R.D. Sharma Solutions Class 8th: Ch 1 Real Numbers Exercise 1.1

Chapter 1 Real Numbers R.D. Sharma Solutions for Class 8th Math Exercise 1.1

Exercise 1.1

1. Add the following rational numbers.

Solution

(i) (-5)/7 and 3/7   
= (-5)/7 + 3/7
= (-5+3)/7
= (-2)/7

(ii) (-15)/4 and 7/4
= (-15)/4 + 7/4
= (-15+7)/4
= (-8)/4
= -2

(iii) (- 8)/11 and (-4)/11 
= (-8)/11 + (-4)/11
= {-8+(-4)}/11
= (-8-4)/11
=(-12)/11

(iv) 6/13 and (-9)/13
= 6/13 + (-9)/13
= {6 + (-9)}/13
= (6-9)/13
=(-3)/13


2.Add the following rational numbers.

Solution

(i) 3/4 and (-5)/8
= 3/4 + (-5)/8
={(6 + (-5)}/8
= (6 - 5)/8
= 1/8

(ii) 5/(-9) and  7/3
=5/(-9) + 7/3
= (-5+ 21)/9
=  16/9

(iii) -3 and 3/5
= -3 + 3/5
= (-15 + 3)/5
= -12/ 5

(iv) -7/27 and 11/18
= -7/27 + 11/18
= (-14 + 33)/54
=  19/54

(v) 31/(-4) and (-5)/8 
= 31/(-4) + (-5)/8
= {-62 + (-5)} /8
= (-62 - 5)/8
= -67/8

(vi) 5/36 and (-7)/12
=  5/36 + (-7)/12
= {5 + ( -21 )}/36
= (5-21)/36
= -16/36
= -4/9

(vii) (- 5)/16 and 7/24
= (-5)/16 + 7/24
= (-15 + 14)/48
= -1/48

(viii) 7/-18 and 8/27
= -7/18 + 8/27
= (-21 + 16)/54
= -5/54

3. Simplify:

Solution

(i)  8/9 + (-11)/6
= {16 + (-33)} /18
= (16 - 33)/18
= -17/18

(ii) 3 + 5/-7
= {21 + (-5)}/7
= (21-5)/7
= 16/7

(iii) 1/(-12) + 2/(-15)
= {- 5 + (-8)}/60
= (-5 - 8)/60
= (-13)/60

(iv) -8/19 + (-4)/57
= {-24 + (-4)}/57
= (-24 - 4)/57
= -28/57

(v) 7/9 + 3/(-4)
= {28 + (-27)} /36
= (28 - 27)/36
= 1/36

(vi) 5/26 + 11/(-39)
= {195 + ( -286 )}/1014
= (195 - 286)/1014
= (-91)/1014
 = (-7)/78

(vii) (-16)/9 + (-5)/12
= {-64 + (-15)}/36
= (-64 - 15)/36
= -79/36

(viii) -13/8 + 5/36
= (-117 + 10)/72
= -107/72

(ix) 0 + (-3)/5
= {0 + (-3)}/5
= (0-3)/5
= -3/5

(x) 1 + (-4)/5
= {5 + (-4)} /5
= (5 - 4)/5
= 1/5

4.Add and express the sum as a mixed fraction:

Solution

(i) -12/5 and 43/10
= (-12)/5 + 43/10
= (- 24 + 43)/10
=  19/10

(ii)  24/7 and -11/4
= 24/7 + (-11)/4
= {96 + (-77)}/28
= (96 - 77)/28
= 19/28

(iii) -31/6 and -27/8
= -31/6 + (-27)/8
= {-124 + (-81)} /24
= (-124 - 81)/24
= -205/24

(iv)  101/6 and 7/8
=101/6 + 7/8
= (404 + 21) / 24
= 425/24


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