All skills Math

Learn Index · Fractions, Decimals, and Percentages Grade 3–5

Equivalent fractions

Fractions that look different but have the same value.

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Same amount, different names

Equivalent fractions look different but name the same amount:

1/2 = 2/4 = 3/6 = 4/8 = 50/100

Picture a chocolate bar. Cut it in 2 and take one piece. Now cut the same bar into 4 and take two pieces. You’ve eaten exactly the same amount.

Using a fraction wall

A fraction wall stacks strips that are all the same length, each cut into a different number of equal pieces:

  • 1 whole
  • 1/2 | 1/2
  • 1/4 | 1/4 | 1/4 | 1/4
  • 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8

Line up the edges: one half covers the same length as two quarters or four eighths.

The rule

Multiply or divide the numerator and denominator by the same number (not zero).

  • Multiply to make larger-looking fractions:
    2/3 × 4/4 = 8/12
  • Divide to make simpler fractions:
    12/18 ÷ 6/6 = 2/3

Why does it work? Multiplying the top and bottom by the same number is the same as multiplying by 1 (like 4/4), and multiplying by 1 doesn’t change the value.

Finding a missing number

Example: 3/5 = ?/20

  • What turns 5 into 20? × 4.
  • Do the same to the top: 3 × 4 = 12.
  • 3/5 = 12/20.

Checking two fractions

Cross-multiply. If the products are equal, the fractions are equivalent.

  • Are 4/6 and 6/9 equivalent? 4 × 9 = 36; 6 × 6 = 36. Yes.
  • Are 2/5 and 3/7 equivalent? 2 × 7 = 14; 5 × 3 = 15. No.

Why equivalent fractions matter

You need them to:

  • Compare fractions (give them the same denominator).
  • Add and subtract fractions.
  • Simplify answers.
  • Change fractions to percentages (e.g. 3/4 = 75/100 = 75%).

Worked examples

Example 1: Write three fractions equivalent to 2/5.

× 2: 4/10; × 3: 6/15; × 10: 20/50.

Example 2: 6/8 = ?/4

8 ÷ 2 = 4, so 6 ÷ 2 = 3. 6/8 = 3/4.

Example 3: Is 5/15 equal to 1/3?

Divide by 5: 1/3. Yes.

Common mistakes

  • Adding the same number to top and bottom: 1/2 is not equal to 2/3 (adding 1 to each changes the value).
  • Changing only the numerator or only the denominator.
  • Thinking 4/8 is bigger than 1/2 because the numbers are bigger.

Try it yourself

  1. 1/3 = ?/12
  2. 10/25 = 2/?
  3. Are 3/4 and 9/12 equivalent?
  4. Write two fractions equivalent to 5/6.

Answers: 1) 4 2) 5 3) yes 4) e.g. 10/12 and 15/18

Quick recap

  • Equivalent fractions have the same value.
  • Multiply or divide top and bottom by the same number.
  • Check with cross-multiplication or a fraction wall.