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xf.kr
mís';eSftd vpj 15 osQ ,d 3 × 3 eSftd oxZ dh jpuk djukA
vko';d lkexzh
l-isQn dkx”k] LosQp isu] isafly] :yj A
jpuk dh fofèk1- ,d l-isQn dkx”k yhft, vkSj ml ij ,d 3 × 3 oxZ okyh fxzM [khafp,] tSlk fd
vkoQfr 1 esa n'kkZ;k x;k gSA
vko`Qfr 1
2- bl fxzM dh izR;sd Hkqtk osQ chp okys oxZ osQ ckgj] vkoQfr 2 esa n'kkZ, vuqlkj] pkj oxZ[khafp,A
vko`Qfr 2
fozQ;kdyki
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
3- vkoQfr 3 esa n'kkZ, vuqlkj la[;kvksa 1 ls 9 dks fyf[k,A
vko`Qfr 3
4- vc] ckgj fy[kh la[;kvksa dks vkoQfr 4 esa rhjksa }kjk n'kkZ, vuqlkj fyf[k,A
vko`Qfr 4
5- vc ckgj cus oxks± dks feVk nhft, vkSj vkoQfr 5 esa n'kkZ, vuqlkj ,d oxZ izkIr dhft,A
vko`Qfr 5
izn'kZuvkoQfr 5 ls ,d eSftd oxZ izkIr gksrk gS] tks 1 ls 9 rd dh la[;kvksa ls cuk gSA blesa izR;sdiafDr] izR;sd LraHk rFkk izR;sd fod.kZ dh la[;kvksa dk ;ksx 15 gS (tks eSftd vpj dgykrk gS)A
26/04/2018
xf.kr
izs{k.kfuEu lkj.kh dks iwjk dhft,&
la[;k ;ksx
fod.kZ 1
fod.kZ 2
LraHk 1
LraHk 2
LraHk 3
iafDr 3
iafDr 2
iafDr 1
eSftd vpj
vuqiz;ksx1- bl fozQ;kdyki }kjk fdlh Hkh eSftd vpj] tSls µ 18] 21] 24 bR;kfn dk 9 ozQekxr
izkoQfrd la[;kvksa osQ mi;ksx ls 3 × 3 eSftd oxZ cuk;k tk ldrk gSA
2- bl fozQ;kdyki dk mi;ksx 5 × 5 eSftd vpj cukus esa fd;k tk ldrk gSA
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
mís';
eSftd vpj 15 osQ ,d 3 × 3 eSftd oxZ dh jpuk djukA
vko';d lkexzh
pkVZ isij] jaxhu dkx”k] LosQp isu] oSaQph] :yj bR;kfnA
jpuk dh fofèk1- ekiu 12 bdkbZ × 12 bdkbZ dk ,d pkVZ isij yhft,A2- bl pkVZ isij ij ,d 3 × 3 dk oxZ cukb,A
izn'kZu1- chp okys oxZ esa] la[;k 5 (= 15 ÷ 3) fyf[k,] ftls
osaQnzh; la[;k dgrs gSaA
2- oasQnzh; la[;k esa 2 tksfM+, vkSj osaQnzh; la[;k esa ls 2?kVkb, rFkk buls izkIr la[;kvksa dks oasQnzh; la[;k osQozQe'k% nkb± vksj vkSj ckb± vksj osQ oxks± esa osaQnzh; iafDrosQ vuqfn'k fyf[k, (vko`Qfr 1)A
3- osaQnzh; la[;k esa 1 tksfM+, vkSj oasQnzh; la[;k esa ls 1?kVkb, rFkk buls izkIr la[;kvksa dks nk,¡ fod.kZ osQvuqfn'k ozQe'k% mQij dh vksj vkSj uhps dh vksj fyf[k,(vko`Qfr 2)A
