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16
8
21 20
12
7
12
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4
6
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5
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4
3
5
7
3
48 49
48
64
45
63
50
70
80
18
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www.asiriyar.com ngUf;fy; - FO tpisahl;L ngUf;fy; tha;gg ; hl;il khzth;fs; fw;wgpd; nfhLf;fg;gl;Ls;s ngUf;fy; ml;ilia xt;nthU khztDf;Fk; nfhLf;fTk.; xUthplk; cs;s fzf;fpw;Fhpa tpil cs;sth;> mjw;Fhpa tpiliaAk;> gpd;gf;fj;jpy; cs;s fzf;ifAk; nrhy;yTk;. mijj;njhlh;e;J nra;aTk;. cjhuzkhf Kjy; khztdplk; cs;s ml;ilapy; jhspd; 9 x4
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%d;whk; khztdplk; cs;s ml;ilapy; Kd;Gwk; 35
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nra;Kiw: Kjy; khztd; 9 X 4 vdg;gbf;f> mjd; tpilahd 36 vd;w ml;ilAs;s khztd; vOe;J 36 vdg;gbj;J gpd;G mNj ml;ilapd; gpd;GwKs;s 7 X 5 vd;w fzf;if gbf;f Ntz;Lk;. mjd; tpilahd 35 vd;w ml;ilAs;s khztd; vOe;J 35 vdg;gbj;J gpd;G mNj ml;ilapd; gpd;GwKs;s 6X 4 vd;w fzf;if gbf;f Ntz;Lk;. ,t;thW njhlh;e;J midj;J khzth;fSk; gq;F ngw nra;aTk;.
19
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www.asiriyar.com Front Sheet - 1
20 63 21 24 20
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Back Sheet - 1
7X3 4X6
4X5 7X9 21
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www.asiriyar.com Front Sheet - 2
50 20 21 63 22
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3X7
10X5
9X7 5X4 23
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Front Sheet - 3
12 10
42 64 24
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6X7 5X2 8X8
10X5
25
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Front Sheet - 4
24 72 35 36 26
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Back Sheet - 4
9X4 7X5
8X9 3X4 27
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www.asiriyar.com gapw;rpj;jhs;-9 1. ngUf;Ff a). 7
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57
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e).
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c) 45 4X __0
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28
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www.asiriyar.com 5. ngUf;fp tpil fhz;f a) 1 4 4 24 576 - - - *
b) 7 5 1 35 - - 5 - 3 *
c)
648 29 - - 2 - - *
29
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www.asiriyar.com gapw;rpj;jhs;-10 1. ngUf;fp tpil fhz;f. a) 328
b)
c)
256 X
121 X
d) 695
256
e)
256 X
765 376 X
378 111 X
2. tpil fhz;f a) 25 x 25
b)
128 x 5
d) 956 x 23
e)
128 x 17
3. a) 328 x 125
b)
256 x 121
d) 578 x 338
e)
358 x 358
c)
735 x 18
c)
765 x 226
4. Mg;gps; xd;wpd; tpiy &.15 vdpy; 20 Mg;gps;fspd; tpiy vd;d?
5. xU Ngdhtpd; tpiy &.24 vdpy; ngl;bapy; cs;s 12 Ngdhf;fspd; tpiy vd;d?
