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GCSE Maths / Edexcel

Ratio as fractions

Connect ratio parts to fractions of a total, and convert between fraction statements and ratio notation.

Ratio, Proportion and RatesFoundation and HigherGrades 4 to 6Focused skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Ratio as fractions

Pearson Edexcel GCSE Maths ratio R4 and R6: connect ratios, fractions and proportional comparisons.

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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 parts. A fraction usually compares one part with the total.

For a ratio a:b, the total number of parts is a + b.

The first part is a / (a + b) of the total. The second part is b / (a + b) of the total.

To change a fraction into a ratio, make sure you know what the other part is. If 3/8 are red, then 5/8 are not red, so red:not red is 3:5.

Many Edexcel mistakes happen when students write 3:8 instead of 3:5 for a fraction of the total.

Key ruleIn a:b, the first part is a / (a + b) of the total.

Worked examples

Ratio to fraction

Red:blue = 3:7. What fraction of the counters are red?

  1. Total parts = 3 + 7 = 10.
  2. Red is 3 parts out of 10.

Answer: 3 / 10

Fraction to ratio

2/5 of a class are boys. Write the ratio boys:girls.

  1. Boys are 2 parts out of 5.
  2. Girls are the remaining 3 parts out of 5.

Answer: 2:3

Find an amount from a fraction link

Orange:apple = 5:3. There are 64 fruits. How many are apples?

  1. Total parts = 8.
  2. Apples are 3/8 of the total.
  3. 3/8 of 64 = 24.

Answer: 24 apples

Common mistakes

  • Using one ratio part as the denominator instead of the total parts.
  • Changing 3/8 into 3:8 when the ratio should be part:remaining part.
  • Forgetting to simplify the final fraction or ratio.
  • Not checking whether the fraction is of the total or of another part.

Quick exercise

Try these before moving to the exam-style questions.

  1. Red:blue = 2:3. What fraction are red?
  2. A:B = 5:7. What fraction is B?
  3. 3/10 of a box are green. Write green:not green.
  4. Boys:girls = 4:5. What fraction are girls?
  5. 1/4 of counters are yellow. Write yellow:not yellow.
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

The ratio of red counters to blue counters is 3:5. What fraction of the counters are red?

ratio to fractionparts and totalfoundation ratio
Standard exam styleFoundation and HigherNon-calculator3 marks

5/12 of a group are adults. Write the ratio adults:children.

fraction to ratioremaining partratio order
ChallengeFoundation and HigherEither4 marks

The ratio of fiction books to non-fiction books is 7:5. There are 144 books altogether. Work out how many books are fiction.

ratio fractionsfraction of amountcontext