fkdñf,a fnod yeÍu i|yd h' 137

11 idOl yd .=Kdldr

fuu mdvu wOHhkh lsÍfuka Tng"

² mQ¾K ixLHdjl idOl yd .=Kdldr fiùug" ² idOl yd .=Kdldr wdY%s; .eg¨ úi`§ug iy ² ixLHdjlaa 2ka" 5ka yd 10ka b;sß ke;s j fnfoa oe hs mÍlaId lsÍug

yelshdj ,efí'

11'1 idOl y÷kd .ekSu

isiqka yh fokl= isák mka;shla i,lkak" iEu fma

fkdñf,a fnod yeÍu i|yd h'138

iEu fma

fkdñf,a fnod yeÍu i|yd h' 139

ksoiqk 1

20ys idOl fidhkak'

20 = 1 « 2020 = 2 « 10 20 = 4 « 5

1" 2" 4" 5" 10 iy 20" 20ys idOl fõ'

igyk

● 0 lsisÿ mQ¾K ixLHdjl idOlhla f,i fkd.efka'

11'1 wNHdih

(1) ysia;ekaj,g wod< mQ¾K ixLHd fhdoñka my; m%ldYk iïmQ¾K lrkak'

(i) 4 = 1 « ''''''''''4 = 2 « '''''1" 2 iy ''''' 4ys idOl fõ'

(ii) 7 = 1 « '''''1 iy ''''' 7ys idOl fõ'

(iii) 8 = 1 « ''''''''''8 = 2 « ''''''''''1" 2 iy '''' 8ys idOl fõ'

(iv) 15 = 1 « '''''15 = 3 « '''''1" 3" ''''' iy ''''15ys idOl fõ'

(v) 24 = 1 « '''''24 = 2 « '''''''''''24 = 3 « '''''''''''24 = 4 « '''''''''''1" 2" '''''''''" '''''''''''" '''''''''" '''''''''" ''''''''' iy ''''' 24ys idOl fõ'

(vi) 18ys idOl ,shQ úg 1" 2" ''''''''''" 6" 9 iy 18 fõ'

(vii) 40ys idOl ,shQ úg 1" 2" '''''''" 5" '''''''''" 10" 20 iy ''''' fõ'

(2) my; oelafjk ixLHdj, idOl fidhkak'

(i) 5 (ii) 27 (iii) 17 (iv) 22 (v) 21

(vi) 31 (vii) 32 (viii) 45 (ix) 50 (x) 60

fkdñf,a fnod yeÍu i|yd h'140

11'2 .=Kk j.=j weiqfrka idOl fiùu

oeka wms my; ±lafjk 10 « 10 .=Kk j.=j Ndú;fhka" mQ¾K ixLHdjl idOl ,nd .kakd wdldrh úuid n,uq'

« 1 3 4 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 8 12 16 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 30 40 50 60 70 80 90 100

4

10

2 5

20

20

20ys idOl lsysmhla fuu .=Kk j.=j weiqfrka ,nd .ksuq' tA i|yd 20" .=‚;h f,i ,eî we;s wjia:d y÷kd .ksuq'

tA wkqj"

20 = 2 « 1020 = 4 « 5

2" 4" 5 iy 10 hk ixLHd 20ys idOl y;rla fõ'

ksoiqk 1

by; .=Kk j.=j weiqfrka ,nd .; yels 72ys idOl fudkjd o?

72 } 8 « 98 iy 9 by; .=Kk j.=fjka ,nd .; yels 72ys idOl folls'

ksoiqk 2

by; .=Kk j.=j weiqfrka ,nd .; yels 18ys idOl fudkjd o?

18 = 3 « 618 = 2 « 92" 3" 6 iy 9 by; .=Kk j.=fjka ,nd .; yels 18ys idOl y;rls'

fkdñf,a fnod yeÍu i|yd h' 141

11'2 wNHdih

(1) 10 × 10 .=Kk j.=j weiqfrka ,nd .; yels" my; i|yka tla tla ixLHdfõ idOl fudkjd o?

(i) 48 (ii) 81 (iii) 2 (iv) 28 (v) 40

(2) 36 mQ¾K ixLHd 2l .=‚;hla f,i ,súh yels wdldr ;=kla 10 × 10 .=Kk j.=j weiqfrka ,ndf.k" my; ysia;eka mqrjkak'

(i) 9 «''''''''' (ii) 4 « ''''''''' (iii) 6 « '''''''''

tu .=‚; weiqfrka ,nd.; yels 36ys idOl wdfrdayK ms

fkdñf,a fnod yeÍu i|yd h'142

6ys idOl fkdjk 4 iy 5 hk ixLHdj,ska 6 fnod n,uq'

