GCSE Maths Practice: fractions

Question 2 of 12

This question practises finding equivalent fractions – a key foundation skill for simplifying, comparing, and adding fractions.

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\( \begin{array}{l}\text{Which fraction is equivalent to }\frac{1}{6}?\end{array} \)

Choose one option:

Multiply numerator and denominator by the same number to form an equivalent fraction. Dividing works the same way in reverse.

Equivalent fractions are fractions that look different but represent the same value. You can create an equivalent fraction by multiplying or dividing both the numerator (top number) and denominator (bottom number) by the same number. This is allowed because it keeps the fraction in the same proportion.

Why this works

A fraction is a division. For example, \(\tfrac{1}{6}\) means “1 divided by 6”. If we multiply the top and bottom by 3, we get \(\tfrac{3}{18}\) which still means “3 divided by 18”. Since both describe the same part of a whole, the fractions are equivalent.

How to form an equivalent fraction

  1. Choose a number to scale by (e.g. ×2, ×3, ÷5).
  2. Multiply or divide the numerator and denominator by the same number.
  3. Do not change just one part — that would change the value of the fraction.

Worked Examples

Example 1: Find a fraction equivalent to \(\tfrac{2}{5}\) with denominator 20.

  • 5 becomes 20 by ×4 → multiply top by 4 too.
  • \(\tfrac{2}{5}=\tfrac{8}{20}\)

Example 2: Are \(\tfrac{3}{9}\) and \(\tfrac{1}{3}\) equivalent?

  • Divide both 3 and 9 by 3 → \(\tfrac{1}{3}\)
  • Yes, they are equivalent.

Example 3: Simplify \(\tfrac{12}{16}\).

  • Divide top and bottom by 4 → \(\tfrac{3}{4}\).

Common Mistakes

  • Changing only the denominator (e.g. \(\tfrac{1}{6}\rightarrow\tfrac{1}{9}\)). This changes the value.
  • Multiplying the top by one number and the bottom by another (not allowed).
  • Forgetting to simplify when the final answer can be reduced.

Quick Check Tips

  • If you multiply top and bottom by the same number, the fraction will stay equivalent.
  • If two fractions simplify to the same simplest form, they are equivalent.
  • You can also convert both to decimals to compare (e.g. \(\tfrac{1}{6}=0.166...\) and \(\tfrac{3}{18}=0.166...\)).

Practice (no answers shown)

  • Write an equivalent fraction to \(\tfrac{4}{7}\) with denominator 21.
  • Which fractions are equivalent? \(\tfrac{6}{12},\ \tfrac{2}{4},\ \tfrac{1}{3}\)
  • Simplify: \(\tfrac{15}{45}\).