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xf.kr s '; eS ftd vpj 15 os Q ,d 3 × 3 eS ftd oxZ dh jpuk djukA vko';d lkexz h l- is Qn dkx”k] Los Qp is u] is a fly] :yj A jpuk dh fofèk 1- ,d l- is Qn dkx”k yhft, vkS j ml ij ,d 3 × 3 oxZ okyh fxz M [kha fp,] tS lk fd vko` Qfr 1 es a n'kkZ ;k x;k gS A vko`Qfr 1 2- bl fxz M dh iz R;s d Hkq tk os Q chp okys oxZ os Q ckgj] vko` Qfr 2 es a n'kkZ , vuq lkj] pkj oxZ [kha fp,A vko`Qfr 2 fo z Q;kdyki 26/04/2018

Lab manual Activity 17 to 27 - NCERT

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Page 1: Lab manual Activity 17 to 27 - NCERT

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

Page 2: Lab manual Activity 17 to 27 - NCERT

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

Page 3: Lab manual Activity 17 to 27 - NCERT

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

Page 4: Lab manual Activity 17 to 27 - NCERT

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

Page 5: Lab manual Activity 17 to 27 - NCERT

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

Page 6: Lab manual Activity 17 to 27 - NCERT

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

Page 7: Lab manual Activity 17 to 27 - NCERT

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

Page 8: Lab manual Activity 17 to 27 - NCERT

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

Page 9: Lab manual Activity 17 to 27 - NCERT

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

Page 10: Lab manual Activity 17 to 27 - NCERT

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

Page 11: Lab manual Activity 17 to 27 - NCERT

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

Page 12: Lab manual Activity 17 to 27 - NCERT

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

Page 13: Lab manual Activity 17 to 27 - NCERT

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

Page 14: Lab manual Activity 17 to 27 - NCERT

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

Page 15: Lab manual Activity 17 to 27 - NCERT

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

Page 16: Lab manual Activity 17 to 27 - NCERT

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

Page 17: Lab manual Activity 17 to 27 - NCERT

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

Page 18: Lab manual Activity 17 to 27 - NCERT

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

Page 19: Lab manual Activity 17 to 27 - NCERT

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

Page 20: Lab manual Activity 17 to 27 - NCERT

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

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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

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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

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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

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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

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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

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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