GCSE Maths Practice: fractions

Question 1 of 12

This question checks your understanding of how to multiply two fractions. Multiply the numerators and denominators separately, then simplify the final result.

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\( \begin{array}{l}\text{Calculate }\frac{1}{3}\times\frac{2}{3}.\end{array} \)

Choose one option:

Multiply the numerators and denominators separately. Cancel common factors early if you can, and always simplify at the end.

Multiplying fractions means finding a fraction of another fraction. In other words, you are taking a part of a part. This skill is essential in many real-life situations — for example, when calculating discounts, scaling recipes, or working with probabilities.

How to Multiply Fractions

  1. Multiply the numerators (top numbers) together to get the new numerator.
  2. Multiply the denominators (bottom numbers) together to get the new denominator.
  3. Simplify the final fraction if possible by dividing top and bottom by their highest common factor (HCF).

Example: \(\tfrac{1}{3}\times\tfrac{2}{3}=\tfrac{2}{9}\). The 2 shows how many parts you have, and the 9 shows how many equal parts the whole is divided into.

Visual Understanding

Imagine a chocolate bar divided into 3 equal columns. You eat one-third of it (\(\tfrac{1}{3}\)). Now, you take two-thirds of that piece (\(\tfrac{2}{3}\) of \(\tfrac{1}{3}\)). Only 2 out of the 9 total small squares are eaten, which is \(\tfrac{2}{9}\). Fraction multiplication simply zooms in on part of a part.

Worked Examples

Example 1: \(\tfrac{2}{5}\times\tfrac{3}{4}\)

  1. Numerators: 2 × 3 = 6
  2. Denominators: 5 × 4 = 20
  3. Result: \(\tfrac{6}{20}=\tfrac{3}{10}\)

Example 2: \(\tfrac{3}{8}\times\tfrac{4}{9}\)

  1. Numerators: 3 × 4 = 12
  2. Denominators: 8 × 9 = 72
  3. Result: \(\tfrac{12}{72}=\tfrac{1}{6}\)

Example 3: \(\tfrac{5}{6}\times\tfrac{3}{5}\)

  1. Cancel the 5s first.
  2. Now \(\tfrac{1}{6}\times3=\tfrac{3}{6}=\tfrac{1}{2}\)

Common Mistakes

  • Adding instead of multiplying: Some students mistakenly do \(\tfrac{1}{3}+\tfrac{2}{3}=\tfrac{3}{6}\). Remember: the question says “of”, not “plus”.
  • Multiplying only the denominators: Always multiply both top and bottom.
  • Forgetting to simplify: Check if both numerator and denominator share a common factor.

Real-Life Uses

  • Cooking: If a recipe needs \(\tfrac{2}{3}\) of a cup of milk but you’re halving the recipe, you find \(\tfrac{1}{2}\times\tfrac{2}{3}=\tfrac{1}{3}\) of a cup.
  • Shopping: A 1/3-off sale followed by another 2/3 reduction of that portion effectively leaves \(\tfrac{2}{9}\) of the original price reduced.
  • Probability: The chance of two independent events both happening is found by multiplying their probabilities, often fractions like \(\tfrac{1}{3}\times\tfrac{1}{2}\).

Study Tip

When multiplying several fractions, line up all numerators in one row and all denominators below. Simplify before multiplying to keep numbers smaller. The more you practise, the faster you’ll recognise opportunities to cancel factors early.

Try These Yourself

  • \(\tfrac{3}{4}\times\tfrac{2}{5}\)
  • \(\tfrac{4}{7}\times\tfrac{3}{8}\)
  • \(\tfrac{1}{2}\times\tfrac{2}{9}\)