4- oasQnzh; la[;k esa 3 tksfM+, vkSj oasQnzh; la[;k esa ls 3?kVkb, rFkk buls izkIr la[;kvksa dks ck,¡ fod.kZ osQvuqfn'k ozQe'k% mQij dh vksj vkSj uhps dh vksj fyf[k,(vko`Qfr 3)A
vko`Qfr 1
vko`Qfr 2
fozQ;kdyki
26/04/2018
xf.kr
5- osaQnzh; la[;k esa ls 4 ?kVkb, vkSj oasQnzh; la[;k esa 4 tksfM+,rFkk buls izkIr la[;kvksa dks oasQnzh; LraHk osQ vuqfn'k ozQe'k%mQij dh vksj vkSj uhps dh vksj fyf[k,A (vko`Qfr 4)A
izs{k.k
vuqiz;ksx1- ;gh fofèk oqQN vU; eSftd vpjksa okys la[;kvksa osQ fy, Hkh iz;qDr dh tk ldrh gSA
(3 osQ xq.kTk)A
2- 1 ls 9 rd dh la[;kvksa dh txg dksbZ Hkh 9 ozQfed izkoQfrd la[;kvksa dks fy;k tkldrk gSA
vko`Qfr 3 vko`Qfr 4
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
mís';xq.kt vkSj xq.ku[kaM Kkr djukA
vko';d lkexzh
,d l-isQn pkVZ isij] :yj] isafly] fofHkUu jaxksa osQ LosQp isuA
jpuk dh fofèk1- ,d pkVZ isij yhft, vkSj ml ij ,d 10 × 10 fxzM [khafp,A
2- iafDr;ksa vkSj LraHkksa ij 1 ls 10 rd la[;k,¡ fyf[k, (vkoQfr 1)A
(iafDr;ksa vkSj LraHkksa osQ Åij ls 10 la[;k,¡ fy[ksaA)
vko`Qfr 1
fozQ;kdyki
26/04/2018
xf.kr
3- LraHk 1 osQ oxks± dks xqykch jax ls jafx,A
4- LraHk 2 esa] izR;sd nwljs oxZ dks ihys jax ls jafx,A
5- LraHk 3 esa] izR;sd rhljs oxZ dks dkys jax ls jafx,A
6- LraHk 4 esa] izR;sd pkSFks oxZ dks yky jax ls jafx,A
7- LraHk 5 esa] izR;sd ik¡pos oxZ dks gjs jax ls jafx,A
8- LraHk 6 esa] izR;sd NBs oxZ dks uhys jax ls jafx,A
9- LraHk 7 esa] izR;sd lkrosa oxZ dks ukjaxh jax ls jafx,A
10- LraHk 8 esa] izR;sd vkBosa oxZ dks ukjaxh jax ls jafx,A
11- LraHk 9 esa] izR;sd ukSosa oxZ dks cSaxuh jax ls jafx,A
12- LraHk 10 esa] izR;sd nlosa oxZ dks Hkwjs jax ls jafx,A (vkoQfr 2)
vko`Qfr 2
izn'kZu1- 1 osQ xq.ktksa dks tkuus osQ fy, 1 osQ uhps osQ LraHk osQ jaxhu oxZ ns[ksaA 1] 2] 3] --- dh iafDr;ksa
osQ lHkh oxZ jaxhu gSaA 1 osQ xq.kt gSa 1] 2] 3] --- (xqykch jax esa) gSaA
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
2- 2 osQ xq.ktksa dks Kkr djus osQ fy, 2 osQ uhps osQ LRakHk osQ jaxhu oxZ ns[ksaA 2] 4] 6] 8] 10dh iafDr osQ oxZ jaxhu gSaA 2 osQ x.kqt gSa] 2] 4] 6] 8] ---
blh rjg nwljh la[;kvksa osQ xq.kt ns[ksaA
3- 1 osQ xq.ku[kaM+ksa dks tkuus osQ fy, 1 dh iafDr osQ jaxhu oxks± dks ns[ksaA osQoy 1 osQ uhps dkoxZ jaxhu gSA 1 dk xq.ku[kaM 1 gSA
