p*Ni<>k s>²yi ni[ rsp\d a¿yis

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[??

Äyi²yi:-

Gnp&Ni<>k s>²yi – S*ºy krti mi[T) s>²yi.

0 1 2 3 4 5 6

Äyi²yi:-

äNp&Ni<>k s>²yi – S&ºy krti nin) s>²yi

0 1 2 3 4 5 6-1-2-3-4-5-6

Äyi²yi:-

(v$¹F s>²yi – S*ºy Y) smin a>tr[ (v$¹F (dSimi> aiv[l) s>>²yi.

0 1 2 3 4 5 6-1-2-3-4-5-6

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.

7ni[ (vri[F)-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[.

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

äN s>²yini[ upyi[g d(ryin) u>Die mipvi miT[ pN Yiy C[.

0102030

-10-20-30-40-50

äN s>²yini[ upyi[g uFir btivvi pN Yiy C[.

Firi[ k[ tmiri (pti a[ kir Kr)dvi miT[ b[ºkmi>Y) $i.1,50,000 n) 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<

s&cni:-

ji[ ki[e s>²yi n) aigL Gn aYvi äN (nSin) n hi[y ti[ t[n[ Gn s>²yi smjv).

9+

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

diKli gNi[. -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 =

-8

-18

14-13

7

11

tmiri jvib ckisi[.

1. 8 + 13 = 212. –22 + -11 = -333. 55 + 17 = 724. –14 + -35 = -49

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 =9 - 5 = 4

mi[T) (nrp[x s>²yi

jvib = - 4

diKli gNi[.

3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 =

-25 – 3 = 2

0 -4

1-1

3

9 – 9 = 0

9 – 5 = 4

7 – 6 = 14 – 3 = 1

7 – 4 = 3

tmiri jvib ckisi[.

1. –12 + 22 = 102. –20 + 5 = -153. 14 + (-7) = 74. –70 + 15 = -55

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvi[.

0 1 2 3 4 5 6-1-2-3-4-5-6

• 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[.

+-

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t.

0 1 2 3 4 5 6-1-2-3-4-5-6+

-

+3 + -5 = -2

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t.

0 1 2 3 4 5 6-1-2-3-4-5-6+

-

+6 + -4 = +2

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t

0 1 2 3 4 5 6-1-2-3-4-5-6+

-

+3 + -7 = -4

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvin) a[k r)t.

0 1 2 3 4 5 6-1-2-3-4-5-6-

+

-3 + +7 = +4

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!

ah)> Yi[Di vFirini udihrNi[ ´viri smj[i.

12 – (-8)

12 + (+8)

12 + 8 = 20

-3 – (-11)

-3 + (+11)

-3 + 11 = 8

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

aipN[ ke r)t[ jiN)S>& k[ '' äN s>²yin) bidbik) a[ Gn s²yini srviLi j[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>&.

Firi[ k[ tm[ a mi>Y) b ai[Ci kri[ Ci[ an[ t[ c bribr C[. a – b = c5 – 2 = 3tmiri[ jvib ckisvi miT[ b an[c um[ri[a = b + c5 = 2 + 3

ai rhyi Yi[Di udihrNi[.a – b = c a = b + c9 – 5 = 4 9 = 5 + 4

a – b = c a = b + c20 – 3 = 17 20 = 3 + 17

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.

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[.

a – b = c a = b + c2 – (-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!

tmiri jvib ckisi[

1. gNi[ : 3 – 10 = 7 ckisi[: 3 = 10 + (-7)

2. gNi[ : 17 – ( 12) = 29

aigLn) AlieD j&ai[ . . . . . . . . . . . . . . . .

ckisi[: 17 = -12 + 29

tmiri jvib ckisi[

1. gNi[: 20 – ( 5) = 25

ckisi[: 20 = -5 + 25

1. gNi[: -7 – ( 2) = -5ckisi[: -7 = -2 + -5

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

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

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 =9 - 5 = 4

mi[T) (nrp[x s>²yi

jvib = - 4

s>²yi r[Kin) mddY) p&Ni<>k s>²yini[ srviLi[ krvi[.

0 1 2 3 4 5 6-1-2-3-4-5-6

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[. +-

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!

aipN[ ke r)t[ jiN)S>& k[ '' äN s>²yin) bidbik) a[ Gn s²yini srviLi j[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>&.

a – b = c a = b + c2 – (-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