30
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www.asiriyar.com gapw;rpj;jhs;-11 1. ngUf;fw;gyidf; fhz;f a. 10 x 9
b. 8 x 7
c. 24 x 6
d. 32 x 12
b. 743 x 18
c. 1008 x 16
d. 2054 x 22
b. 225x40
c. 426x426
d. 256x76
b. 756x1
c. 5461x325
d. 248x36
2. ngUf;Ff a. 347 x 21
3. kjpg;G fhz;f a. 408x200 4. tpil fhz;f a. 16x16
ngUf;fy; tha;gg ; hl;il gad;gLj;jp tpil fhz;f 1) 4
X --------- = 16
2) 6
X --------- = 30
3) ---- X 3
= 21
4) 8
X8
= --------
5) 9
X ------- = 72
6) 7
X ------- = 56
7) 8
X ------- = 0
8) 6
X ------- = 6
9) --- X ----- = 100 10) 1
X ------ = 4
11) --- X ------- = 56 12) ---- X 9
= 36
13) ---- X ------- = 16 14) 5
X ------ = 15
15) 4
X ------- = 0
31
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www.asiriyar.com 2. 6 cld; 4 Ig; ngUf;fpdhy; vd;d tUk;? 3. xt;nthUthplKk; 10 kpl;lha;fs; cs;sd. vdpy; 5 Nghplk; cs;s nkhj;j kpl;lha;fspd; vz;zpf;if vt;tsT? 4. 8 cld; ve;j vz;izg;ngUf;fpdhy; 32 tUk;?
32
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www.asiriyar.com tFj;jy; : Kiw : 1
16 ÷ 3
16 15 14
13 12 11
10 9 8
7 6 5
4 3 2
1
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7
2
8
3
9
4
5
6
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Kiw : 2 5875 ÷16 16
33
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tFf;Fk; vz;iz 9 Kiw $l;bf; nfhs;s (xd;wd; fPo; xd;whf) Ntz;Lk;. tFgLk; vz;zpy; 5875-y; 58 vd;gJ 3 Kiwf;Fs; te;Js;sJ. 4 Kiwapy; 64 cs;sJ. ,J 58-I tpl mjpfk;. vdNt
34
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www.asiriyar.com gapw;rpj;jhs;-12 tFj;jy; : 1. ml;ltizapy; tpisahl;L X
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
2
2
4
6
8
10
12
14
16
18
3
3
6
9
12
15
18
21
24
27
4
4
8
12
16
20
24
28
32
36
5
5
10
15
20
25
30
35
40
45
6
6
12
18
24
30
36
42
48
54
7
7
14
21
28
35
42
49
56
63
8
8
16
24
32
40
48
56
64
72
9
9
18
27
36
45
54
63
72
81
cjhuzk; : 10 vd;w vz;zpw;F 10 I tl;lkpl;L mt;ntz;zpw;F epiu thpir> epuy; thpirapy; cs;s vz;izAk; nfhz;L 10÷2 = 5, 10÷5 = 2 vd mwpayhk;. j). 56÷7
s). 63÷7
b). 24÷8
k). 36÷6
t). 28÷4
c). 30÷6
L). 18÷9
u). 20÷5
d). 48÷8
m). 45÷5
v). 3÷1
e). 54 ÷6
n). 81÷9
w). 9÷1
f). 27÷3
o). 48÷6
x). 12÷2
g). 72÷9
p). 21÷7
y). 40÷5
h). 72÷8
q). 35÷5
z). 56÷8
i). 27÷9
r). 16÷4
2. a). 9÷3
35
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www.asiriyar.com gapw;rpj;j hs; - 13 1 tFf;f a) 8 ÷ b) 6 ÷ c) 10 ÷ d) 4 ÷
2 2 2 2
2 a) b) c) d)
7 9 5 6
÷ ÷ ÷ ÷
2 2 2 3
a) b) c) d)
8 9 7 8
÷ ÷ ÷ ÷
3 3 3 4
a) b) c) d)
12 14 15 20
÷ ÷ ÷ ÷
2 3 3 4
a) b) c) d)
18 16 15 25
÷ ÷ ÷ ÷
4 4 5 5
a) b) c) d)
24 36 64 78
÷ ÷ ÷ ÷
6 4 6 6
a) b) c) d)
49 64 72 81
÷ ÷ ÷ ÷
7 8 8 9
3
4
5
6
7
36
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www.asiriyar.com 8a) b) c) d)
8 9 7 5
÷ ÷ ÷ ÷
8 9 7 5
a) b) c) d)
6 7 4 8
÷ ÷ ÷ ÷
1 1 1 1
9
10 1-
a) 2
24 2
b) 3
2-
c)
--
86
3
96
6 2
6
37
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www.asiriyar.com gapw;rpj;jhs;-14 1. tFj;J tpil fhz;f. a. 369÷3 b. 424÷2
o. 200÷2
3. tpil fhz;f
2. tFf;f
c. 555÷5
a. 5525÷5
a. 2000÷10
d. 714÷7
b. 8199÷9
b. 9900÷100
e. 168÷8
c. 8648÷2
c. 2500÷10
f.