4- 2 osQ xq.ku[kaMksa dks Kkr djus osQ fy,] 2 dh iafDr osQ jaxhu oxks± dks ns[ksaA 1 vkSj 2 osQ uhpsokys oxZ jaxhu gSaA 2 osQ xq.ku[kaM 1 vkSj 2 gSaA
blh rjg nwljh la[;kvksa osQ xq.ku[kaM ns[ksaA
izs{k.kfuEu lkj.kh dks iwjk djsa&
la[;k xq.kt xq.ku[kaM
1 1, 2, 3, ... 1
2 ––– –––
3 ––– –––
4 ––– –––
5 ––– –––
6 6 1, 2, 3, 6
7 ––– –––
8 ––– –––
9 ––– –––
10 ––– –––
vuqiz;ksx1- ;g fozQ;kdyki la[;kvksa osQ xq.ktksa vkSj xq.ku[kaMksa dks Li"V djus osQ fy, mi;ksxh gSA
2- ;g fozQ;kdyki vHkkT; la[;kvksa dh voèkkj.kk dks] mu iafDr;ksa dh lgk;rk ls ftuesa osQoynks oxZ jaxs gq, gSa] Li"V djus osQ fy, Hkh fd;k tk ldrk gSA
3- bl fozQ;kdyki dks vkxs 20 rd dh la[;k,¡ ysdj foLrr fd;k tk ldrk gSA
26/04/2018
xf.kr
mís';,d nh gqbZ la[;k (eku yhft, 18) osQ xq.ku[kaM Kkr djukA
vko';d lkexzh
i;kZIr la[;k eas cVu] dkx”k] isafly@isuA
jpuk dh fof/18 cVu yhft, vkSj mUgsa iafDr;ksa esa uhps n'kZk, vuqlkj bl rjg O;ofLFkr dhft, fd gj iafDresa leku la[;k esa cVu gksaA
1- cVuksa dks ,d iafDr esa vkÑfr 1 esa n'kkZ, vuqlkj O;ofLFkr dhft,A
vkÑfr 1
2- bUgh cVuksa dks vkÑfr 2 esa n'kkZ, vuqlkj nks iafDr;ksa esa O;ofLFkr dhft,A
vkÑfr 2
3- cVuksa dks vkÑfr 3 esa n'kkZ, vuqlkj rhu iafDr;ksa esa O;ofLFkr dhft,A
vkÑfr 3
4- bu cVuksa dks vkÑfr 4 esa n'kkZ, vuqlkj 6 iafDr;ksa esa O;ofLFkr dhft,A vkÑfr 4
5- cVuksa dks vkÑfr 5 esa n'kkZ, vuqlkj 9 iafDr;ksa esa O;ofLFkr dhft,A
fozQ;kdyki
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
vkÑfr 6
6- cVuksa dks 18 iafDr;ksa esa O;ofLFkr dhft, (vkÑfr 6)A
çn'kZu1- vkÑfr 1 esa cVuksa dh O;oLFkk dks 18 = 1 × 18 osQ :i esa O;Dr
fd;k tk ldrk gS (iafDr;ksa dh la[;k × LraHkksa dh la[;k)2- vkÑfr 2 esa] cVuksa dh O;oLFkk dks 18 = 2 × 9 osQ :i esa O;Dr fd;k
tk ldrk gSA3- blh çdkj] vkÑfr 3 ls] 18 = 3 × 6;
vkÑfr 3 ls] 18 = 3 × 6;vkÑfr 4 ls] 18 = 6 × 3;vkÑfr 5 ls] 18 = 9 × 2 rFkkvkÑfr 6 ls] 18 = 18 × 1
vr%] 18 osQ xq.ku[kaM+ 1] 2] 3] 6] 9 vkSj 18 gSaAblh çdkj] vU; la[;kvksa] tSls 20] 24] 28] bR;kfn osQ xq.ku[akMçkIr fd, tk ldrs gSaA
çs{k.kfuEufyf[kr lkj.kh dks iwjk dhft,&
la[;k iafDr;¡k (R) LraHk (C) (R × C) xq.ku[kaM
18 1 18 1 × 18 ––, ––
2 9 2 × 9 ––, ––
3 6 3 × 6 ––, ––
20 1 20 –– × –– ––, ––
2 10 –– × –– ––, ––
