Page 109 - Start Up Mathematics_4

Solution: (a) 45 = 9 × 5.

So, the numerator 4 should also be multiplied by 5.

4 = 4 × 5 = 20
9 9 × 5 45

(b) 12 = 3 × 4.
So, the denominator 5 should also be multiplied by 4.

3 = 3 × 4 = 12
5 5 × 4 20

(c) 63 ÷ 9 = 7.
So, the numerator should also be divided by 9.

54 = 54 ÷ 9 = 6
63 63 ÷ 9 7

Checking the Equivalence of Two Fractions
Remember
To check the equivalence of two fractions, cross-multiply, i.e.,
multiply the numerator of one fraction with the denominator of Cross-multiply:
l
the other fraction. If their products are equal, the fractions are m p
=
q
equivalent. l × q = p × m
2 6
Example 5: Are and equivalent fractions?
7 21
2 6
Solution: 2 × 21 = 42 7 × 6 = 42
7 21
2
Since the products are equal, and 6 are equivalent fractions.
7 21
4 8
Example 6: Are and equivalent fractions?
5 15
4 8
Solution: 4 × 15 = 60 5 × 8 = 40
5 15
4
Since the products are not equal, and 8 are not equivalent fractions.
5 15

EXERCISE 8.1

1
1. Represent in three different ways and write the fraction for each.
2

1
2

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