Pirmyx smikawvw di gtwe ivamjk num srl krn dw fmg
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pirmyX sMiKAwvW dI GtwE, ivAMjk nUM srl krn dw FMg. -. klws:- s`qvIN ivSw:- gixq AiDAwie:- 2 iqAwr krqw:- jiqMdrjIq (mYQ mwstr) s.s.s.s simtRI rof luiDAwxw. pUrv igAwn prK. sMiKAw iksnUM AwKdy hn? sMmpUrn sMiKAw qoN quhwfw kI Bwv hY? pirmyX sMiKAw qoN quhwfw kI Bwv hY?

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Pirmyx smikawvw di gtwe ivamjk num srl krn dw fmg

pirmyX sMiKAwvW dI GtwE, ivAMjk nUM srl krn dw FMg

-

klws:- s`qvIN

ivSw:- gixq

AiDAwie:- 2

iqAwr krqw:-

jiqMdrjIq (mYQ mwstr)

s.s.s.s simtRI rof luiDAwxw


Purv igawn prk
pUrvigAwnprK

  • sMiKAw iksnUM AwKdy hn?

  • sMmpUrn sMiKAw qoN quhwfw kI Bwv hY?

  • pirmyX sMiKAw qoN quhwfw kI Bwv hY?

  • ik pirmyX sMiKAw dI Gtwau kIqI jw skdw hY?

  • Awau pirmyX sMiKAwvW dy Gtwau bwry ivsQwr pUrvk jwxdy hW?


  • swnUM pqw hY ik jy x Aqy y do sMpUrn sMiKAwvW hox qW x iv`coN y Gtwaux dw mqlb hY[

  • x iv`c –y dw joV Bwv

    X-y= x+(-y)

-

-

7/9

4/9



jy igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[p/q Aqy r/s do pirmyX sMiKAwvW hox qW

p/q – r/s = p/q + (-r/s)


audwhrx:- igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

1/4 nUM 2/3 iv`coN

2/3 – 1/4

=2/3 + (-1/4)

= 2*4+(-1)*3/3*4

=8+(-3)/12

=5/12


gux 1 igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

joV dy guxw leI x+y = y+x s`c huMdw hY[ prMqU Gtwau dy gux iv`c x-y = y-x s`c nhI huMdw[

pr iDAwn idau ik x-y = -(y-x) ho skdw hY[


gux 2 igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

joV dy gux leI (x+y) + z = x+(y+z) s`c huMdw hY[ prMqU Gtwau dy gux leI (x-y)-z = x-(y-z) kyvl z=0 leI s`c hY[

bwkI iksy pirmyX sMiKAw leI nhIN


gux 3:- igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

joV leI 0 dw gux hY:-

pr Gtwau dy leI, x-0 =x swrIAW pirmyX sMiKAwvW leI s`c hY, pr 0 – x = x kyvl x = 0 leI hI s`c hY[


ivAMjk nUM srl krn dw FMg igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

AsIN ie`k ivAMjk

9/10 + 2/3 + 2/5 + (-2/15) + 5/2 – 7/6 nUM srl krky ie`k pirmyX sMiKAw dy rUp iv`c ilKxw cwhuMdy hW , do-do sMiKAwvW lY ky h`l krn dI jgHw hyT ilKy pgW duAwrw vI h`l kIqw jw skdw hY[


pg 1 igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

ivAMjk nUM pirmyX sMiKAW iv`c ilKx leI sB qoN pihlW AsIN hr pRwpq krdy hW jo ik swnUM ivAMjk dy swry hrW dy l.s.v. qoN imldw hY (audwhrx iv`c 10, 3, 5, 15, 2, 6 dw l.s.v. = 30 hY[)


pg 2. igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[

pirmyX sMiKAw dw AMS AsIN hyT ilKy pgW iv`c pRwpq krWgy

1) pihlI sMiKAw dy hr nwl l.s.v. nUM Bwg krky BwgPl pRpq krdy hW (audwhrx iv`c hr = 10 Aqy l.s.v. = 30/10 krky BwgPl = 3 pRpq krdy hW)


2)pihlI sMiKAw dy AMS nUM igAw hY Aqy s`jy pwsy (-) icMnH dw ArQ hY sMmpUrn sMiKAw dw irxwqmk hoxw[(a) iv`c pRwpq BwgPl nwl guxw krky ie`k sMpUrn sMiKAw pRpq krdy hW (audwhrx iv`c pihlI sMiKAw dw AMS = 9 hY Aqy (a) iv`coN pRpq BwgPl = 3 hY qW AsIN 9*3=27 pRpq krdy hW[


3) ivAMjk dIAW swrIAW sMiKAwvW leI pg 2 (a) Aqy (b) nUM duhrwauNdy hW (audhrx iv`c ies qrHW pRpq hox vwlIAW sMpUrn sMiKAwvW qrqIb vwr 20,12,-4,75,-35 hn)


4) ies qrHW pRpq sMiKAwvW dy ivckwr auhI icMnH lgwauNdy hW, jo ivAMjk iv`c lwgvIA pirmyX sMiKAwvW dy ivckwr l`gy hn[ audwhrx iv`c ies qrHW pRwpq sMpUrn sMiKAw hY 27+20+12+(-4)+75-351


pg 2 iv`c pRpq ivAMjk qoN srl krky pRpq sMiKAw hI srl kIqI pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)


pg 3 pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)

pRpq sMKAw nUM sB qoN srl rUp iv`c ilKdy hW (auprokq audwhrx iv`c swnUM 95/30 srl krn qy pirmyX sMiKAw 19/6 pRpq huMdI hY[)


AiBAws pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)


H l kro
h`l pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)kro

  • Gtwau

  • 1/4 nUM 2/3 iv`coN

  • -3/7 nUM 5/9 iv`coN

  • 7/10 nUM -4/15 iv`coN

  • -6/7 nUM -2/49 iv`coN


h`l pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)

  • 1/4 nUM 2/3 5/12

  • -3/7 nUM 5/9 62/63

  • 7/10 nUM -4/15 -29/30

  • -6/7 nUM -2/49 40/49


sRoq pirmyX sMiKAw dw AMS hY (audwhrx iv`c pRpq AMS 95 hY)

pMjwb skUl is`iKAw borf dI 7vIN dI ihswb dI pwT pusqk


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