.......... .......... –– × –– ––, ––
24 –– –– –– × –– ––, ––
–– –– –– × –– ––, ––
.......... .......... –– × –– ––, ––
28 –– –– –– × –– ––, ––
.......... .......... –– × –– ––, ––
vuqç;ksxbl fØ;kdyki dk mi;ksx fdlh la[;k osQ xq.ku[akMkass] xq.ktksa osQ vFkZ dks Li"V djus osQ fy, fd;ktk ldrk gSA
vkÑfr 5
26/04/2018
xf.kr
mís';fo|kfFkZ;ksa dh gFksfy;ksa osQ ekiksa dh rqyuk djukA
vko';d lkexzh,d oxkZdkj fxzM isij] jaxhu isafly@isu] dkx”kA
jpuk dh fof/1- cPpksa dks ik¡p&ik¡p osQ lewgksa esa foHkkftr dhft,A2- ,d oxkZdkj fxzM isij yhft,A3- fdlh ,d lewg osQ ,d cPps ls ml ij iatk j[kokb,A vc iats dh ckgjh lhek osQ vuqfn'k
isafly ?kqekdj fxzM isij ij iats dh vkÑfr çkIr dhft,A
çn'kZu1- tc cPph fxzM isij ij vius ck,¡ gkFk dk iatk j[krh gS] rc og nk,¡ gkFk ls iasfly ;k
isu dks iats osQ vuqfn'k ?kqekdj fxzM ij mldh ifjlhek cuk nsxhA2- vc bl ifjlhek osQ vanj osQ oxks± dks fxfu,A blosQ fy, vk/s] oxZ dks
1
2 oxZ] vk/s lsvf/d ;k iw.kZ oxZ dks 1 oxZ yhft, rFkk vk/s ls de dks NksM+ nhft,A
3- lewg osQ vU; lnL; bls ,d lkj.kh esa fjdkWMZ djasxsA4- ;g lewg osQ çR;sd cPps osQ fy, fd;k tk,xkA
çs{k.kcPpk oxks± dh la[;k (vk/s oxks± dh vk/ksa dk {ks=kiQy (oxZ
ls vf/d ;k iw.kZ) la[;k (vk/s) ;ksx bdkbZ esa)
1 70 20 10 70 + 10 = 10
2 – – – –
3 – – – –
vuqç;ksxbl fozQ;kdyki dk foLrkj iÙks vkSj nwljh oLrqvksa dk {ks=kiQy fudkyus osQ fy, fd;k tk ldrk gSA
fozQ;kdyki
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
mís';fofHkUu oLrqvksa dk iz;ksx djrs gq,] ?ku vkSj ?kukHkksa osQ tky cukukA
vko';d lkexzh
[kkyh pkWd dk fMCck] feBkbZ dk fMCck] twrksa dk fMCck] isLVªhckWDl bR;kfn] isu@isafly] oSaQph] dkMZcksMZ] l-isQn dkx”k] lsyksVsiA
jpuk dh fofèk1- ,d lqfoèkktud eki dk dkMZcksMZ yhft, vkSj ml ij ,d l-isQn dkx”k fpidkb,A
2- fdlh fMCcs ;k ckWDl (eku yhft, isLVªh ckWDl) dks mlosQ eksM+ osQ vuqfn'k [kksydj iSQyknhft,A
3- bls dkMZcksMZ ij jf[k, rFkk bldh ifjlhek [khafp, rFkk blosQ eksM+ osQ vuqfn'k Hkh js[kk,¡[khafp,] tSlk uhps n'kkZ;k x;k gS&
izn'kZu1- bl izdkj izkIr vkdkj ,d ?kukHk (isLVªh ckWDl) dk tky gSA
2- ;fn bls fcanqfdr js[kkvksa osQ vuqfn'k eksM+k tk,] rks ,d ?kukHk (ckWDl) izkIr gksrk gSA