6

1

44

6 ÷ 4 = 1 hs b;sß 2 hs' 6

1

1

55

6 ÷ 5 = 1 hs b;sß 1 hs' fï wkqj 6ys idOl jk 1" 2" 3 iy 6 u.ska 6 b;sß ke;s j fnfoa' 6ys idOl fkdjk 4 iy 5ka" 6 fn¥ úg ms

fkdñf,a fnod yeÍu i|yd h' 143

11'3 wNHdih

(1) fn§fï l%ufhka my; oelafjk ixLHdj, idOl ;=k ne.ska fidhkak' (i) 28 (ii) 32 (iii) 54 (iv) 90 (v) 21

(2) 6" 84ys idOlhla fõo@ fn§fï l%ufhka ms

fkdñf,a fnod yeÍu i|yd h'144

ksoiqk 1

14, 2ys .=Kdldrhla oe hs 2ka fn§fuka úuikak'

14140

7

214" 2ka b;sß ke;s j fnfok neúka 14" 2ys .=Kdldrhls'

ksoiqk 2 42, 3ys .=Kdldrhla oe hs 3ka fn§fuka úuikak'

42312

14

3

120

42" 3ka b;sß ke;s j fnfok neúka 42" 3ys .=Kdldrhla fõ'

« 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

(i) § we;s .=Kk j.=j msgm;a lr .kak'(ii) tys we;s 2ys tla tla .=Kdldrh jgd rjqula w¢kak'(iii) tys we;s 3ys .=Kdldr jk ixLHd jglr ;%sfldaKhla w¢kak' (iv) rjqu iy ;%sfldaKh hk ixfla; fol u fh§ we;s ixLHd 5la

,shkak'(v) 2ys iy 3ys .=Kdldrhla jk l=vd;u ixLHdj l=ula o@

(vi) rjqu iy ;%sfldaKh fh§ we;s ixLHd 6ys .=Kdldr nj Tng fmfka' ta wkqj 6ys .=Kdldrhla wksjd¾hfhka u fjk;a ljr ixLHd foll .=Kdldrhla jkafka o@

(vii) by; ks.ukh wkqj 15 hkq 15ys .=Kdldrhls' th fjk;a ljr ixLHd foll .=Kdldrhla fõ o@

(viii) 45 hkq ljr ixLHdj, .=Kdldrhla jkafka o@

ls%hdldrlu 1

fkdñf,a fnod yeÍu i|yd h' 145

11'4 wNHdih

(1) 10g jvd úYd, 2ys .=Kdldr 5la ,shkak'

(2) 1;a 20;a w;r we;s 3ys .=Kdldr 4la ,shkak'

(3) 1;a 25;a w;r we;s 4ys .=Kdldr ish,a, ,shkak'

(4) my; oelafjk ixLHdj,ska ;=fkys .=Kdldr f;dard ,shkak' 26, 60, 115, 48, 29, 14, 27

(5) 1;a 100;a w;r"

(i) 9ys .=Kdldr lShla ;sfí o@

(ii) tAjd w;=ßka 9ys úYd,;u .=Kdldrh l=ula o@

(6) 18ys .=Kdldrhla jk ixLHd 3la ,shkak'

(7) 150g wvq 9ys úYd,;u .=Kdldrh l=ula o@

(8) my; i|yka tla tla ixLHdj i|yd .=Kdldr 5la ne.ska ,shkak'

(i) 4 (ii) 13 (iii) 15 (iv) 18 (v) 20

(9) ysia ;eka iïmQ¾K lrkak'

(i) 10ys iEu .=Kdldrhla u wksjd¾hfhka u ''''''''' iy '''''''' ys .=Kdldrhla fõ'

(ii) 11«7 = 77' 77 ixLHdj '''''''' ys .=Kdldrhls' 77 ixLHdj '''''' ys .=Kdldrhls'

(10) 3 iy 4 hk ixLHd foflys u .=Kdldrhla jk ixLHd folla ,shkak'

(11) 2" 3 iy 4 hk ixLHd ;=fkys u .=Kdldrhla jk ixLHdjla ,shkak'

fkdñf,a fnod yeÍu i|yd h'146

² idOl yd .=Kdldr wdY%s; .eg¨ úi`§u oeka wms idOl yd .=Kdldr wdY%s; .eg¨ úi|uq'

ksoiqk 1

wem,a f.ä 30la tl u md¾i,hl fyda iEu md¾i,hlg u iudk wem,a f.ä ixLHdjla ne.ska fyda ;sfnk fia md¾i,a l< hq;= j we;' tf,i wem,a f.ä .Kk md¾i,a l< yels wdldr .Kk fidhkak' tla tla wjia:dfõ md¾i,hl we;s wem,a f.ä .Kk yd md¾i,a .Kk fidhkak'

md¾i,hl we;s wem,a f.ä ixLHdfõ;a Bg wod< md¾i,a ixLHdfõ;a .=‚;fhka wem,a f.ä ixLHdj ,efí' tneúka md¾i,hl we;s wem,a f.ä ixLHdj yd Bg wod< md¾i,a ixLHdj 30ys idOl hq., u.ska oelaúh yels h' 30 = 1 « 30 30 = 6 « 5 30 = 2 « 15 30 = 10 « 3 30 = 3 « 10 30 = 15 « 2 30 = 5 « 6 30 = 30 « 1

