p*Ni<>k s>²yi ni[ rsp\d a¿yis

1. p*Ni<>k s>²yi ni[ rsp\d a¿yis

2. tm[ S&> S)KSi[? • p&Ni<>k s>²yin) Äyi²yi. • p&Ni<>k s>²yi srviLi an[ bidbik) krvini (nymi[. • ai (nymi[ sici C[ t[ si(bt krvin) p´Ft). S>& tm[ t]yir Ci[??

3. Äyi²yi:- • Gnp&Ni<>k s>²yi – S*ºy krti mi[T) s>²yi. 0 1 2 3 4 5 6

4. Äyi²yi:- äNp&Ni<>k s>²yi – S&ºy krti nin) s>²yi -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

5. Äyi²yi:- • (v$¹F s>²yi – S*ºy Y) smin a>tr[ (v$¹F (dSimi> aiv[l) s>>²yi. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

6. 7 -7 ni[ (vri[F) Äyi²yi:- • p&Ni<>k s>²yi : dr[k p&N< s>²yi an[ s>²yir[Ki pr S&ºy Y) (v$´F (dSimi> srKi a>tr[ aiv[l) äN s>²yi.

7. Äyi²yi:- • (nrp[x m*Ãy -ki[e pN (ch`n vgrn) s>²yin&> m*Ãy • (nrp[x m*Ãy - ki[e pN p\kirni (ch`nn[ ´yinmi> l)Fi (vni s>²yini ai>kDik)y m*Ãyn[ (nrp[x m*Ãy kh[ C[. 9 aYvi -9 n&> (nrp[x m*Ãy 9 C[.

8. äN s>²yini[ upyi[g tipmin mipvi miT[ Yiy C[.

9. äN s>²yini[ upyi[g d(ryin) u>Die mipvi miT[ pN Yiy C[. 30 20 10 0 -10 -20 -30 -40 -50

10. äN s>²yini[ upyi[g uFir btivvi pN Yiy C[. Firi[ k[ tmiri (pti a[ kir Kr)dvi miT[ b[ºkmi>Y) $i.1,50,000n) li[n l)F). jyir[ t[ai[ p]si gNti hti Ryir[ t[mN[ b>kmi> d[v&> C[ t[ dSi<vvi miT[. - 1,50,000 $i.um[yi<

11. s&cni:- • ji[ ki[e s>²yi n) aigL Gn aYvi äN (nSin) n hi[y ti[ t[n[ Gn s>²yi smjv). 9 +

12. p*Ni<>k s>²yini srviLi ni[ (nym • (nym 1:-ji[ b>ºn[ p&N<i>k s>²yi ai[ni (cMn srKi hi[y ti[ t[mni (cMn[ avgN) n[ p\Ym n>br siY[> b)ji n>br ni[ srviLi[ krvi[ an[ jvib aigL t[ s>²yiai[n&> (cMn m&kv&>. 9 + 5 = 14 -9 + -5 = -14

13. diKli gNi[. -8 • -3 + -5 = • 4 + 7 = • (+3) + (+4) = • -6 + -7 = • 5 + 9 = • -9 + -9 = 11 7 -13 14 -18

14. tmiri jvib ckisi[. 1. 8 + 13 = 21 2. –22 + -11 = -33 3. 55 + 17 = 72 4. –14 + -35 = -49

15. p*Ni<k s>²yini srviLini[ (nym • (nym 2:- ji[ b>ºn[ p*Ni<>k s>²yia[ini (cMn j&di j&di hi[y ti[, t[mni (cMn avgN)n[ mi[T) s>²yi mi>Y) nin) s>²yin) bidbik) krv) an[ p(rNimmi> mi[T) s>²yin&> (cMn m&kv&> mi[T) (nrp[x s>²yi -9 + +5 = jvib = - 4 9 - 5 = 4

16. diKli gNi[. -2 5 – 3 = 2 • 3 + -5 = • -4 + 7 = • (+3) + (-4) = • -6 + 7 = • 5 + -9 = • -9 + 9 = 7 – 4 = 3 3 4 – 3 = 1 -1 7 – 6 = 1 1 9 – 5 = 4 -4 0 9 – 9 = 0

17. tmiri jvib ckisi[. 1. –12 + 22 = 10 2. –20 + 5 = -15 3. 14 + (-7) = 7 4. –70 + 15 = -55

18. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvi[. • ji[ Fnp*Ni<>k um[rvi[ hi[y ti[ t[ p*Ni<>k j[Tli a[km jmN)bij& Ksv&> pD[. • ji[ äN p*Ni><k um[rvi[ hi[y ti[ t[ p*Ni<>k j[Tli a[km a>tr Dib) bij& Ksv&> pD[. - +

19. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t. +3 + -5 = -2 + -

20. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t. +6 + -4 = +2 + -

21. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t +3 + -7 = -4 + -

22. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t. -3 + +7 = +4 - +

23. p&Ni<>ks>²yi n) bidbik)ni (nymi[ äN s>²yin) bidbik) krv) an[ Gn s>²yini srviLi[ krvi[ b>ºn[ a[k srK) r)t C[. (nSin) bdli[ an[ srviL[i kri[. 2 – (-7) a[ 2 + (+7) n) bribr C[ 2 + 7 = 9!

