If you’re learning about fractions, you’ve probably heard the term “equivalent fractions” before. But what exactly are they?

Simply put, equivalent fractions are fractions that represent the same value but are written in different ways.

For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent half of a whole. Similarly, $\frac{3}{6}$ and $\frac{5}{10}$ are equivalent fractions because they also both represent half of a whole.

Understanding equivalent fractions is important because they allow us to compare and manipulate fractions more easily.

What Are Equivalent Fractions?

Equivalent fractions have different numerators and denominators but represent the same value.

A fraction is made up of two parts: the numerator and the denominator. The numerator represents the part being considered, and the denominator represents the total number of equal parts.

For example, $\frac{1}{3}$ and $\frac{2}{6}$ are equivalent because:

$$ \frac{1}{3} = \frac{2}{6} $$

Examples

$$ \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} $$

$$ \frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} $$

$$ \frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{12}{16} = \frac{15}{20} $$

How To Find Equivalent Fractions

Multiply by a Common Factor

For example, to find an equivalent fraction of $\frac{3}{4}$:

$$ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} $$

To add $\frac{1}{4} + \frac{1}{6}$, first find the LCM of 4 and 6, which is 12.

Convert both to equivalent fractions:

$$ \frac{1}{4} = \frac{3}{12},\quad \frac{1}{6} = \frac{2}{12} $$

Then add:

$$ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $$

Divide by a Common Factor

Simplify $\frac{6}{12}$:

$$ \frac{6}{12} = \frac{6 \div 6}{12 \div 6} = \frac{1}{2} $$

Simplify $\frac{8}{24}$ using GCF of 8:

$$ \frac{8}{24} = \frac{8 \div 8}{24 \div 8} = \frac{1}{3} $$

Are These Fractions Equivalent?

Check: $\frac{3}{4}, \frac{12}{16}, \frac{33}{44}$

Simplify each:

$$ \frac{3}{4} = \frac{3}{4},\quad \frac{12}{16} = \frac{3}{4},\quad \frac{33}{44} = \frac{3}{4} $$

All simplify to $\frac{3}{4}$, so they are equivalent.

Checking by Decimal

Convert each to decimal:

$$ \frac{3}{4} = 0.75,\quad \frac{12}{16} = 0.75,\quad \frac{33}{44} = 0.75 $$

Same decimal value confirms they are equivalent.

Summary

Equivalent fractions are different ways of expressing the same value. You can find them by multiplying or dividing both the numerator and denominator by the same number.

Examples:

  • Multiply: $\frac{2}{3} = \frac{4}{6}$
  • Divide: $\frac{6}{9} = \frac{2}{3}$

They are useful for comparing, adding, and subtracting fractions with different denominators.