The 3-Step Method
1Start with a fraction.
Here is one half — 1 of 2 equal pieces.
2Cut every piece in half.
Now you have a new fraction — 2 of 4 pieces. The amount hasn't changed.
3Cut every piece in half again.
The amount is the same — 4 of 8 pieces — but the pieces are smaller.
Worked Example
Find two fractions that are equivalent to 12.
Watch Out! Common Mistakes
This is wrong. They are equal. 24 is just 12 cut into smaller pieces.
This is wrong. You must multiply both the top and the bottom by the same number: 12 = 24.
There are infinitely many! Keep multiplying top and bottom by the same number.
⬇ Cheat Sheet
- Multiply or divide the numerator AND denominator
- …by the same number.
- The value stays the same.
📖 Continue Your Journey
Quick summary
- Equivalent fractions have different numbers but the same value: 1/2 = 2/4 = 4/8.
- Multiply or divide the numerator AND denominator by the same number to make an equivalent fraction.
- There are infinitely many equivalent fractions for any fraction.
- Changing only the top or only the bottom changes the value — you must change both.
Frequently asked questions
What are equivalent fractions?
Equivalent fractions are fractions that look different but represent the same amount. For example, 1/2, 2/4 and 4/8 are all exactly half.
How do you find an equivalent fraction?
Multiply (or divide) the numerator and the denominator by the same number. For example, 1/2 × 2/2 = 2/4, and 1/2 × 4/4 = 4/8.
Why do children need equivalent fractions?
Equivalent fractions are the key to comparing, ordering, adding and subtracting fractions with different denominators — all of which appear in Year 5–6 maths and 11+ exams.
Is 1/2 bigger than 2/4?
No — they are equal. 2/4 is just 1/2 cut into smaller pieces. This is one of the most common misconceptions children have.
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