) 16 {H$.J«°. 635 J«°_ 2) 60 {H$.J«°. 782 J«°_ 3) 28 {H$.J«°.

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133

4) 36 {H$.J«°. 70 J«°_ 5) 22 {H$.J«°. 330 J«°_IV 1) 15 {H$.J«°. 30 J«°_ 2) 35 {H$.J«°. 125 J«°_3) 30 {H$.J«°. 395 J«°_ 4) 34 {H$.J«°. 70 J«°_5) 40 {H$.J«°. 89 J«°_V 1) 8 {H$.J«°. 250 J«°_ 2) 39 {H$.J«°. 500 J«°_3) 88,500 {H$.J«°. 4) 4,600 J«°_ 5) 19 {H$.J«°.

ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` 6.2 6.2 6.2 6.2 6.2II. 1) 500 {_.cr 2) 6,000 {cQ>a 3) {cQ>a 4) 8 {cQ>aIII. 1) 10 {cQ>a 500 {cQ>a 2) 42 {cQ>a 550 {_.cr3) 39 {cQ>a 650 {_.cr 4) 16 {H$cmo {cQ>a 150 {cQ>aIV. 1) 9 {cQ>a 600 {_.cr 2) 39 {cQ>a 900 {_.cr3) 29 {cQ>a 950 {_.cr 4) 20 {cQ>a 250 {cQ>aV. 1) 4 {cQ>a 750 {_.cr 2) 8 {cQ>a 250 {_.cr 3) 6 ~mQ>ë`m4) 6 {cQ>a100 {_.cr 5) 412 {cQ>a 500 {_.cr 6) 150 {_.cr7) 500 {_.cr

àH$aU-7àH$aU-7àH$aU-7àH$aU-7àH$aU-7ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` 7.1 7.1 7.1 7.1 7.1III. 1) 11 : 25 pm. 2) 12 : 35 pm. 3) 2 : 45 pm.

4) 6 : 40 pm. 5) 8 : 30 am. 6) 11 : 55 am.

ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` 7.2 7.2 7.2 7.2 7.2II. 1) 10 Vm. 50 {_. 2) 5 Vm. 50 {_. 3) 6 Vm.30 {_.4) 8 Vm. 20 {_ 5) 4 Vm. 34 {_.35 go. 6) 7 Vm. 21 {_.10 go7) 9 Vm.11{_. 10 go. 8) 6 d. 3 _. 9) 10 d. 3 _.

ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` ñdmÜ`m` 7.3 7.3 7.3 7.3 7.3II. 1) 2 Vm. 20 {_. 2) 1 Vm. 20 {_. 25 go. 3) 2 Vm. 40 {_.

4) 30 {_. 5) 2 Vm. 49 {_. 45 go. 6) 1 Vm. 55 {_. 52 go.

7) 2 Vm. 50 {_. 50go 8) 2 d. 8 _. 9) 2 d 9 _. 10) 2 d. 6 _.

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ñdmÜ`m 7.41) 8 Vm. 2) 2 Vm. 30 {_. 3) 11Vm. 30{_. 4) 28 {Xdg5) 4Vm. 30{_. 6) 5 Vmg 7) 8 Vmg 8) 24-03-2017

àH$aU-8ñdmÜ`m` 8.1

1. a) b) c) d) 2. a) (2) b) (1) c) (1) d (3)5. a) b) c) d) 7. a) 818 c) 18081 f) MAM

ñdmÜ`m` 8.2{Xcocm Vº$m

\o$ar

\o$ar

\o$ar

\o$ar

\o$ar{MÌ W 8

3) a) H, I, N, O, S, Z b) N c) MàH$aU-9

ñdmÜ`m` 9.1I. a) Mm¡ag b) XmoZ c) EH$, EH$II. a) b) c) d)

e) f) g) h) i) j) k) l ) m) n) o) p)

III. KZ - 2, KZm`V - 1 d¥Îm{MVr - 3 e§Hy$ - 2IV. a) g_moarc ~mOy b) C§Mr c) AmamIS>m

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mathematics - kar textbooks/class5/5th... · 2019. 8. 19. · pb i h$zm©q>h$ gah$ma j{uv 5...

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