3- blesa loZle vk;rksa osQ rhu ;qXe gSaA
fozQ;kdyki
26/04/2018
xf.kr
izs{k.klkj.kh dks iwjk dhft,&
ozQe la[;k ckWDl ;k fMCck vk;rksa dh oxks± dhla[;k la[;k
1 isLVªh ckWDl 6 0
2 pkWd dk fMCck –– ––
3 feBkbZ dk fMCck –– ––
4 twrksa dk fMCck –– ––
vuqiz;ksx;g fozQ;kdyki 3D vkdkjksa osQ tkyksa dh voèkkj.kk rFkk muosQ iQydksa] fdukjksa vkSj 'kh"kks± dksle>kus osQ fy, mi;ksxh gSA bu tkyksa dk mi;ksx fofHkUu iSfoaQx ckWDlksa dks cukus esa Hkh fd;k tkldrk gSA
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
mís';
3-D vkdkjksa esa 2-D vkdkjksa dh igpku djukA
vko';d lkexzh
pkWd dk fMCck] cksry dk <Ddu] dVksjk] ekfpl dh fMCch]isafly ckWDl] isLVªh ckWDl bR;kfn] dkMZcksMZ] xksan] dkx”k]isafly] jcM+] l-isQn dkx”kA
jpuk dh fofèk1- ,d dkMZcksMZ yhft, vkSj ml ij ,d l-isQn dkx”k fpidkb,A
2- dksbZ 3-D oLrq (eku yhft, ,d pkWd dk fMCck) yhft, vkSj mls dkMZcksMZ ij jf[k,A
3- dkMZcksMZ ij fLFkr blosQ iQyd dh ifjlhek dk vuqjs[k.k dhft,A blh izdkj] pkWd osQ fMCcsosQ vU; iQydksa dh ifjlhek,¡ [khafp,A
4- ;g izfozQ;k nwljh oLrqvksa osQ fy, nksgjkb;s vkSj tgk¡ Hkh gks losQ mudh ifjlhek dks vuqjsf[krdhft,A
izn'kZu1- dkMZcksMZ ij nh gqbZ oLrq (pkWd dk fMCck) dh ifjlhek,¡ 3-D vkdkjksa esa fofHkUu 2-D
vkdkjksa dks n'kkZrh gSaA
fozQ;kdyki
26/04/2018
xf.kr
izs{k.klkj.kh dks iwjk dhft,µ
ozQe la[;k oLrq dk uke 2-D vkdkj
oxZ vk;r o`Ùk
1 pkWd dk fMCck
2 cksry dk <Ddu
3 dVksjk
4 isafly ckWDl
5 isLVªh ckWDl. .. .. .
vuqiz;ksx;g fozQ;kdyki cPpksa dks fofHkUu 3-D vkdkjksa dks le>us esa enn djsxkA
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
mís';,d la[;k fijkfeMA
jpuk dh fof/1- uhps n'kkZ, vuqlkj fijkfeM cukb,&
2-
vkb, [ksysan'kkZ, x, iSVuZ dh igpku dj fijkfeMksa osQ [kkyh ckWDlksa dks HkjsaA
fozQ;kdyki[[ksy]
26/04/2018
xf.kr
mís';[kkyh cDls HkjukA
vkb, [ksysala[;kvksa 20] 30] 40] 50 vkSj 60 dks bl izdkj fyf[k, fd izR;sd iafDr vkSj izR;sd LraHk esala[;kvksa dk oqQy ;ksx uhps fn, vuqlkj gks&
(i)
(ii)
(iii)
lHkh laHko mÙkjksa dks fyf[k,A
fozQ;kdyki[[ksy]
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
,d la[;k igsyhfxzM esa uhps fy[kh gqbZ lHkh la[;kvksa dks Hkfj,&
602 2317 12446
105 2488 17629
172 6156 32042
400 8041 26141
