Free GCSE Maths lesson: Ratio, Proportion and Rates
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Lesson 18 · GCSE / Key Stage 4 · Maths · Ratio, Proportion and Rates

Ratio and Fractions

Learn how ratio parts connect to fractions of the whole, so you can choose the right denominator and avoid a common GCSE trap.

Qualification: GCSE Key Stage 4 Subject: Maths Strand: Ratio, Proportion and Rates

GCSE specification fit

A key link between ratio, fractions and proportion.

GCSE questions often move between ratio language and fraction language. This lesson focuses on the safest method: add the ratio parts to find the whole, then write each part as a fraction of that whole.

QualificationGCSE Mathematics
Key stageKey Stage 4
StrandRatio, Proportion and Rates
Tier guidanceFoundation and Higher

What you will learn

  • How to connect a part-to-part ratio to fractions of the whole.
  • How to add ratio parts to find the denominator.
  • How to convert ratio statements into fractions.
  • How to convert fractional statements into ratios.
  • How to keep the order of the ratio matched to the words in the question.
  • How to check denominators by adding total parts.

Why this matters

Ratio and fraction language appears in probability, mixtures, recipes, surveys, similar shapes and percentage work.

A ratio such as 2 : 3 does not mean the first amount is automatically 23 of the whole. The whole has 2 + 3 = 5 parts, so the first amount is 25 of the whole.

Prior knowledge

You should already be comfortable with:

  • reading ratio notation such as 4 : 7,
  • knowing that ratio order matters,
  • simplifying equivalent ratios,
  • understanding numerator and denominator,
  • simplifying fractions where possible.

Clear explanation

Part-to-part ratios and fractions of the whole

A ratio compares parts with each other. A fraction of the whole compares one part with the total.

red : blue = 2 : 3 total parts = 2 + 3 = 5 red is 25 of the whole blue is 35 of the whole

The denominator is 5, not 3, because the whole group is made from both colours together.

Converting a ratio into fractions

To convert a ratio into fractions of the whole:

1. Add the ratio parts. 2. Use the total as the denominator. 3. Use each ratio part as the matching numerator. 4. Check the fractions add to 1 whole.
boys : girls = 4 : 5 total parts = 4 + 5 = 9 boys = 49, girls = 59 check: 49 + 59 = 99 = 1

Converting fractions into a ratio

If fractions describe parts of the same whole, their numerators can become ratio parts once the denominators match.

A class is 38 Year 10 and 58 Year 11. The denominator 8 means 8 equal parts in the whole. Year 10 : Year 11 = 3 : 5

If one fraction is given and there are only two categories, subtract from 1 whole to find the other fraction.

If 27 of counters are green, then 57 are not green. green : not green = 2 : 5

Checking denominators by adding total parts

The total number of ratio parts is the denominator for fractions of the whole. This quick check catches many mistakes.

ratio = 3 : 4 : 5 total parts = 3 + 4 + 5 = 12 fractions of the whole are 312, 412 and 512

If a total amount is given, the same parts check still works: with 60 counters in the ratio 3 : 4 : 5, one part is 60 ÷ 12 = 5, so the first group is 3 × 5 = 15 counters.

A simple visual check

This bar shows the ratio red : blue = 2 : 3. There are 5 equal parts in total, so the red fraction is 25 and the blue fraction is 35.

Ratio 2 to 3 shown as fractions of a whole Five equal boxes show that two red parts are two fifths of the whole and three blue parts are three fifths of the whole. 2 parts = 2/5 3 parts = 3/5

Worked examples

Example 1: Ratio to fractions

The ratio of cats to dogs is 3 : 7. What fraction of the animals are cats?

total parts = 3 + 7 = 10 cats are 3 out of 10 parts
Answer: 310 of the animals are cats.

Example 2: Three-part ratio to fractions

A recipe has flour : sugar : butter = 5 : 2 : 3. What fraction of the mixture is butter?

total parts = 5 + 2 + 3 = 10 butter is the third part, so butter = 310
Answer: 310 of the mixture is butter.

Example 3: Fraction to ratio

49 of a group are adults. The rest are children. Write the ratio adults : children.

children = 99 − 49 = 59 adults : children = 4 : 5
Answer: 4 : 5.

Example 4: Convert and simplify

In a survey, 615 chose tea and 915 chose juice. Write the ratio tea : juice in simplest form.

tea : juice = 6 : 9 6 : 9 = 2 : 3
Answer: 2 : 3.

Quick checks

Choose an answer, then check your thinking.

1. The ratio red : blue is 2 : 5. What fraction of the whole is red?

2. The ratio A : B : C is 1 : 3 : 4. What fraction is B?

3. 311 of counters are yellow. The rest are green. What is yellow : green?

Practice questions

Question 1

The ratio apples : oranges is 4 : 5. What fraction of the fruit are apples?

Reveal answer and marking guidance

Answer: 49.

Marking: 4 + 5 = 9 total parts; apples are 4 of those 9 parts.

Question 2

A bag has red : blue : green counters in the ratio 2 : 3 : 7. What fraction of the counters are green?