819÷9
d. 4218÷6
d. 8000÷100
g. 882÷2
e. 4848÷4
e. 2000÷20
h. 366÷6
f.
f.
i.
164÷4
g. 4914÷7
g. 4900÷70
j.
129÷3
h. 6408÷8
h. 4000÷400
k. 248÷8
i.
5305÷5
i.
270÷ 27
l.
j.
80824÷8
j.
480÷ 16
639÷9
3693÷3
500÷ 50
m. 273÷3
k. 16428÷2
k. 4800÷24
n. 324÷4
l.
l.
96369÷3
64000÷8
38
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www.asiriyar.com gapw;rpj;jhs;-15 1. tFj;J kPjp fhz;f a. 484÷3 b. 784÷7 c. 956÷8 2. d. 254÷4 e. 379÷6 f.
899÷8
3. g. 658÷7 h. 768÷5 i.
856÷7
j.
1142÷3
4. k. 7453÷2 l.
9575÷6
5. m. 8495÷7 n. 2593÷4 o. 6779÷9 6. p. 2596÷6 q. 3759÷8 r.
8657÷7
7. s. 415÷415 t.
6756÷1
u. 9670÷1
39
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www.asiriyar.com gapw;rpj;jhs;-16 1. tFj;J kPjp fhz;f a. 24 ÷ 12 b. 39÷ 13 c. 75÷ 15 d. 125 ÷ 15 2. a. 84 ÷ 16 b. 128 ÷ 12 c. 325 ÷ 24 d. 256 ÷ 16 3. a. 250 ÷ 10 b. 75 ÷ 10 c. 120 ÷ 10 d. 780 ÷ 10 4. a. 1142÷3 b. 7453÷2 c. 9575÷6 5. a. 586 ÷ 13 b. 674 ÷ 12 c. 842 ÷ 14 d. 784 ÷ 16 6. a. 856 ÷ 10 b. 945 ÷ 10 c. 460 ÷ 15 d. 655 ÷ 18 7. a. 816 ÷ 20 b. 746 ÷ 18 c. 956 ÷ 17 d. 415 ÷ 15 8. a. 5480 ÷ 10 b. 7986 ÷ 12 c. 8572 ÷ 14 d. 9655 ÷ 15
40
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www.asiriyar.com gapw;rpj;jhs; : 17 1. xUthplk; 6 Mg;gps;fs; cs;sd. mjid 3 NgUf;F rkkhf nfhLj;jhy; xt;nthUtH ngWk; Mg;gps;fspd; vz;zpf;if ahJ? 2. RNu\; xU thuj;jpy; 42 kzp Neuk; gbf;fpwhH vdpy; mtH ruhrhpahf xt;nthU ehSk; gbf;Fk; Neuk; vt;tsT? 3. je;ij jd;dplk; cs;s &.600-id jd; ehd;F kfd;fSf;F rkkhfg; gphpj;Jf; nfhLj;jhy; xt;nthU kfDf;Fk; fpilf;Fk; njhif vt;tsT? 4. xUtH jd; FLk;g tpohtpw;F 40 fpNyh fpuhk; jf;fhspia &.840/-f;F thq;fpdhH vdpy; 1 fpNyh fpuhk; jf;fhspapd; tpiy vd;d? 5. 10>000 kzpfis 5000 kzpfshf vj;jid egHfSf;F gphpj;J nfhLf;fyhk;? 6. xUthplk; cs;s 645 yl;Lfis 32 khzth;fSf;F rkkhf nfhLj;jhy; kPjKs;s yl;Lfspd; vz;zpf;if vd;d? 7. 54 vd;w vz;Zld; ve;j vz;fisf; $l;Lk;NghJ 2> 3> 4> 5> 6 My; tFgLk;?
