EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Ratio & Proportion · Foundation & Higher

Simplifying ratios

A ratio compares two or more quantities. Simplifying a ratio means dividing all parts by their highest common factor.

Revising simplifying ratios the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Simplifying ratios GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Divide all parts of the ratio by their HCF to simplify.
  • 2Ratios must be in the same units before simplifying.
  • 3A ratio of 2:3 means for every 2 of the first quantity, there are 3 of the second.
  • 4To write a ratio in the form 1:n, divide both parts by the first number.
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Worked examples

Example 1

Simplify the ratio 24:36

Working

  1. HCF of 24 and 36 = 12
  2. 24 ÷ 12 = 2, 36 ÷ 12 = 3
Answer2:3
Example 2

Write 45 cm : 1.2 m as a ratio in its simplest form.

Working

  1. Convert to same units: 45 cm : 120 cm
  2. HCF of 45 and 120 = 15
  3. 45 ÷ 15 = 3, 120 ÷ 15 = 8
Answer3:8
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Common mistakes

✗Not converting to the same units before simplifying.
✗Only dividing one part of the ratio by the HCF.
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Exam tips

✓Always convert to the same unit first — look out for mixed units (cm and m, g and kg).
✓Check by multiplying back up to confirm the simplified ratio is equivalent.

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