Reveal answer and marking guidance

Answer: 712.

Marking: Total parts = 2 + 3 + 7 = 12; green is the third part, so green is 7 out of 12 parts.

Question 3

58 of a class travel by bus. The rest walk. Write the ratio bus : walk.

Reveal answer and marking guidance

Answer: 5 : 3.

Marking: The whole is 88. Walking is 38, so bus : walk = 5 : 3.

Question 4

In a team, juniors : seniors = 7 : 11. What fraction of the team are seniors?

Reveal answer and marking guidance

Answer: 1118.

Marking: Total parts = 7 + 11 = 18; seniors are 11 of those 18 parts.

Question 5

A drink is concentrate : water = 1 : 6. What fraction of the drink is water?

Reveal answer and marking guidance

Answer: 67.

Marking: Total parts = 1 + 6 = 7; water is 6 out of 7 parts.

Question 6

1220 of a group chose option A and 820 chose option B. Write the ratio A : B in simplest form.

Reveal answer and marking guidance

Answer: 3 : 2.

Marking: A : B = 12 : 8, then divide both parts by 4 to simplify to 3 : 2.

Question 7

The ratio blue : red : yellow beads is 5 : 6 : 9. What fraction of the beads are not red?

Reveal answer and marking guidance

Answer: 710.

Marking: Total parts = 5 + 6 + 9 = 20. Not red is 5 + 9 = 14 parts, so the fraction is 1420 = 710.

Question 8

311 of a packet are strawberry sweets. The rest are lemon sweets. There are 40 lemon sweets. How many strawberry sweets are there?

Reveal answer and marking guidance

Answer: 15 strawberry sweets.

Marking: Lemon sweets are 811 of the packet, so strawberry : lemon = 3 : 8. If 8 parts = 40, then 1 part = 5 and 3 parts = 15.

Question 9

In a club, 25 of the members are juniors and 14 are seniors. The rest are adults. Write the ratio juniors : seniors : adults in its simplest form.

Reveal answer and marking guidance

Answer: 8 : 5 : 7.

Marking: Use twentieths: juniors are 820 and seniors are 520. Adults are 720, so the ratio is 8 : 5 : 7.

Question 10

In a library, fiction : non-fiction = 7 : 5. 38 of the non-fiction books are science books. There are 90 science books. How many books are in the library altogether?

Reveal answer and marking guidance

Answer: 576 books.

Marking: If 38 of the non-fiction books is 90, then all non-fiction books = 90 ÷ 3 × 8 = 240. In the ratio fiction : non-fiction = 7 : 5, 5 parts = 240, so 1 part = 48 and 12 parts = 576.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For ratio and fraction links, marks usually come from treating the total number of ratio parts as the denominator, matching each named part to the correct numerator, and converting fractions to a shared whole before writing a ratio.

Common mistakes

  • Using the other part as the denominator: in 2 : 5, the first part is 27 of the whole, not 25.
  • Forgetting to add all parts: in 1 : 3 : 4, the denominator is 8, not 4.
  • Reversing the ratio: if the question asks for adults : children, keep adults first.
  • Missing the rest of the whole: if 310 are red, the rest are 710.
  • Not simplifying a final ratio: 12 : 8 is correct working, but the simplest ratio is 3 : 2.

Extension challenge

In a club, the ratio of Year 10 pupils to Year 11 pupils is 3 : 5. Then 6 Year 10 pupils join, and the new ratio becomes 2 : 3. How many pupils were in the club at the start?

Reveal answer

Answer: 144 pupils.

Original numbers can be written as 3x and 5x. After 6 Year 10 pupils join, the ratio is (3x + 6) : 5x = 2 : 3. So 3 × (3x + 6) = 2 × 5x, giving 9x + 18 = 10x and x = 18. Original total = 3x + 5x = 8x = 144.

Correction check: 54 Year 10 and 90 Year 11 gives 144 at the start. After 6 join, 60 : 90 simplifies to 2 : 3.

Exam-board guidance

Moving between ratios and fractions is common across GCSE Maths. The reliable method is always to identify the whole before choosing a denominator.

AQA GCSE Maths

Add the ratio parts first so the denominator is the whole, then check whether the question wants a fraction of the whole, a fraction of another part, or the remaining part.

OCR GCSE Maths

Label part-to-part ratios and part-to-whole fractions separately before simplifying, especially when one category is described as "the rest".

Pearson Edexcel GCSE Maths

Show total parts clearly, then simplify fractions only after each numerator has been matched to the correct ratio part, category order and whole.

Eduqas GCSE Maths

Expect ratio and fraction links in practical contexts. Rewriting the same information as both a ratio and fractions can make the wording clearer.

WJEC Wales

Use total parts to connect ratios with fractions, then state what the fraction represents in the real quantity or numeracy context.

CCEA GCSE Maths

A clear total-parts line shows why the denominator is the whole, which helps protect method marks when the final ratio also needs simplifying or a remaining part must be found.

Next lesson

Next, use proportional reasoning to compare deals and solve worded problems in Proportion Problems and Best Buys.

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