Page 36 - Start Up Mathematics_7

Solution: (a) (b)

1 2
Example 11: Find: (a) of 52 (b) of 27
2 3

1 1 52 2 2 54
Solution: (a) of 52 = × 52 = = 26 (b) of 27 = × 27 = = 18
2 2 2 3 3 3
1
Example 12: Multiply and express as a mixed fraction: (a) 4 × 5 (b) 5 × 6 1
5 4
1 26 104 4 1 25 125 1
Solution: (a) 4 × 5 = 4 × = = 20 (b) 5 × 6 = 5 × = = 31
5 5 5 5 4 4 4 4
1 1 5 2
Example 13: Find: (a) of 2 (b) of 8
2 4 8 3

1 1 1 9 1 9 9 1
Solution: (a) of 2 = of = × = = 1
2 4 2 4 2 4 8 8
5 2 5 26 5 26 130 65 5
(b) of 8 = of = × = = = 5
8 3 8 3 8 3 24 12 12
Example 14: Anjan and Debashish went for a picnic. They bought a 2 litre water bottle. Anjan
3
consumed of the water. Debashish consumed the remaining water.
5
(a) How much water did Anjan drink?

(b) What fraction of the total quantity of water did Debashish drink?
3 3 6 1
Solution: (a) Anjan consumed of 2 L = × 2 L = L or 1 L
5 5 5 5
3
(b) Fraction of water consumed by Debashish = 1 –
5

5 – 3 2
= =
5 5
Example 15: Divya and Shefali sold raffle tickets for Diwali mela worth ` 4,200. If Shefali sold

3
2 times of what Divya sold, how much did each sell?
4
3
Solution: Sales of Divya and Shefali are in the ratio 1 : 2 = 1 : 11 = 4 : 11
4 4
The sum of the terms of the ratios = 4 + 11 = 15
 The total sales is ` 4,200

∴ Divya sold tickets worth = 4 × ` 4,200 = ` 1,120
15

Shefali sold tickets worth = 11 × ` 4,200 = ` 3,080
15

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