#### 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

= 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