## Chapter 9 Rational Numbers Exercise 9.2

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

= 5/4 - 11/4

= [5 - 11/4]

= -6/4

= -3/2

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

Answer:

Answer:

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)**

Answer:

LCM of 10 and 15 = 30

Answer:

= -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)**

Answer:

Answer:

= 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)**

Answer:

Answer:

= -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**

Answer:

Answer:

= -2/3 + 0

= -2/3

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

Answer:

Answer:

= -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

Answer:

(i) 7/24 - 17/36

Answer:

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)**

Answer:

Answer:

= -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)**

Answer:

Answer:

= -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**

Answer:

Answer:

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**

Answer:

Answer:

-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)**

Answer:

Answer:

= 9/2 × -7/4

= 9×-7/2×4

= -63/8

**(ii) (3/10) × (-9)**

Answer:

Answer:

= 3/10 × -9/1

= 3×-9/10×1

= -27/10

**(iii) (-6/5) × (9/11)**

Answer:

Answer:

= -6×9/5×11

= -54/55

**(iv) (3/7) × (-2/5)**

Answer:

Answer:

= 3×-2/7×5

= -6/35

**(v) (3/11) × (2/5)**

Answer:

Answer:

= 3×2/11×5

= 6/55

**(vi) (3/-5) × (-5/3)**

Answer:

Answer:

= 3×-5/-5×3

= 1×-1/-1×1

= -1/-1

= 1

**Question 4: Find the value of:**

(i) (-4) ÷ (2/3)

Answer:

(i) (-4) ÷ (2/3)

Answer:

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

= -4×3/1×2

= -2×3/1×1

= -6

**(ii) (-3/5) ÷ 2**

Answer:

Answer:

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

= -3×1/5×2

= -3/10

**(iii) (-4/5) ÷ (-3)**

Answer:

Answer

= -4/5 × 1/-3 (reciprocal of -3 is 1/-3)

= -4 × 1/5 × -3

= -4/-15

= 4/15

**(iv) (-1/8) ÷ 3/4**

Answer:

Answer:

= -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**

Answer:

Answer:

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

= -2×7/13×1

= -14/13

**(vi) (-7/12) ÷ (-2/13)**

Answer:

Answer:

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

= -7× 13/12× -2

= -91/-24

= 91/24

**(vii) (3/13) ÷ (-4/65)**

Answer:

Answer:

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

= 3 × 65/13 × -4

= 195/-52

= -15/4

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