GCSE Maths / Edexcel

Writing and simplifying ratios

Write ratios in the correct order, use matching units, and simplify ratios by dividing every part by the same factor.

Ratio, Proportion and RatesFoundation and HigherGrades 3 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Writing and simplifying ratios

Pearson Edexcel GCSE Maths ratio R1 and R3: use ratio notation and express ratios in their simplest form.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A ratio compares amounts. The order matters: red:blue is not the same as blue:red unless the amounts are equal.

Ratios must compare the same type of quantity. If the question gives centimetres and metres, convert to the same unit before simplifying.

To simplify a ratio, divide every part by the highest common factor. Each part must be divided by the same number.

A simplified ratio can still have more than two parts, such as 2:3:5. The same rule applies to every part.

For Edexcel marks, show the unit conversion and the common factor when the numbers are not already easy.

Key ruleSimplify a ratio by dividing every part by the same highest common factor.

Worked examples

Simplify two parts

Simplify 12:18.

  1. The highest common factor of 12 and 18 is 6.
  2. 12 / 6 = 2 and 18 / 6 = 3.

Answer: 2:3

Convert units first

Simplify 40 cm:1 m.

  1. Convert 1 m to 100 cm.
  2. The ratio is 40:100.
  3. Divide both parts by 20.

Answer: 2:5

Three-part ratio

Simplify 15:25:35.

  1. The highest common factor of 15, 25 and 35 is 5.
  2. Divide every part by 5.

Answer: 3:5:7

Common mistakes

  • Changing the order of the ratio.
  • Forgetting to convert units before simplifying.
  • Dividing only one part of the ratio.
  • Using a common factor but not the highest common factor when the question asks for simplest form.

Quick exercise

Try these before moving to the exam-style questions.

  1. Simplify 8:12.
  2. Simplify 21:35.
  3. Simplify 18:24:30.
  4. Simplify 75 cm:1.5 m.
  5. Write 4 red counters and 10 blue counters as red:blue in simplest form.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Simplify the ratio 16:24.

ratio notationsimplifying ratiosfoundation ratio
Standard exam styleFoundation and HigherNon-calculator3 marks

Simplify 45 cm:1.2 m.

ratio unitsmetric conversionmethod marks
ChallengeFoundation and HigherEither4 marks

A necklace has silver, black and white beads in the ratio 18:30:42. Write the ratio in its simplest form.

three-part ratiohighest common factorratio order