NCERT Solutions Class 7th Maths Chapter – 8 Rational Numbers Exercise – 8.2

1. Find the sum-

(i) 5/4 + (-11/4)
Solution – 5/4 + (-11/4) = 5 – 11/4 = -6/4 = -6 ÷ 2/4 ÷ 2 = -3/2

(ii) 5/3 + 3/5
Solution – 5 × 5/3 × 5 + 3 × 3/5 × 3
[∴ LCM of 3 and 5 = 15]
= 25/15 + 9/15 = 25 + 9/15 = 34/15 = 2 4/15

(iii) -9/10 + 22/15
Solution – -9/10 + 22/15 = -9 × 3/10 × 3 + 22 × 2/15 × 2
[∴ LCM of 10 and 15 = 30]
= -27/30 + 44/30 = -27 + 44/30 = 17/30 

(iv) -3/-11 + 5/9
Solution – -3/-11 + 5/9 = 3/11 + 5/9 = 3 × 9/11 × 9 + 5 × 11/9 × 11
[∴ LCM of 9 and 11 = 99]
= 27/99 + 55/99 = 27 + 55/99 = 82/99

(v) -8/19 + (-2) 57
Solution – -8/19 + (-2) 57 = -8 × 3/19 × 3 – 2 × 1/57 × 1
= -24/57 – 2/57 = -24 – 2/57 = -26/57

(vi) -2/3 + 0
Solution – -2/3 + 0 = -2/3 + 0/3 = -2 + 0/3 = -2/3

(vii) -2 1/3 + 4 3/5
Solution – -2 1/3 + 4 3/5 = -2 1/3 + 4 3/5 = -7/3 + 23/5
= -7 × 5/3 × 5 + 23 × 3/5 × 3
[∴ LCM of 3 and 5 = 15]
= -35/15 + 69/15 = -35 + 69/15 = 34/15 = 2 4/15

2. Find

(i) 7/24 – 17/36
Solution – 7/24 – 17/36
LCM of 24 and 36 = 72
= 7 × 3/24 × 3 – 17 × 2/36 × 2 = 21/72 – 34/72 = -13/72

(ii) 5/63 – (-6/21)
Solution – 5/63 – (-6/21) = 5/63 + 6/21
LCM of 63 and 21 = 63
= 5 × 1/63 × 1 + 6 × 3/21 × 3 = 5/63 + 18/63 = 5 + 18/63 = 23/63

(iii) -6/13 – (-7/15)
Solution – -6/13 – (-7/15) = -6/13 + 7/15
LCM of 13 and 15 = 195
= -6 × 15/13 × 15 + 7 × 13/15 × 13
= -90/195 + 91/195 = -90 + 91/195 = 1/195

(iv) -3/8 – 7/11
Solution – -3/8 – 7/11
LCM of 8 and 11 = 88
-3 × 11 – 7 × 8/11 × 8 = -33/88 – 56/88
= -33 – 56/88 = -89/88 = -1 1/88

(v) -2 1/9 – 6
Solution – -2 1/9 – 6 = 19/9 – 6/1
[LCM of 9 and 1 = 9]
∴ -19 × 1/9 × 1 – 6 × 9/1 × 9 = -19/9 – 54/9 = -19 – 54/9
= -73/9 = -8 1/9

3. Find the product-

(i) 9/2 × (-7/4)
Solution – (i) 9/2 × (-7/4) = 9 × (-7)/2 × 4 = -63/8 = -7 7/8

(ii) 3/10 × (-9)
Solution – 3/10 × (-9) = 3/10 × -9/1
= 3 × (-9)/10 × 1 = -27/10 = -2 7/10

(iii) -6/5 × 9/11
Solution – -6/5 × 9/11 = -6 × 9/5 × 11 = -54/55

(iv) 3/7 × (-2/5)
Solution – 3/7 × (-2/5) = 3 × (-2)/7 × 5 = -6/35

(v) 3/11 × 2/5
Solution – 3/11 × 2/5 = 3 × 2/11 × 5 = 6/55

(vi) 3/-5 × -5/3
Solution – 3/-5 × -5/3 = -3/5 × -5/3 = (-3) × (-5)/5 × 3 = 15/15 = 1

4. Find the value of-

(i) (-4) ÷ 2/3
Solution – (-4) ÷ 2/3 = -4 × 3/2
= -4/1 × 3/2 = -12/2 = -12 ÷ 2/2 ÷ 2 = -6

(ii) -3/5 ÷ 2
Solution – -3/5 ÷ 2 = -3/5 ÷ 2/1 = -3/5 × 1/2 = -3/10

(iii) -4/5 ÷ (-3)
Solution – -4/5 ÷ (-3) = -4/5 + -3/1 = -4/5 × -1/3
= (-4) × (-1)/5 × 3 = 4/15

(iv) -1/8 ÷ 3/4
Solution – -1/8 ÷ 3/4 = -1/8 × 4/3
= -1 × 4/8 × 3 = -4/24 = -4 ÷ 4/24 ÷ 4 = -1/6

(v) -2/13 ÷ 1/7
Solution – -2/13 ÷ 1/7 = -2/13 × 7/1
= -2 × 7/13 × 1 = -14/13 = -1 1/13

(vi) -7/12 ÷ (-2/13)
Solution – -7/12 ÷ (-2/13) = -7/12 × (-13/2)
= (-7) × (-13)/12 × 2 = 91/24 = 3 19/24

(vii) 3/13 ÷ (-4/65)
Solution – 3/13 ÷ (-4/65) = 3/13 × (65/-4) = 3 × 65/-13 × 4 = 195/-52
= 195 ÷ 5/-52 ÷ 13 = 15/-4 = -3 3/4