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:**

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

\(\frac{21}{60} \frac{21 ÷ 3}{60 ÷ 3} = \frac{7}{20}\)

\(\frac{12}{15} \frac{12 ÷ 3}{15 ÷ 3} = \frac{4}{5}\)

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

\(\frac{27}{81} \frac{27 ÷ 3}{81 ÷ 3} = \frac{9}{27} \frac{9 ÷ 3}{27 ÷ 3} = \frac{3}{9} \frac{3 ÷ 3}{9 ÷ 3} = \frac{1}{3}\)

**Related Concepts**

**● ****Fraction as a Part of a Whole**** **

**● ****Fraction as a Part of Collection**

**● ****Proper Fraction and Improper Fraction**

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