41
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www.asiriyar.com gapw;rpj;jhs; : 18 1. tFf;f a. 8 ÷ 4
b. 24 ÷ 8
c. 74 ÷ 2
2.
a. 156 ÷ 7
b. 1257 ÷ 6
c. 5078 ÷ 9
3.
a. 75 ÷ 75
b. 65 ÷ 1
c. 405 ÷ 405
4.
a. 87 ÷ 8
b. 100 ÷ 10
c. 936 ÷ 3
5.
a. 44000 ÷ 440
b. 938 ÷ 13
c. 560250 ÷ 51
6. Mrphpahplk;
d. 40402040 ÷ 20
cs;s 528 Nehl;L Gj;jfq;fis 75 khzth;fSf;F rkkhf
nfhLf;f Ntz;Lk; vdpy; kPjKs;s Nehl;L Gj;jfq;fs; vj;jid? 7. ngUf;fp tpil vOJ : a. 328 X 64
b. 720 x 65
42
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www.asiriyar.com gapw;rpj;jhs; : 19 1.
$l;Lf : a. 3467
b. 1005 + 759 + 26 + 7 = ?
439 270
2. m). m[a; Kjy; gUtj;NjHtpy; ngw;w kjpg;ngz;fs; gpd;tUkhW. jkpo;-85> Mq;fpyk;-78> fzpjk;-95> mwptpay;-90> r%f mwptpay; -86. mtH ngw;w nkhj;j kjpg;ngz;fs; vt;tsT? 3. a. 7598
b. 7456 + 3694 - 250
3499
4. epuQ;rdplk; &.1850 cs;sJ. mjpy; &.825-f;F Gj;jfq;fs; thq;FfpwhH. mthplk; kPjKs;s gzk; vt;tsT? 5. a. 545 +
= 756
b. 650 -
= 320
6. ngUf;Ff : 476 X 27 7. tFj;J kPjp fhz;f. a. 1058 ÷ 6 b. 756 ÷ 12
43
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www.asiriyar.com kP.rp.k fhZk; Kiw klq;F Kiw: ,uz;L vz;fspd; kPrr ; pW nghJ klq;F fhz nfhLf;fg;gl;l vz;fspis jdpj;jdpNa mNj vz;Zld; $l;l Ntz;Lk;. tpil xNu khjphp tUk; tiu ,k;Kiw njhlu Ntz;Lk;.; xNu khjphp tUk; vz;Nz kP.rp.k vdg;gLk;. cjhuzk;: 16> 24 d; kP.rp.k fhz;f 16
24
16 +
24+ 24
32
48
16 + 48 vdNt kP k.P rp.k = 48 fhuzp Kiwapy; kP.rp.k kw;Wk; kP. ngh.t fhzy; 30> 42 2 30
2 42
3 15
3 21
5 5
7 7
1
1
30 d; fhuzpfs; = 2
x 3 x5
42 d; fhuzpfs; = 2
x 3
x7
kP.ngh.t = nghJthd fhuzpfspd; ngUf;Fj;njhif = 2 x 3 = 6 kP.rp.k = nghJthd fhuzp x tpLgl;l fhuzp = 2 x 3 x 5 x 7 = 6 x 35 = 210 44
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www.asiriyar.com gpd;dk; gpd;dk; - tpsf;fk;
= ¼ = njhFjp/gFjp
= 2/7 rkhd gpd;dq;fs;: xNu msit my;yJ xNu kjpg;ig Fwpf;Fk; gpd;dq;fisr; rkhd gpd;dq;fs; vd;fpNwhk;.
