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# Q.4 Find the equivalent fraction of $$\frac{3}{5}$$having (a) denominator 20 (b) numerator 9 (c) denominator 30 (d) numerator 27

(a) We require denominator 20
Let M be the numerator of the fractions
$$\therefore \frac{M}{20} = \(\frac{3}{5}$$
5 × M = 20 × 3
M = (20 × 3) ÷ 5 = 12
Therefore the required fraction is $$\frac{12}{20}$$
(b) We require numerator 9
Let N be the denominator of the fractions
$$\therefore \frac{9}{N} = \(\frac{3}{5}$$
3 × N = 9 × 5
N = (9 × 5) ÷ 3 = 15
Therefore the required fraction is $$\frac{9}{15}$$
(c) We require denominator 30
Let D be the numerator of the fraction
$$\therefore \frac{D}{30} = \(\frac{3}{5}$$
5 × D = 3 × 30
D = (3 × 30) ÷ 5
= 18
Therefore the required fraction is $$\frac{18}{30}$$
(d) We require numerator 27
Let X be the denominator of the fraction
$$\therefore \frac{27}{X} = \(\frac{3}{5}$$
3 × X = 5 × 27
X = (5 × 27) ÷ 3 = 45
Therefore the required fraction is $$\frac{27}{45}$$