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## Chapter 9 Rational Numbers Exercise 9.2

Question 1: Find the sum:
(i) (5/4) + (-11/4)

= 5/4 - 11/4
= [5 - 11/4]
= -6/4
= -3/2

(ii) (5/3) + (3/5)

LCM of 3 and 5 = 15
= 5/3 = [5×5/3×5] = 25/15
= 3/5= [3×3/5×3] = 9/15
= 25/15 + 9/15
= 25 + 9/15
= 34/15

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

(iv) (-3/-11) + (5/9)

= 3/11 + 5/9
LCM of 11 and 9 = 99
= 3/11 = [3×9/11×9] = 27/99
= 5/9 = [5×11/9×11] = 55/99
= 27/99 + 55/99
= 27 + 55/99
= 82/99

(v) (-8/19) + (-2/57)

= -8/19 - 2/57
LCM of 19 and 57 = 57
= -8/19 = [-8×3/19×3] = -24/57
= -2/57 = [-2×1/57×1] = -2/57
= -24/57 - 2/57
= -24 - 2/57
= -26/57

(vi) -2/3 + 0

= -2/3 + 0
= -2/3

(vii) -2 1/3 + 4 3/5

= -2 1/3 = -7/3
= 4 3/5 = 23/5
-7/3 + 23/5
LCM of 3 and 5 = 15
= -7/3= [-7×5/3×5] = -35/15
= 23/5 = [23×3/15×3] = 69/15
= -35/15 + 69/15
= -35 + 69/15
= 34/15

Question 2: Find
(i) 7/24 - 17/36

LCM of 24 and 36 = 72
= 7/24 = [7×3/24×3] = 21/72
= 17/36 = [17×2/36×2] = 34/72
= 21/72 - 34/72
= 21 - 34/72
= -13/72

(ii) 5/63 – (-6/21)

= -6/21 = -2/7
= 5/63 - (-2/7)
= 5/63 + 2/7
LCM of 63 and 7 = 63
= 5/63 = [5×1/63×1] = 5/63
= 2/7 = [2×9/7×9] = 18/63
= 5/63 + 18/63
= 5 + 18/63
= 23/63

(iii) -6/13 – (-7/15)

= -6/13 + 7/15
LCM of 13 and 15 = 195
= -6/13 = [-6×15/13×15] = -90/195
= 7/15 = [7×13/15×13] = 91/195
= -90/195 + 91/195
= -90 + 91/195
= 1/195

(iv) -3/8 – 7/11

LCM of 8 and 11 = 88
= -3/8 = [-3×11/8×11] = -33/88
= 7/11 = [7×8/11×8] = 56/88
= -33/88 - 56/88
= -33 - 56/88
= -89/88

(v) -2 1/9 - 6

-2 1/9 = -19/9
-19/9 - 6
LCM of 9 and 1 = 9
= -19/9 = [-19×1/9×1] = -19/9
= 6/1 = [6×9/1×9] = 54/9
= -19/9 - 54/9
= -19 - 54/9
= -73/9

Question 3: Find the product:
(i) (9/2) × (-7/4)

= 9/2 × -7/4
= 9×-7/2×4
= -63/8

(ii) (3/10) × (-9)

= 3/10 × -9/1
= 3×-9/10×1
= -27/10

(iii) (-6/5) × (9/11)

= -6×9/5×11
= -54/55

(iv) (3/7) × (-2/5)

= 3×-2/7×5
= -6/35

(v) (3/11) × (2/5)

= 3×2/11×5
= 6/55

(vi) (3/-5) × (-5/3)

= 3×-5/-5×3
= 1×-1/-1×1
= -1/-1
= 1

Question 4: Find the value of:
(i) (-4) ÷ (2/3)

= -4/1 × 3/2 (reciprocal of 2/3 is 3/2)
= -4×3/1×2
= -2×3/1×1
= -6

(ii) (-3/5) ÷ 2

= -3/5 × 1/2 (reciprocal of 2/1 is 1/2)
= -3×1/5×2
= -3/10

(iii) (-4/5) ÷ (-3)
:
= -4/5 × 1/-3 (reciprocal of -3 is 1/-3)
= -4 × 1/5 × -3
= -4/-15
= 4/15

(iv) (-1/8) ÷ 3/4

= -1/8 × 4/3 (reciprocal of 3/4 is 4/3)
= -1×4/8×3
= -1×1/2×3
= -1/6

(v) (-2/13) ÷ 1/7

= -2/13 × 7/1 (reciprocal of 1/7 is 7/1)
= -2×7/13×1
= -14/13

(vi) (-7/12) ÷ (-2/13)

= -7/12 × 13/-2 (reciprocal of -2/13 is 13/-2)
= -7× 13/12× -2
= -91/-24
= 91/24

(vii) (3/13) ÷ (-4/65)

= 3/13 × 65/-4 (reciprocal of -4/65 is 65/-4)
= 3 × 65/13 × -4
= 195/-52
= -15/4