Page 37 - Start Up Mathematics_7

EXERCISE 2.2

1. Represent diagrammatically:
2 1 1 3 1 4 1 1
(a) 2 × = 1 (b) 3 × = (c) 4 × = (d) 4 × = 1
3 3 6 6 8 8 3 3
2. Multiply and write the following in the simplest form:
3 3 3 1
(a) 2 × (b) 12 × (c) × 8 (d) 6 ×
4 5 4 3
1
2
1
3
(e) 12 × (f) 4 × 5 (g) 14 × 3 (h) 2 × 21
4 2 7 14
3. Find:
1 3 1
(a) of (i) 24 (ii) 28 (iii) 18 (iv) 9
4 4 2
5
1
(b) of (i) 20 (ii) 24 (iii) 36 (iv) 42 5
6 6 6
5
4. Vineeta completed of her homework on Saturday. How much homework is left to be
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completed on Sunday?
5. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained
2
5 litres of water. Vidya consumed of the water. Pratap consumed the remaining water.
5
(a) How much water did Vidya drink?
(b) What fraction of the total quantity of water did Pratap drink?

Case II: Fraction multiplied by a fraction
To understand multiplication of two fractions, we perform the following activity:

Maths Lab Activity

Fraction Multiplied by a Fraction
1 4
Let’s find the product of two fractions, i.e., × . 4
2
9
4
We first represent by shaded region as shown in Fig. 1. 9
9 Fig. 1
1 4
Now of may be represented by half of the shaded region as shown in Fig. 2.
2 9

1 4 2
Therefore, × = .
2 9 9 2
9
1 9
Evaluate: × Fig. 2
3 16

The product of two fractions is obtained by simply multiplying the numerator with numerator and the
a c ac
denominator with denominator, i.e., × = .
b d bd

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