# Convert a Fraction to an Equivalent Fraction

To learn how to convert a fraction to an equivalent fraction let us first recall ‘what are equivalent fractions?’

Equivalent fractions are the fractions having different numerators and denominators but representing equal value to each other.

Example to make the fractions equivalent:

$$1\over 3$$ = $$\frac{1 × 2}{3 × 2}$$ = $$\frac{1 × 3}{3 × 3}$$ = $$\frac{1 × 4}{3 × 4}$$ = $$\frac{1 × 5}{3 × 5}$$ = $$\frac{1 × 6}{3 × 6}$$

$$\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18}$$

There are two ways to make the fraction equivalent:

1. Equivalent fraction can be built to very large numbers.

2. Equivalent fraction can be reduced to the smaller number.

How to convert a fraction to an equivalent fraction with a larger denominator?

If the numerator and denominator of a fraction are multiplied by the same number, the value of the fraction does not change and an equivalent fraction is obtained.

For example:

$\frac{1}{2} \frac{1 × 2}{2 × 2} = \frac{2}{4} \frac{1 × 5}{2 × 5}= \frac{5}{10} \frac{1 × 7}{2 × 7} = \frac{7}{14} \frac{1 × 9}{2 × 9} = \frac{9}{18}$

$\frac{1}{4} \frac{1 × 2}{2 × 4} = \frac{2}{8} \frac{1 × 4}{4 × 4} = \frac{4}{16} \frac{1 × 6}{4 × 6} = \frac{6}{24} \frac{1 × 8}{4 × 8} = \frac{8}{32}$

$\frac{2}{3} \frac{2 × 2}{3 × 2} = \frac{4}{6} \frac{2 × 5}{3 × 5} = \frac{10}{15} \frac{2 × 7}{3 × 7} = \frac{14}{21} \frac{2 × 9}{3 × 9} = \frac{18}{27}$

$\frac{1}{5} \frac{1 × 3}{5 × 3} = \frac{3}{15} \frac{1 × 6}{5 × 6} = \frac{6}{30} \frac{1 × 8}{5 × 8} = \frac{8}{40} \frac{1 × 10}{5 × 10} = \frac{10}{50}$

$\frac{3}{7} \frac{3 × 2}{7 × 2} = \frac{6}{14} \frac{3 × 5}{7 × 5} = \frac{15}{35} \frac{3 × 8}{7 × 8} = \frac{24}{56} \frac{3 × 9}{7 × 9} = \frac{27}{63}$

How to convert a fraction to an equivalent fraction with a smaller denominator?

If the numerator and denominator of a fraction are divided by the same number, the value of the fraction does not change and an equivalent fraction is obtained.

For example:

$$\frac{16}{64} \frac{16 ÷ 2}{64 ÷ 2} = \frac{8}{32} \frac{8 ÷ 2}{32 ÷ 2} = \frac{4}{16} \frac{4 ÷ 2}{16 ÷ 2} = \frac{2}{8} \frac{2 ÷ 2}{8 ÷ 2} = \frac{1}{4}$$

$$\frac{21}{60} \frac{21 ÷ 3}{60 ÷ 3} = \frac{7}{20}$$

$$\frac{12}{15} \frac{12 ÷ 3}{15 ÷ 3} = \frac{4}{5}$$

$$\frac{30}{45} \frac{30 ÷ 3}{45 ÷ 3} = \frac{10}{15} \frac{10 ÷ 5}{15 ÷ 5} = \frac{2}{3}$$

$$\frac{27}{81} \frac{27 ÷ 3}{81 ÷ 3} = \frac{9}{27} \frac{9 ÷ 3}{27 ÷ 3} = \frac{3}{9} \frac{3 ÷ 3}{9 ÷ 3} = \frac{1}{3}$$

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