Equivalent Fractions Worksheet (original) (raw)

Last Updated : 23 Jul, 2025

Equivalent fractions are different fractions that represent the same value or proportion of a whole. They can be found by multiplying or dividing both the numerator and the denominator by the same non-zero number.

In this article, we will learn how to solve equivalent fractions.

What are Equivalent Fractions?

Equivalent fractions represent the same value or proportion, even though they have different numerators (top numbers) and denominators (bottom numbers). They describe the same part of a whole or the same ratio between two quantities.

For example, the fractions \frac{1}{2}​ and \frac{2}{4}​ are equivalent because both represent the same amount: half of a whole.

How to Determine Equivalent Fractions?

To determine if two fractions are equivalent, you can multiply or divide both the numerator and the denominator of one fraction by the same non-zero number. If the resulting fraction matches the other fraction, then the two are equivalent.

**Example 1: Find equivalent fraction of \frac{1}{3}.

**Solution:

So, \frac{1}{3} and \frac{2}{6}are equivalent fractions.

**Example 2: Find equivalent fraction of \frac{4}{5}​.

**Solution:

So, \frac{4}{5}​ and \frac{12}{15}​ are equivalent fractions.

Equivalent Fractions: Solved Examples

**Example 1: Are \frac{12}{16} and \frac{3}{4} equivalent fractions?

**Solution:

Simplify \frac{12}{16}​ by dividing both by 4: \frac{12 \div 4}{16 \div 4} = \frac{3}{4}

So, they are equivalent.

**Example 2: Simplify the fraction \frac{18}{27}​.

**Solution:

The GCD of 18 and 27 is 9.

Divide both by 9: \frac{18 \div 9}{27 \div 9} = \frac{2}{3}​.

**Example 3: Find an equivalent fraction for \frac{4}{5}​ with a denominator of 20.

**Solution:

Multiply the numerator and denominator by 4: \frac{4 \times 4}{5 \times 4} = \frac{16}{20}​.

**Example 4: Are \frac{10}{15}**​ and \frac{2}{3}**​ equivalent fractions?

**Solution:

Simplify \frac{10}{15} by dividing both by 5: \frac{10 \div 5}{15 \div 5} = \frac{2}{3}.

**So, they are equivalent.

Example 5: Simplify the fraction \frac{20}{30}.

**Solution:

The GCD of 20 and 30 is 10.

Divide both by 10: \frac{20 \div 10}{30 \div 10} = \frac{2}{3}​.

**Example 6: Find an equivalent fraction for \frac{7}{9} with a numerator of 14.

**Solution:

Multiply the numerator and denominator by 2: \frac{7 \times 2}{9 \times 2} = \frac{14}{18}.

**Example 7: Are \frac{9}{12}**​ and \frac{3}{4}​ **equivalent fractions?

**Solution:

Simplify \frac{9}{12} by dividing both by 3: \frac{9 \div 3}{12 \div 3} = \frac{3}{4}​.

So, they are equivalent.

**Example 8: Simplify the fraction \frac{16}{24}**​.

**Solution:

The GCD of 16 and 24 is 8.

Divide both by 8: \frac{16 \div 8}{24 \div 8} = \frac{2}{3}​.

**Example 9: Find an equivalent fraction for \frac{5}{7} with a denominator of 21.

**Solution:

Multiply the numerator and denominator by 3: \frac{5 \times 3}{7 \times 3} = \frac{15}{21}​.

**Example 10: Are \frac{3}{4}​ and \frac{6}{8}**​ equivalent fractions?

**Solution:

Multiply \frac{3}{4}​ by 2: \frac{3 \times 2}{4 \times 2} = \frac{6}{8}​.

So, \frac{3}{4}​ and \frac{6}{8}​ are equivalent.

Worksheet: Equivalent Fractions

**Instructions: Simplify the following fractions and find their equivalent forms.

**Q1: Find equivalent fraction of \frac{8}{12}

**Q2: Find equivalent fraction of \frac{6}{9}​

**Q3: Find equivalent fraction of \frac{15}{20}​

**Q4: Find equivalent fraction of \frac{10}{25}

**Q5: Find equivalent fraction of\frac{14}{21}​

**Q6: Find an equivalent fraction for \frac{2}{3} with a numerator of 10

**Q7: Simplify \frac{28}{35}​

**Q8: Find an equivalent fraction for \frac{3}{4} with a denominator of 16

**Q9: Are \frac{9}{12}​ and \frac{6}{8}​ equivalent?

**Q10: Simplify \frac{18}{24}

**Read More,