431 8463 68314
546 8662
569
fozQ;kdyki[igsyh]
26/04/2018
xf.kr
,d ozQkWl la[;k [ksyfn, gq, ozQkWl la[;k [ksy dks ck,¡ ls nk,¡ vkSj Åij ls uhps esa nh gqbZ leL;kvksa dks gy djrs gq,Hkfj,&
vko`Qfr 1
ck,¡ ls nk,¡ (iafDr) Åij ls uhps (LraHk)1. 28 + 54 1. 332 + 520
3. 17 × 3 2. 5000 – 2841
4. 655 – 398 5. 147 × 5
6. 92 – 16 6. 50 + 20 + 5
8. 234 × 4 7. 500 + 100 + 75
10. 500 + 72 9. 8 × 8
12. 18 × 3 11. 2000 + 400 + 80 + 5
13. 540 + 4 14. 700 – 248
15. 300 – 215
16. 227 – 175
fozQ;kdyki[[ksy]
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
ifjdyuksa dh oqQN laf{kIr fof/;k¡la[;kvksa osQ ;ksx] ?kVkus] xq.ku vkSj foHkktu tSlh lafØ;kvksa ls fo|kFkhZ ifjfpr gSaA vusd fLFkfr;ksaesa ;g vko';d gks tkrk gS fd oqQN lafØ;k,¡ eu esa gh dh tk,¡A efLr"d esa gh dh xbZ ;s lafØ;k,¡oqQN laf{kIr fof/;ksa osQ vk/kj ij dh tkrh gaSA bl izkstsDV esa] ifjdyuksa dh oqQN laf{kIr fof/;ksals voxr djkus dk iz;Ru fd;k x;k gSA
tc ekuo us la[;kvksa vkSj fxuus dh fof/;ksa dh [kkst dh] rc og viuh u;h /kj.kkvksa ijeksfgr gks x;kA tSls&tSls le; O;rhr gksrk x;k] ekuo us vkSj vf/d Kku vftZr fd;k rFkktSls&tSls mldk thou vkSj vf/d tfVy gksrk x;k] mlus ifjdyuksa osQ dk;Z dks laf{kIr djus dhfof/;ksa dh [kkst djuh izkjaHk dj nhA blls vcsdl] y?kqx.kd] oSQyoqQysVj vkSj oaQI;wVj tSls la;a=kksadk fodkl gqvkA
;|fi ekuo us [kkst djus dh bruh {kerk n'kkZbZ gS] fiQj Hkh ^ifjdyu osQ dkS'kyksa* dhvko';drk dks feVk;k ugha tk ldrkA dksbZ O;fDr vius ijpwu dh nqdku osQ fcy vFkok viuscSad osQ [kkrs osQ fooj.k dh tk¡p djus osQ fy, lnSo ,d ifjdyu la;a=k ysdj ugha py ldrkAijarq ekufld vadxf.kr dks djus esa rs”kh ykus dh vusd fof/;k¡ gSaA ;s laf{kIr fof/;k¡] le; dhcpr osQ lkFk&lkFk] ,d O;fDr dh ifjdyu {kerk ls nwljksa dks vk'p;Zpfdr djrh gSaA
mís'; ifjdyuksa osQ fy, laf{kIr fof/;ksa dks le>uk vkSj mudk mi;ksx djukA
fooj.k1- fdlh la[;k dk 5 ls xq.ku
fdlh la[;k dks 5 ls xq.kk djus osQ fy,] igys ml la[;k dks 2 ls foHkkftr dhft, vkSj izkIrHkkxiQy dks 10 ls xq.kk dj nhft,A (vFkok nh gqbZ la[;k dks 10 ls xq.kk dhft, vkSj izkIrxq.kuiQy dks 2 ls Hkkx dhft,)A
mnkgj.kkFkZ % (a) 42 × 5
izkstsDV
26/04/2018
xf.kr
pj.k 1 : la[;k dks 2 ls Hkkx nhft,
42 ÷ 2 = 21