tneúka wem,a f.ä 30 md¾i,a l< yels wdldr 8la fõ'

md¾i,hl wem,a f.ä 1la úg md¾i,a .Kk 30ls'

md¾i,hl wem,a f.ä 2la úg md¾i,a .Kk 15ls'

md¾i,hl wem,a f.ä 3la úg md¾i,a .Kk 10ls'

md¾i,hl wem,a f.ä 5la úg md¾i,a .Kk 6ls'

md¾i,hl wem,a f.ä 6la úg md¾i,a .Kk 5ls'

md¾i,hl wem,a f.ä 10la úg md¾i,a .Kk 3ls'

md¾i,hl wem,a f.ä 15la úg md¾i,a .Kk 2ls'

md¾i,hl wem,a f.ä 30la úg md¾i,a .Kk 1ls'

fkdñf,a fnod yeÍu i|yd h' 147

11'5 wNHdih

^1& ldnka mEkl ñ, re 12ls' tu j¾.fha mEka 8l ñ, lSh o@ th 8ys yd 12ys .=Kdldrhla fõ o@

^2& ksjilg Èklg jrla c,h .e¨ï 75la mqrjk msrjqï hka;%hla we;' fuu msrjqï hka;%h i;shla ;=< § mqrjk jdr .Kk yd tA i|yd wjYH c, m%udKh fidhkak'

^3& rUqgka f.ähl ñ, re 6ls'

fkdñf,a fnod yeÍu i|yd h'148

² ixLHdjla foflka fnfoa oe hs mÍlaId lsÍu

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

² by; ixLHdj,ska foflka fnfok tla tla ixLHdj jgd rjqula ne.ska w¢kak'

² tys §" foflka fnfok ixLHdj, tlia:dkfha we;s b,lalï ,shd olajkak'

² túg Tng 2" 4" 6" 8" 0 hk b,lalï ,efí' tu b,lalï o foflka fnfok nj ksÍlaIKh lrkak'

² foflka fkdfnfok ^rjqï fkdfh¥& ixLHdj, tlia:dkfha b,lalu n,kak'

tu b,lalï 1, 3, 5, 7 iy 9 fõ' fuu b,lalï foflka fkdfnfoa'

ls%hdldrlu 2

fï wkqj ixLHdjl tlia:dkfha b,lalu foflka fnfoa kï" tu ixLHdj 2ka fnfoa' tfia u hï lsis ixLHdjl tlia:dkfha b,lalu foflka fkdfnfoa kï" tu ixLHdj foflka fkdfnfoa'

² ixLHdjla mfyka fnfoa oe hs mÍlaId lsÍu

5, 10, 15, 20, 25, 30, 35, 40, 45, ''' jeks mfyys .=Kdldr ish,a, mfyka b;sß ke;s j fnfok nj ñka fmr bf.k .;af;uq'

fïjdfha tlia:dkfha we;s b,lalu foi n,kak' fuu ixLHdj, tlia:dkfha b,lalu iEu úg u 0 fyda 5 fyda fõ'

fuf,i hï ixLHdjl tlia:dkfha b,lalu 0 fyda 5 fyda fõ kï" tu ixLHdj mfyka b;sß ke;s j fnfoa'

² ixLHdjla oyfhka fnfoa oe hs mÍlaId lsÍu

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, ''' hk 10ys .=Kdldr 10ka b;sß ke;s j fnfok nj óg fmr bf.k .;af;uq'

fïjdfha tlia:dkfha we;s b,lalu foi n,kak'

fuu ixLHdj, tlia:dkfha b,lalu iEu úg u 0 fõ'

fkdñf,a fnod yeÍu i|yd h' 149

fuf,i" hï ixLHdjl tlia:dkfha we;s b,lalu 0 fõ kï" tu ixLHdj 10ka b;sß ke;s j fnfoa'

11'6 wNHdih

^1& my; oelafjk ixLHd w;=ßka foflka b;sß ke;s j fnfok ixLHd f;dard ,shkak'

25, 33, 42, 57, 64, 69, 126, 135, 148, 250, 331, 1457, 3263, 4584, 2689, 3150,

^2& 128 hk b,lalï 4lska hq;a fuu ixLHdj 2ka b;sß ke;s j fnfoa kï" ysia fldgqjg ;sìh yels b,lalï fudkjd o@

^3& fldgqfjys" § we;s ixLHd w;=ßka" bÈß fldgqj,g .e

fkdñf,a fnod yeÍu i|yd h'150

^5& foflka fnfok ixLHd wdfrdayK ms

fkdñf,a fnod yeÍu i|yd h' 151

^7& oyfhka fnfok ixLHd wdfrdayK ms