• Key Stage 2 • Fractions
Equivalent fractions are fractions that look different but are the same size, such as 1/2 and 2/4. Children start learning about them in Year 3 and use them in almost every fractions topic after that. This guide explains what equivalent fractions are, how to find them, a chart of common equivalents and practice questions with answers.
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The Quick Answer
- Equivalent fractions are fractions with the same value, for example 1/2 = 2/4 = 3/6.
- To find one, multiply or divide the numerator and denominator by the same number: 2/3 = 4/6 (both multiplied by 2).
- Children meet equivalent fractions with small denominators in Year 3, families of equivalent fractions in Year 4 and equivalents in tenths and hundredths in Year 5.
- Equivalent fractions are the key to simplifying fractions and adding fractions with different denominators.
What Are Equivalent Fractions?
A fraction has two parts. The numerator (top number) says how many parts you have. The denominator (bottom number) says how many equal parts the whole is split into.
If you cut a pizza into 2 equal pieces and eat 1, you have eaten 1/2. If you cut the same pizza into 4 equal pieces and eat 2, you have eaten 2/4. The pieces are a different size, but the amount eaten is the same. So 1/2 and 2/4 are equivalent fractions.
Remember: the denominator can change, but the fraction only stays the same size if the numerator changes in the same way.
How to Find Equivalent Fractions
Multiply the numerator and the denominator by the same number.
- 1/3 × 2 on top and bottom = 2/6
- 1/3 × 3 on top and bottom = 3/9
- 1/3 × 4 on top and bottom = 4/12
Divide the numerator and the denominator by the same number.
- 8/12 ÷ 2 on top and bottom = 4/6
- 8/12 ÷ 4 on top and bottom = 2/3
Missing numbers. For 3/4 = ?/20, ask what 4 has been multiplied by to make 20. The answer is 5, so multiply 3 by 5 too: 3/4 = 15/20.
Tip: a fraction wall is a great way to see equivalent fractions. Strips of the same length are split into halves, thirds, quarters and so on, so children can see which pieces line up.
Equivalent Fractions Chart
| Fraction | Equivalent fractions |
|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10, 6/12, 50/100 |
| 1/3 | 2/6, 3/9, 4/12, 5/15 |
| 2/3 | 4/6, 6/9, 8/12, 10/15 |
| 1/4 | 2/8, 3/12, 4/16, 25/100 |
| 3/4 | 6/8, 9/12, 12/16, 75/100 |
| 1/5 | 2/10, 3/15, 4/20, 20/100 |
| 2/5 | 4/10, 6/15, 8/20, 40/100 |
| 1/10 | 2/20, 10/100 |
How to Check if Two Fractions Are Equivalent
There are two quick ways.
- Look for the multiplier. For 3/5 and 12/20, 3 × 4 = 12 and 5 × 4 = 20. Both numbers have been multiplied by 4, so the fractions are equivalent.
- Simplify both fractions. 4/6 and 6/9 both simplify to 2/3, so they are equivalent.
Common Mistakes
- Adding instead of multiplying. Adding 1 to the top and bottom of 1/2 gives 2/3, which is not equivalent. Always multiply or divide.
- Changing only one number. Doubling the denominator of 1/4 without doubling the numerator gives 1/8, which is half the size.
- Thinking a bigger denominator means a bigger fraction. 1/8 is smaller than 1/4 because the whole is split into more pieces.
What Children Learn in Each Year
| Year | National curriculum expectation |
|---|---|
| Year 3 | Recognise and show equivalent fractions with small denominators, using diagrams. |
| Year 4 | Recognise and show families of common equivalent fractions, using diagrams. |
| Year 5 | Identify, name and write equivalent fractions of a given fraction, including tenths and hundredths. |
| Year 6 | Use common factors to simplify fractions and common multiples to give fractions the same denominator. |
Equivalent Fractions Practice Questions
- 1/2 = ?/8
- 1/3 = ?/12
- 3/4 = ?/20
- 2/5 = ?/10
- 6/9 = 2/?
- 10/15 = ?/3
- 7/10 = ?/100
- Are 4/6 and 6/9 equivalent?
- Write three fractions equivalent to 3/5.
- Which of these is not equivalent to 1/4: 2/8, 3/12, 4/12 or 25/100?
Show the answers
- 4
- 4
- 15
- 4
- 3
- 2
- 70
- Yes. Both simplify to 2/3.
- For example 6/10, 9/15 and 12/20
- 4/12 (it is equivalent to 1/3)
Frequently Asked Questions
What are equivalent fractions?
Fractions that have the same value, even though they use different numbers. For example, 1/2, 2/4 and 5/10 are all equivalent.
How do you find equivalent fractions?
Multiply or divide the numerator and the denominator by the same number. For example, 2/5 × 3 on top and bottom = 6/15.
What year do children learn equivalent fractions?
Children start in Year 3 with small denominators. By Year 5 they find equivalent fractions including tenths and hundredths.
What is an equivalent fraction for 3/4?
6/8, 9/12, 12/16 and 75/100 are all equivalent to 3/4.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study. Practice questions written by Monster Learning.