pj.k 2 : HkkxiQy dks 10 ls xq.kk dhft,A
21 × 10 = 210
vr% 42 × 5 = 210
;k
pj.k 1 : la[;k dks 10 ls xq.kk dhft,A
42 × 10 = 420
pj.k 2 : xq.kuiQy dks 2 ls Hkkx nhft,A
420 ÷ 2 = 210
vr% 42 × 5 = 210
(b) 67 × 5
pj.k 1 : 67 × 10 = 670
pj.k 2 : 670 ÷ 2 = 335
vr% 67 × 5 = 335
2- fdlh la[;k dk 25 ls xq.kuµ
nh gqbZ la[;k dks 100 ls xq.kk dhft, vkSj fiQj xq.kuiQy dks 4 ls Hkkx nhft,A
mnkgj.kkFkZ % (a) 16 × 25
pj.k 1 : la[;k dks 100 ls xq.kk dhft,A
16 × 100 = 1600
pj.k 2 : xq.kuiQy dks 4 ls Hkkx nhft,A
1600 ÷ 4 = 400
vr% 16 × 25 = 400
(b) 81 × 25
pj.k 1 : 81 × 100 = 8100
pj.k 2 : 8100 ÷ 4 = 2025
vr% 81 × 25 = 2025
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
3- fdlh la[;k dks 5 ls Hkkx nsukµ
nh gqbZ la[;k dks 2 ls xq.kk dhft, rFkk xq.kuiQy dks 10 ls Hkkx nhft,A
mnkgj.kkFkZ % (a) 32 ÷ 5
pj.k 1 : 32 dks 2 ls xq.kk dhft,A
32 × 2 = 64
pj.k 2 : izkIr xq.kuiQy dks 10 ls Hkkx nhft,A
64 ÷ 10 = 6.4
vr% 32 ÷ 5 = 6.4
(b) 121 ÷ 5
pj.k 1 : 121 × 2 = 242
pj.k 2 : 242 ÷ 10 = 24.2
vr% 121 ÷ 5 = 24.2
4- fdlh la[;k dks 25 ls Hkkx nsukµ
nh gqbZ la[;k dks 4 ls xq.kk dhft, rFkk izkIr xq.kuiQy dks 100 ls Hkkx nhft,A
mnkgj.kkFkZ % (a) 5 ÷ 25
pj.k 1 : la[;k 5 dks 4 ls xq.kk dhft,A
5 × 4 = 20
pj.k 2 : xq.kuiQy 20 dks 100 ls Hkkx nhft,A
20 ÷ 100 = 0.20
vr% 5 ÷ 25 = 0.20
(b) 215 ÷ 25
pj.k 1 : 215 × 4 = 860
pj.k 2 : 860 ÷ 100 = 8.6
vr% 215 ÷ 25 = 8.6
26/04/2018
xf.kr
5- fdlh la[;k esa 9] 99] 999] --- dks tksM+ukµ
9 tksM+us osQ fy,] nh gqbZ la[;k esa 10 tksfM+, rFkk izkIr ;ksx esa ls 1 ?kVkb,A 99 tksM+us osQ fy,]nh gqbZ la[;k esa 100 tksfM+, rFkk izkIr ;ksx esa ls 1 ?kVkb,] bR;kfnA
mnkgj.kkFkZ % (a) 2 + 9
pj.k 1 : nh gqbZ esa 10 tksfM+,A
2 + 10 = 12
pj.k 2 : ;ksx esa ls 1 ?kVkb,A
12 –1 = 11
vr% 2 + 9 = 11
(b) 18 + 99
pj.k 1 : 18 + 100 = 118
pj.k 2 : 118 – 1 = 117
vr% 18 + 99 = 117
(c) 124 + 999
pj.k 1 : 124 + 1000 = 1124
pj.k 2 : 1124 – 1 = 1123
vr% 124 + 999 = 1123
6- fdlh la[;k dks 9] 99] 999] --- ls xq.kk djukµ
9 ls xq.kk djus osQ fy, µ nh gqbZ la[;k dks 10 ls xq.kk dhft, rFkk izkIr xq.kuiQy esa ls ml la[;kdks ?kVkb,A
mnkgj.kkFkZ % (a) 8 × 9
pj.k 1 : nh gqbZ la[;k dks 10 ls xq.kk dhft,A
8 × 10 = 80
