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Academy11+

11+ Maths · Topic explained

Equivalent fractions and simplifying

Is half a pizza the same as 2 quarters? What about 4 eighths?

The big idea

Equivalent fractions look different but are the same amount: multiply or divide the top and bottom by the same number.

Picture it

Cut every slice in half again: more slices, but exactly the same amount of pizza.

Key words

equivalent
Worth the same, even though it looks different.
simplify
Divide the top and bottom by the same number to make a fraction with smaller numbers.
simplest form
When the top and bottom can't be divided by the same number any more.
common factor
A number that divides into both the top and the bottom.

Worked examples

  1. 1Warm-up

    Fill the gap: 1/2 = ?/8

    • 2 × 4 = 8, so multiply the top by 4 too
    • 1/2 = 4/8
  2. 211+ standard

    Simplify 18/24

    • 6 divides into 18 and 24
    • 18 ÷ 6 = 3 and 24 ÷ 6 = 4
    • 18/24 = 3/4
  3. 311+ standard

    Which is not equal to 2/3: 4/6, 6/9, 8/12 or 10/16?

    • 4/6, 6/9 and 8/12 all simplify to 2/3
    • 10/16 simplifies to 5/8
    • 10/16 is the odd one out
  4. 411+ standard

    Which is bigger: 3/5 or 5/8?

    • Make the bottoms the same: 40
    • 3/5 = 24/40 and 5/8 = 25/40
    • 5/8 is bigger (just!)

The common mistake

The mistake

2/3 = 4/5, because you add 2 to the top and the bottom.

Instead

Multiply (or divide) the top and bottom by the same number: 2/3 = 4/6.

Why: Adding changes the amount; multiplying just cuts the same amount into more pieces.

Where it comes up in the 11+

Giving answers in simplest form, matching equal fractions, and comparing fractions with different denominators.

The video

Video coming soon

We're making a short video that explains equivalent fractions and simplifying step by step. Until then, everything it covers is on this page.

Free printable

Equivalent fractions and simplifying worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Simplify 15/20.

    • 3/5
    • 3/4
    • 5/4
    • 1/5
    Show the answer

    3/4

    Divide top and bottom by 5.

  2. 2. Fill the gap: 3/4 = ?/20

    • 12
    • 15
    • 16
    • 17
    Show the answer

    15

    4 × 5 = 20, so 3 × 5 = 15.

  3. 3. Which is equivalent to 1/2: 3/5, 4/8, 5/12 or 6/10?

    • 3/5
    • 4/8
    • 5/12
    • 6/10
    Show the answer

    4/8

    4 is half of 8.