## Chapter 2 Fractions and Decimals Exercise 2.4

Question 1: Find:
(i) 12 ÷ 3/4

= 12 x reciprocal of 3/4
= 12 × 4/3
= 48/3
= 16

(ii) 14 ÷ (5/6)

= 14 × reciprocal of 5/6
= 14 × 6/5
= 84/5

(iii) 8 ÷ (7/3)

= 8 × reciprocal of 7/3
= 8 × 3/7

(iv) 4 ÷ (8/3)

= 4 × reciprocal of 8/3
= 4 × 3/8
= 12/8
= 3/2

(v) 3 ÷ 2 1/3

= 2 1/3 = 7/3
= 3 ÷ 7/3
= 3 × reciprocal of 7/3
= 3 × 3/7
= 9/7

(vi) 5 ÷ 3 4/7

= 3 4/7 = 25/7
= 5 ÷ 25/7
= 5 × reciprocal of 25/7
= 5 × 7/25
= 35/25
= 7/5

Question 2: Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) 3/7

Reciprocal of 3/7 is 7/3
Therefore, it is an improper fraction.

(ii) 5/8

Reciprocal of 5/8 is 8/5
Therefore, it is an improper fraction.

(iii) 9/7

Reciprocal of 9/7 is 7/9
Therefore, it is a proper fraction.

(iv) 6/5

Reciprocal of 6/5 is 5/6
Therefore, it is a proper fraction.

(v) 12/7

Reciprocal of 12/7 is 7/12
Therefore, it is a proper fraction.

(vi) 1/8

Reciprocal of 1/8 is 8/1 or 8
Therefore, it is a whole number.

(vii) 1/11

Reciprocal of 1/11 is 11/1 or 11
Therefore, it is a whole number.

Question 3: Find:
(i) (7/3) ÷ 2

= 7/3 × reciprocal of 2
= 7/3 × 1/2
= 7 × 1/3 × 2
= 7/6

(ii) (4/9) ÷ 5

= 4/9 × reciprocal of 5
= 4/9 × 1/5
= 4 × 1/9 × 5
= 4/45

(iii) (6/13) ÷ 7

= 6/13 × reciprocal of 7
= 6/13 × 1/7
= 6 × 1/13 × 7
= 6/91

(iv) 4 1/3 ÷ 3

= 4 1/3 = 13/3
= 13/3 × reciprocal of 3
= 13/3 × 1/3
= 13 × 1/3 × 3
= 13/9

(v) 3 1/2 ÷ 4

= 3 1/2 = 7/2
= 7/2 × reciprocal of 4
= 7/2 × 1/4
= 7 × 1/2 × 4
= 7/8

(vi) 4 3/7 ÷ 7

= 4 3/7 = 31/7
= 31/7 × reciprocal of 7
= 31/7 × 1/7
= 31 × 1/7 × 7
= 31/49

Question 4: Find:
(i) (2/5) ÷ (1/2)

= 2/5 × reciprocal of 1/2
= 2/5 × 2/1
= 2 × 2/5 × 1
= 4/5

(ii) (4/9) ÷ (2/3)

= 4/9 × reciprocal of 2/3
= 4/9 × 3/2
= 4 × 3/9 × 2
= 2 × 1/3 × 1
= 2/3

(iii) (3/7) ÷ (8/7)

= 3/7 × reciprocal of 8/7
= 3/7 ×7/8
= 3 × 7/7 × 8
= 3 × 1/1 × 8
= 3/8

(iv) 2 1/3 ÷ (3/5)

= 2 1/3 = 7/3
= 7/3 × reciprocal of 3/5
= 7/3 × 5/3
= 7 × 5/3 × 3
= 35/9

(v) 3 1/2 ÷ (8/3)

= 3 1/2 = 7/2
= 7/2 × reciprocal of 8/3
= 7/2 × 3/8
= 7 × 3/2 × 8
= 21/16

(vi) (2/5) ÷ 1 1/2

= 1 1/2 = 3/2
= 2/5 × reciprocal of 3/2
= 2/5 × 2/3
= 2 × 2/5 × 3
= 4/15

(vii) 3 1/5 ÷ 1 2/3

= 3 1/5 = 16/5
= 1 2/3 = 5/3
= 16/5 × reciprocal of 5/3
= 16/5 × 3/5
= 16 × 3/5 × 5
= 48/25

(viii) 2 1/5 ÷ 1 1/5