## Chapter 2 Fractions and Decimals Exercise 2.2

Question 1: Which of the drawings (a) to (d) show:
(i) 2 × (1/5) (ii) 2 × 1/2 (iii) 3 × 2/3 (iv) 3 × 1/4

(i) 2 × 1/5 represents figure (d).
(ii) 2 × 1/2 represents figure (b).
(iii) 3 × 2/3 represents figure (a).
(iv) 3 × 1/4 represents figure (c).

Question 2: Some pictures (a) to (c) are given below. Tell which of them show:
(i) 3 × (1/5) = (3/5) (ii) 2 × (1/3) = (2/3) (iii) 3 × (3/4) = 2 1/4

(i) 3 × 1/5 = 3/5 represents figure (c).
(ii) 2 × 1/3 = 2/3 represents fig (a).
(iii) 3 × 3/4 = 2 1/4 represents figure (b).

Question 3: Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 × (3/5)

= 7/1 × 3/5
= 7 × 3/1 × 5
= 21/5
= 4 1/5

(ii) 4 × (1/3)

= 4/1 × 1/3
= 4 × 1/1 × 3
= 4/3
= 1 1/3

(iii) 2 × (6/7)

= 2/1 × 6/7
= 2 × 6/1 × 7
= 12/7
= 1 5/7

(iv) 5 × (2/9)

= 5/1 × 2/9
= 5 × 2/1 × 9
= 10/9
= 1 1/9

(v) (2/3) × 4

= 2/3 × 4/1
= 2 × 4/3 × 1
= 8/3
= 2 2/3

(vi) (5/2) × 6

= 5/2 × 6/1
= 5 × 6/2 × 1
= 30/2
= 15

(vii) 11 × (4/7)

= 11/1 × 4/7
= 11 × 4/1 × 7
= 44/7
= 6 2/7

(viii) 20 × (4/5)

= 20/1 × 4/5
= 20 × 4/1 × 5
= 80/5
= 16

(ix) 13 × (1/3)

= 13/1 × 1/3
= 13 × 1/1 × 3
= 13/3
= 4 1/3

(x) 15 × (3/5)

= 15/1 × 3/5
= 15 × 3/1 × 5
= 45/5
= 9

(i) 1/2 of the circles in box (a)
(ii) 2/3 of the triangles in box (b)
(iii) 3/5 of the squares in the box (c)

(i) 12 × 1/2 = 12/2 = 6

(ii) 9 × (2/3) = 18/3 = 6

(iii) 15 × 3/5 = 45/5 = 9

Question 5: Find:
(a) 1/2 of (i) 24 (ii) 46
(i) 24
= 1/2 × 24
= 24/2
= 12

(ii) 46
= 1/2 × 46
= 46/2
= 23

(b) 2/3 of (i) 18 (ii) 27

(i) 18
= 2/3 × 18
= 2 × 6
= 12

(ii) 27
= 2/3 × 27
= 2 × 9
= 18

(c) 3/4 of (i) 16 (ii) 36

(i) 16
= 3/4 × 16
= 3 × 4
= 12

(ii) 36
= 3/4 × 36
= 3 × 9
= 27

(d) 4/5 of (i) 20 (ii) 35
(i) 20
= 4/5 × 20
= 4 × 4
= 16

(ii) 35
= 4/5 × 35
= 4 × 7
= 28

Question 6: Multiply and express as a mixed fraction:
(a) 3 × 5 1/5
= 5 1/5 = 26/5
= 3 × 26/5
= 78/5
= 15 3/5

(b) 5 × 6 3/4

= 6 3/4 = 27/4
= 5 × 27/4
= 135/4
= 33 3/4

(c) 7 × 2 1/4

= 2 1/4 = 9/4
= 7 × 9/4
= 63/4
= 15 3/4

(d) 4 × 6 1/3

= 6 1/3 = 19/3
= 4 × 19/3
= 76/3
= 25 1/3

(e) 3 1/4 × 6

= 3 1/4 = 13/4
= 13/4 × 6
= 13/2 × 3
= 39/2
= 19 1/2

(f) 3 2/5× 8

= 3 2/5 = 17/5
= 17/5 × 8
= 136/5
= 27 1/5

Question 7: Find:
(a) 1/2 of (i) 2 3/4 (ii) 4 2/9

(i) 2 3/4
= 2 3/4 = 11/4
= 1/2 × 11/4
= 1/2 × 11/4
= 1 × 11/2 × 4
= 11/8
= 1 3/8

(ii) 4 2/9
= 4 2/9 = 38/9
= 1/2 × 38/9
= 1/2 × 38/9
= 1 × 38/2 × 9
= 38/18
= 19/9
= 2 1/9

(b) 5/8 of (i) 3 5/6 (ii) 9 2/3

(i) 3 5/6
= 3 5/6 = 23/6
= 5/8 × 23/6
= 5/8 × 23/6
= 5 × 23/8 × 6
= 115/48
= 2 19/48

(ii) 9 2/3
= 9 2/3 = 29/3
= 5/8 × 29/3
= 5/8 × 29/3
= 5 × 29/8 × 3
= 145/24
= 6 1/24

Question 8: Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres water. Vidya consumed 2/5 of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

(i)
Amount of water in the water bottle = 5 litres
Amount of water consumed by Vidya = 2/5 of 5 litres
= 2/5 × 5
= 2 litres
Therefore, the total amount of water drank by Vidya is 2 litres

(ii)
Amount of water in the water bottle = 5 litres
Amount of water consumed by Pratap = ?
= (1 - water consumed by Vidya)
= 1 - (2/5)
= 5-2/5
= 3/5
Therefore, total amount of water consumed by Pratap = 3/5 of 5 litres
= 3/5 × 5
= 3 litres
Therefore, the total amount of water drank by Pratap is 3 litres.