FRACTIONS, DECIMALS AND PERCENTAGES

Equivalent Fractions

Learn the reliable method for equivalent fractions, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Equivalent fractions name the same value with different numerators and denominators.

Picture itCount equal parts of one whole
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Find a number that divides or multiplies both parts.
  2. Apply the same operation to numerator and denominator.
  3. For simplest form, continue until no common factor remains.
a/b = (a × n)/(b × n)
3 · WORKED EXAMPLES

See the method in action

Example 1

Which fraction with denominator 42 is equivalent to 5/7?

  1. The denominator is multiplied by 6, so multiply the numerator by 6 too: 5/7 = 30/42.
Answer: 30/42
Example 2

Which fraction with denominator 228 is equivalent to 6/19?

  1. The denominator is multiplied by 12, so multiply the numerator by 12 too: 6/19 = 72/228.
Answer: 72/228
4 · ELEVENSPRINT TIP

A useful shortcut

Whatever you do to the bottom, do to the top.

5 · COMMON MISTAKES

Watch out for these

Changing only one number

Both numerator and denominator must change by the same factor.

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.