24. ah)> Yi[Di vFirini udihrNi[ ´viri smj[i. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8

25. tmiri jvib ckisi[ 1. 8 – (-12) = 8 + 12 = 20 2. 22 – (-30) = 22 + 30 = 52 3. – 17 – (-3) = -17 + 3 = -14 4. –52 – 5 = -52 + (-5) = -57

26. aipN[ ke r)t[ jiN)S>& k[ '' äN s>²yin) bidbik) a[ Gn s²yini srviLij[v) j k\)yi C["" S>& a[ sic&> C[? aipN[ bidbik) c[k krvimiT[ j[ r)t ni[ upyi[g kr)a[ C)a[ a[j r)t ni[ upyi[g jvib ckisvi kr)S>&.

27. Firi[ k[ tm[ a mi>Y) b ai[Ci kri[ Ci[ an[ t[ c bribr C[. a – b = c 5 – 2 = 3 tmiri[ jvib ckisvi miT[ b an[c um[ri[ a = b + c 5 = 2 + 3

28. ai rhyi Yi[Di udihrNi[. a – b = c a = b + c 9 – 5 = 4 9 = 5 + 4 a – b = c a = b + c 20 – 3 = 17 20 = 3 + 17

29. bidbik) ckisvi miT[ j[ r)t ni[ upyi[g Yiy C[ t[j r)t ni[ upyi[g äN s>²yin) bidbik) miT[ pN kr) Skiy.

30. ji[ a – b = c,an[…. 2 – (-5) 2 + (+5), a[ bribr 7, ti[ cili[ t[ sic& C[ k[ Ki[T& t[ ckisvi miT[ aipN[[ äN s>²yi ni[ upyi[g kr)a[.

31. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 ji[y>& ai r)t[ Yiy C[ n[ a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 hi!

32. tmiri jvib ckisi[ 1. gNi[: 3 – 10 = 7 ckisi[: 3 = 10 + (-7) 2. gNi[: 17 – ( 12) = 29 ckisi[: 17 = -12 + 29 aigLn) AlieD j&ai[ . . . . . . . . . . . . . . . .

33. tmiri jvib ckisi[ 1. gNi[: 20 – ( 5) = 25 ckisi[: 20 = -5 + 25 1. gNi[: -7 – ( 2) = -5 ckisi[: -7 = -2 + -5

34. aipN[ p*Ni<>k s>²yini srviLi bidbik) (vS[ GN&> S)²yi. cili[ p&nrivt<n kr)a[ !

35. p*Ni<>k s>²yini srviLi ni[ (nym • (nym 1:-ji[ b>ºn[ p&N<i>k s>²yi ai[ni (cMn srKi hi[y ti[ t[mni (cMn[ avgN) n[ p\Ym n>br siY[> b)ji n>br ni[ srviLi[ krvi[ an[ jvib aigL t[ s>²yiai[n&> (cMn m&kv&>. 9 + 5 = 14 -9 + -5 = -14

36. p*Ni<k s>²yini srviLini[ (nym (nym 2:- ji[ b>ºn[ p*Ni<>k s>²yia[ini (cMn j&di j&di hi[y ti[, t[mni (cMn avgN)n[ mi[T) s>²yi mi>Y) nin) s>²yin) bidbik) krv) an[ p(rNimmi> mi[T) s>²yin&> (cMn m&kv&> -9 + +5 = mi[T) (nrp[x s>²yi jvib = - 4 9 - 5 = 4

37. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvi[. ji[ Fnp*Ni<>k um[rvi[ hi[y ti[ t[ p*Ni<>k j[Tli a[km jmN)bij& Ksv&> pD[. ji[ äN p*Ni><k um[rvi[ hi[y ti[ t[ p*Ni<>k j[Tli a[km a>tr Dib) bij& Ksv&> pD[. - +

38. p&Ni<>k s>²yi n) bidbik)ni (nymi[ äN s>²yin) bidbik) krv) an[ Gn s>²yini srviLi[ krvi[ b>ºn[ a[k srK) r)t C[. (nSin) bdli[ an[ srviL[i kri[. 2 – (-7) a[ 2 + (+7) n) bribr C[ 2 + 7 = 9!

39. aipN[ ke r)t[ jiN)S>& k[ '' äN s>²yin) bidbik) a[ Gn s²yini srviLij[v) j k\)yi C["" S>& a[ sic&> C[? aipN[ bidbik) c[k krvimiT[ j[ r)t ni[ upyi[g kr)a[ C)a[ a[j r)t ni[ upyi[g jvib ckisvi kr)S>&.

40. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 ji[y>& ai r)t[ Yiy C[ n[ ! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 hi