=½
= 2/4
= 4/8
,jpy;
½ = 2/4 = 4/8
45
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www.asiriyar.com gapw;rpj;jhs; - 20 I) kP.rp.k kw;W k; kP.ngh.t fhz;f klq;F Kiwapy;
1)
12> 36
2)
15> 45
3)
18> 72
4)
5> 20
5)
13> 65
6)
5> 18
7)
7> 21
8)
42> 118
II) fhuzp Kiwapy; kP.rp.k kw;W k; kP. ngh. t fhz;f
1) 6>30 2) 12> 64 3) 20> 125 4) 34> 102 5) 24> 72 6) 36> 54 7) 108> 48 8) 84> 160
46
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www.asiriyar.com gapw;rpj;jhs; - 21 Xhpd gpd;dq;fis $l;Lf:
I) 1 1
3
2
+
3 2
=
4
5
+
1 3
2
5
=
6
7
+
7
7
=
5
11 =
4
6
+
6 4
5
9
+
7 6
7 =
9
=
9
2
9
-
9
2 7
1
3
-
8 8
3
=
2
7
-
=
7
1 9
5
-
5
3 =
7 10
10
-
10
3 =
10
47
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www.asiriyar.com KOf;fs; mwpKfg;gLj;Jjy; vz; Nfhl;bd; %yk; khzth;fSf;F Fiw vz;fs;> G+r;rpak;> kpif vz;fs; Nghd;wtw;iw mwpKfg;gLj;Jjy;.
-4
-3
-2
-1
0
1
2
3
4
5
6
KOf;fspy; ,uz;L vz;fisf; nfhLj;J mtw;wpy; vJ nghpaJ? vJ rpwpaJ? vd;gij fz;lwptJ vt;thW vd;W gy tpsf;fq;fisf;$wp Ghpa itj;jy;.
vLj;Jf;fhl;L:1)
-10
<
+3
2)
+7
>
-12
3)
+32
<
+38
4)
-6
<
-5
5)
-10
>
-12
KOf;fspy; ngUf;fy; KOf;fspy; ngUf;fy; nraiyr; nra;Ak;NghJ ,U gbfis kdjpy; itj;Jf; nfhs;sr;nra;jy; Ntz;Lk;. Kjy;gb – Fwpiag;ngUf;Fjy; ,uz;lhk;gb – vz;izg;ngUf;Fjy;
Fwpiag; ngUf;Ftjw;F ,e;f Kf;Nfhz tbtj;ijg; gad;gLj;jf;$Wjy;. 48
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www.asiriyar.com +
Fwpiag; ngUf;Ftjw;F ,e;j Kf;Nfhz tbtj;ijg; gad;gLj;j f; $Wjy;.
-
-
(+) × (-) =
-
(-) × (+) =
-
(-) × (-)
= +
+ VNjDk; ,U Fwpiaf; ngUf;Ftjw;F mjidg; glj;jpy; iffshy; kiwj;J %d;whtij tpilahf vOjr; nrhy;Yjy; (+) × (+) mjhtJ ,uz;L vz;fSk; kpif vz;zhf te;jhy; ngUf;fp + Fwpia ,lr; nrhy;Yjy; Ntz;Lk;. ,uz;lhk; gbf;F>ngUf;fy; tha;g g ; hl;il ed;F kddk; nra;ar; nrhy;yp mjd; %yk; vz;fisg; ngUf;fp vOjr; nrhy;Yjy; vLj;Jf;fhl;L:1. (+3) × (-7) = -21 2. (-2) × (+4) = - 8 3. (-3) × (-3)
= +9
Fwpg;G: ,k;Kiwapy; gapw;rpfs; ngw;w gpd;dh; Fwp xNu khjphp te;jhy; $l;ly; Fwp vd;Wk;>Fwp khwp te;jhy; fopj;jy; Fwp ,l Ntz;Lk; vd;Wk; mwpa itj;jy;. KOf;fspy ; tFj;j y; KOf;fspy; tFj;j y; nra;Ak; NghJ Fwpfis Kjypy; tFj;J gpd;dh; vz;fis tFf;fr; nrhy;y Ntz;Lk;. Fwpfis tFf;f>ngUf;fYf;F vd;d Kiwig; gpd;g w;wpNdhNkh>mijNa gpd;gw;wr; nrhy;Yjy;. Fwpfis tFj;j gpd;dh;>tof;fk; Nghy vz;fis tFj;J vOjr; nrhy;Yjy; Ntz;Lk;. vLj;Jf;fhl;L:-
