How to Find Equivalent Fractions

Understanding Equivalent Fractions

Let’s take a quick look at equivalent fractions. Equivalent fractions may look different, but they represent the exact same value. In other words, the fractions are equal even though the numbers look different.

For example, \large \frac{1}{2} and \large \frac{2}{4} are equivalent fractions because they represent the same amount.

The rule is this: if you multiply or divide the numerator and denominator by the same number, you create an equivalent fraction.

---

Steps to Find Equivalent Fractions

1. 1. Start with the original fraction.
   2. Choose the same number to multiply or divide both the numerator and denominator by.
   3. Rewrite the fraction.
   4. Check your work to make sure the value stayed the same.

Here is a basic example:

Find two equivalent fractions for \large \frac{3}{5}

Example: Multiplying to Create Equivalent Fractions

Step 1: Multiply the numerator and denominator by the same number.

Let’s multiply both by 2.

\large \frac{3\times 2}{5\times 2}=\frac{6}{10}

Step 2: Multiply by another common number.

Now let’s multiply both by 3.

\large \frac{3\times 3}{5\times 3}=\frac{9}{15}

Step 3: Notice the pattern.

\large \frac{3}{5}=\frac{6}{10}=\frac{9}{15}

Different fractions, same value. That’s the whole idea behind equivalent fractions.

Example Using Division

Find an equivalent fraction for \large \frac{12}{18}

The numerator and denominator are both divisible by 6.

\large 12 \div 6=2

\large 18 \div 6=3

\large \frac{12}{18}=\frac{2}{3}

Why Equivalent Fractions Matter

Equivalent fractions are used all the time when solving math problems. They help you simplify fractions and find common denominators when adding or subtracting fractions.

For example, to solve:

\large \frac{1}{2}+\frac{1}{4}

You need equivalent fractions with the same denominator before adding.

Understanding equivalent fractions is a key step to mastering all fraction operations.

---

Watch John explain fractions in a simple way:

Watch this fraction shortcut too:

Practice Problems

Create one equivalent fraction for each problem:

1. \large \frac{1}{4}

2. \large \frac{2}{3}

3. \large \frac{5}{8}

Answers

1. \large \frac{1}{4}=\frac{2}{8}

2. \large \frac{2}{3}=\frac{4}{6}

3. \large \frac{5}{8}=\frac{10}{16}

Common Mistakes

• Do not add the same number to the numerator and denominator. Equivalent fractions come from multiplying or dividing.
• Do not multiply the numerator and denominator by different numbers.
• Always keep the fraction balanced by doing the same thing to the top and bottom.

Need More Help with Fractions?

Our full math courses include complete lessons, worksheets, quizzes, and step-by-step solution videos to help students truly master fractions.

Check out our full Pre-Algebra or Math Foundations course to learn much, much more!