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
Answer:
(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)
Answer:
= 7/1 × 3/5
= 7 × 3/1 × 5
= 21/5
= 4 1/5
(ii) 4 × (1/3)
Answer:
= 4/1 × 1/3
= 4 × 1/1 × 3
= 4/3
= 1 1/3
(iii) 2 × (6/7)
Answer:
= 2/1 × 6/7
= 2 × 6/1 × 7
= 12/7
= 1 5/7
(iv) 5 × (2/9)
Answer:
= 5/1 × 2/9
= 5 × 2/1 × 9
= 10/9
= 1 1/9
(v) (2/3) × 4
Answer:
= 2/3 × 4/1
= 2 × 4/3 × 1
= 8/3
= 2 2/3
(vi) (5/2) × 6
Answer:
= 5/2 × 6/1
= 5 × 6/2 × 1
= 30/2
= 15
(vii) 11 × (4/7)
Answer:
= 11/1 × 4/7
= 11 × 4/1 × 7
= 44/7
= 6 2/7
(viii) 20 × (4/5)
Answer:
= 20/1 × 4/5
= 20 × 4/1 × 5
= 80/5
= 16
(ix) 13 × (1/3)
Answer:
= 13/1 × 1/3
= 13 × 1/1 × 3
= 13/3
= 4 1/3
(x) 15 × (3/5)
Answer:
= 15/1 × 3/5
= 15 × 3/1 × 5
= 45/5
= 9
Question 4: Shade:
(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
Answer:
(i) 24
= 1/2 × 24
= 24/2
= 12
(ii) 46
= 1/2 × 46
= 46/2
= 23
(b) 2/3 of (i) 18 (ii) 27
Answer:
(i) 18
= 2/3 × 18
= 2 × 6
= 12
(ii) 27
= 2/3 × 27
= 2 × 9
= 18
(c) 3/4 of (i) 16 (ii) 36
Answer:
(i) 16
= 3/4 × 16
= 3 × 4
= 12
(ii) 36
= 3/4 × 36
= 3 × 9
= 27
(d) 4/5 of (i) 20 (ii) 35
Answer:
(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
Answer:
= 5 1/5 = 26/5
= 3 × 26/5
= 78/5
= 15 3/5
(b) 5 × 6 3/4
Answer:
= 6 3/4 = 27/4
= 5 × 27/4
= 135/4
= 33 3/4
(c) 7 × 2 1/4
Answer:
= 2 1/4 = 9/4
= 7 × 9/4
= 63/4
= 15 3/4
(d) 4 × 6 1/3
Answer:
= 6 1/3 = 19/3
= 4 × 19/3
= 76/3
= 25 1/3
(e) 3 1/4 × 6
Answer:
= 3 1/4 = 13/4
= 13/4 × 6
= 13/2 × 3
= 39/2
= 19 1/2
(f) 3 2/5× 8
Answer:
= 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
Answer:
(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
Answer:
(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?
Answer:
(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.
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