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www.asiriyar.com 1. (-8) ÷ (+2)
= -4
2. (+12) ÷ (-3) = - 4 3. (-6) ÷ (-3)
= +2
4. (-15) ÷ (-5)
= +3
5. (+10) ÷ (-2) = - 5 6. (-20) ÷ (+4) = - 5 1.ngUf;fy; tha;g g ; hl;il kddk; nra;ar; nrhy;Yjy; 2.KOf;fspy; $l;ly;>fopj;jy; 3.KOf;fspy; ngUf;fy;>tFj;jy; KOf;fspy; $l;ly; fopj;jy; KOf;fs; vd;gJ kpif vz;fs;>Fiw vz;fs;>G+r;rpak; Mfpa %d;Wk; Nrh;e;jjhFk;. ,jpy; $l;ly; nraiyr; nra;Ak; NghJ vz;fspd; Fwpfs; xNu khjphpahf ,Ue;jhy; $l;b mNj Fwpia ,lNtz;Lk;. vLj;Jf;fhl;L: 1. (+2) + (+3) = +21 2. (+11) + (+4) = +15 3. (-7) + (-3)
= -10
4. (-4) + (-6)
= -10
kpif vz; kw;Wk; Fiw vz; fye;J xNu fzf;fpy; te;jhy; Fwpiag; ghh;ff ; hky; nghpa vz;zpypUe;J rpwpa vz;izf; fopj;J nghpa vz;zpd; Fwpia ,lr; nrhy;Yjy; Ntz;Lk;. vLj;Jf;fhl;L: 1. (-3) + (+1)
= -2
2. (+7) + (-2)
= +5
3. (-9) + (+1)
= -8
4. (-2) + (+8)
= +6
5. (-1) + (+11)
= +10
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KOf;fspd; fopj;jy; KOf;fspy; fopj;jy; nra;Ak; NghJ ,uz;lhtJ vz;zpd; Fwpia khw;wp $l;lr; nrhy;y Ntz;Lk;. tof;fk; Nghy>$l;ly; nraiy vt;thW nra;a Ntz;Lk; vd;w tjpfisg; gad;gLj;j p $l;lr; nrhy;y Ntz;Lk;. vLj;Jf;fhl;L: 1 (-7) - (-3) Kjy; gb
= (-7) – (-3)
,uz;lhk; gb = - 4 vLj;Jf;fhl;L : 2 (+3) – (+8) = (+3) + (-8) =-5
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www.asiriyar.com gapw;rpj;j hs; - 22 1.ngUf;fw;gyidf; fhz;f a) . 10 × 9
b). 8 × 7
c) 24 ×6
d) 32 ×12
b) 743 ×18
c) 1008 ×16
d) 2054 ×22
c) 426 ×426
d) 256 × 76
2. ngUf;Ff. a) 347 × 21
3.kjpg;G fhz;f a) 408 × 200 b) 225 ×40 4.tpil fhz;f a) 16 × 16
b) 756 × 1
c) 5461 × 325 d) 248 × 36
2) ngUf;fp tpil fhz;f 1) 7 2 35 X
2)
848 27
360
--6
- - -*
- - -*
X
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topfhl;Ljy; jy jpU. ,uh. KUfd; M.Sc., M.Ed., M.Phil., Kjd;ikf; fy;tp mYtyh;> jpUg;G+h;.
jahhpg;G cjtp njhlf;ff; fy;tp mYtyh;> Mrphpah; gapw;Weh;fs; kw;Wk; Mrphpah;fs; FO nghq;fYhh; xd;wpak;
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