pj.k 2 : xq.kuiQy esa ls la[;k 8 dks ?kVkb,A
80 – 8 = 72
vr% 8 × 9 = 72
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
(b) 23 × 99
pj.k 1 : la[;k 23 dks 100 ls xq.kk dhft,A
23 × 100 = 2300
pj.k 2 : xq.kuiQy esa ls la[;k 23 dks ?kVkb,A
2300 – 23 = 2277
vr% 23 × 99 = 2277
7- fdlh la[;k esa ls 9] 99] 999] --- ?kVkuk
9 ?kVkus osQ fy, µ la[;k esa 1 tksfM+, rFkk izkIr ;ksx esa ls 10 ?kVkb,A
99 ?kVkus osQ fy, µ la[;k esa 1 tksfM+, rFkk izkIr ;ksx esa ls 100 ?kVkb,] bR;kfnA
mnkgj.kkFkZ % (a) 24 – 9
pj.k 1: 24 esa 1 tksfM+,A
24 + 1 = 25
pj.k 2 : ;ksx esa ls 10 ?kVkb,A
25 – 10 = 15
vr% 24 – 9 = 15
(b) 256 – 99
pj.k 1 : 256 + 1 = 257
pj.k 2 : 257 – 100 = 157
vr% 256 – 99 = 157
(c) 1457 – 999
pj.k 1 : 1457 + 1 = 1458
pj.k 2 : 1458 – 1000 = 458
vr% 1457 - 999 = 458
26/04/2018
xf.kr
8- bdkbZ osQ vad 5 okyh la[;k dk Lo;a mlls xq.kk djuk
(a) eku yhft, fd la[;k 135 gSA
fcuk bdkbZ osQ vad osQ cuh la[;k = 13
13 vkSj (13 + 1) dks xq.kk djus ij] gesa 13 × 14 = 182
izkIr gksrk gSA
bdkbZ osQ vadkas dk xq.kuiQy = 5 × 5 = 25
vr% 135 × 135 = 18225
(b) 45 × 45
fcuk bdkbZ osQ vad ls cuh la[;k = 4
4 vkSj (4 + 1), vFkkZr~ 5 dks xq.kk djus ij] gesa 4 × 5 = 20
izkIr gksrk gSA
bdkbZ osQ vadksa dk xq.kuiQy = 25
vr% 45 × 45 = 2025
9- fdlh la[;k dks 11 ls xq.kk djukµ
fdlh la[;k dks 11 ls xq.kk djus osQ fy, igys la[;k dks 10 ls xq.kk dhft, rFkk izkIrxq.kuiQy esa og la[;k tksfM+,A
mnkgj.kkFkZ % (a) 13 × 11
pj.k 1 : la[;k dks 10 ls xq.kk dhft,A
13 × 10 = 130
pj.k 2 : xq.kuiQy esa ogh la[;k tksfM+,A
130 + 13 = 143
vr% 13 × 11 = 143
(b) 25 × 11
pj.k 1 : 25 × 10 = 250
pj.k 2 : 250 + 25 = 275
vr% 25 × 11 = 275
26/04/2018
iz;ksx'kkyk iqfLrdk µ izkjafHkd Lrj
1- la[;k izfr:iA
2- bl le; fofHkUu Hkk"kkvksa esa iz;ksx fd, tkus okys la[;k¡dA
3- izkphu dky esa iz;qDr la[;k¡dksa osQ ckjs esaA
4- la[;kvksa dk fofHkUu rjhdksa ls xq.ku (ikB~;iqLrd esa fn, x, rjhdksa ls fHkUu)A
5- oqQN bykdksa osQ ekufp=kksa dk laxzg vkSj muosQ egRoiw.kZ fu'kkuksa osQ ckjs esa ppkZA
6- VSuxzkWe osQ VqdM+ksa dh enn ls fofHkUu vkoQfr;ksa dks cukukA
7- fdlh nh gqqbZ rkjh[k ls laxr lIrkg osQ fnu dks igpkuuk (oSQysaMj ,oa mlosQ mi;ksx)A
izkstsDV~l dhizLrkfor lwph
26/04/2018