Free GCSE Maths lesson: Ratio, Proportion and Rates

Free LessonsGCSE / Key Stage 4Maths → Ratio: Sharing Into Parts

Lesson 17 · GCSE / Key Stage 4 · Maths · Ratio, Proportion and Rates

Ratio: Sharing Into Parts

Learn a calm, reliable method for dividing a total into unequal shares using total parts, one part and a final check.

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

GCSE specification fit

A core ratio skill for money, groups, recipes and measures.

GCSE ratio questions often ask you to divide a total into unequal parts. This lesson focuses on the parts method: add the ratio parts, find one part, then scale each share.

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

What you will learn

  • How to add ratio parts to find the total number of equal parts.
  • How to find the value of one part.
  • How to share a total into two parts.
  • How to share a total into three parts.
  • How to interpret which unequal share belongs to which person or category.
  • How to check that your shares add back to the total.

Why this matters

Sharing into a ratio is useful when prize money is split, ingredients are mixed, groups are divided or distances are compared.

In exams, the method is often worth marks even when the numbers are simple. Clear working helps you avoid mixing up the bigger and smaller shares.

Prior knowledge

You should already be comfortable with:

  • reading ratio notation such as 3 : 5,
  • knowing that the order of a ratio matters,
  • multiplying and dividing whole numbers,
  • adding several parts accurately,
  • checking whether an answer is sensible in context.

Clear explanation

The parts method

A ratio tells you how many equal parts belong to each share. To share a total in a ratio:

1. Add the ratio parts. 2. Divide the total by the number of parts. 3. Multiply one part by each ratio number. 4. Check the shares add back to the total.

Sharing into two parts

Share £40 in the ratio 3 : 5. The total number of parts is:

3 + 5 = 8 parts

Each part is worth:

£40 ÷ 8 = £5

Now multiply by each ratio part:

first share = 3 × £5 = £15 second share = 5 × £5 = £25 check: £15 + £25 = £40

Sharing into three parts

The same method works for three-part ratios. Share 60 sweets in the ratio 2 : 3 : 5.

total parts = 2 + 3 + 5 = 10 one part = 60 ÷ 10 = 6 sweets shares = 2 × 6, 3 × 6, 5 × 6 shares = 12, 18, 30 check: 12 + 18 + 30 = 60

Interpreting unequal shares

If the question says Ali : Bea = 2 : 7, Bea gets the larger share because 7 parts is more than 2 parts.

Keep the names in the same order as the ratio. Do not swap the answers at the end.

A simple visual check

This bar shows £40 shared in the ratio 3 : 5. There are 8 equal boxes, so each box is £5.

Ratio share bar for £40 in the ratio 3 to 5 Eight equal boxes are split into three blue boxes worth £15 and five green boxes worth £25, showing that each part is £5. 3 parts = £15 5 parts = £25

Worked examples

Example 1: Share £36 in the ratio 1 : 5.

Add the parts, then find one part.

1 + 5 = 6 parts £36 ÷ 6 = £6 per part shares: 1 × £6 = £6 and 5 × £6 = £30
Answer: £6 and £30.

Example 2: Nina and Omar share 72 points in the ratio 4 : 5.

The order is Nina : Omar, so Nina gets 4 parts and Omar gets 5 parts.

4 + 5 = 9 parts 72 ÷ 9 = 8 points per part Nina = 4 × 8 = 32, Omar = 5 × 8 = 40
Answer: Nina gets 32 points and Omar gets 40 points.

Example 3: Share 84 kg in the ratio 2 : 3 : 7.

This is a three-part ratio, so add all three parts.

2 + 3 + 7 = 12 parts 84 ÷ 12 = 7 kg per part 2 × 7 = 14 kg, 3 × 7 = 21 kg, 7 × 7 = 49 kg check: 14 + 21 + 49 = 84
Answer: 14 kg, 21 kg and 49 kg.

Example 4: Find the larger share.

Jamie and Kai share £96 in the ratio Jamie : Kai = 5 : 7. How much more does Kai get?

5 + 7 = 12 parts £96 ÷ 12 = £8 per part Jamie = 5 × £8 = £40, Kai = 7 × £8 = £56 £56 - £40 = £16
Answer: Kai gets £16 more than Jamie.

Quick checks

Choose an answer, then check your thinking.

1. Share £30 in the ratio 2 : 3. What is one part worth?

2. A total of 45 is shared in the ratio 1 : 4. What is the larger share?

3. Share 48 in the ratio 2 : 4 : 6. Which set of shares is correct?

Practice questions

Question 1

Share £24 in the ratio 1 : 3.

Reveal answer and marking guidance

Answer: £6 and £18.

Marking: 1 + 3 = 4 parts; £24 ÷ 4 = £6; shares are 1 × £6 and 3 × £6.

Question 2

Share 56 counters in the ratio 3 : 5.

Reveal answer and marking guidance

Answer: 21 counters and 35 counters.

Marking: 3 + 5 = 8 parts; 56 ÷ 8 = 7; shares are 3 × 7 = 21 and 5 × 7 = 35.

Question 3

Aisha and Ben share £63 in the ratio Aisha : Ben = 2 : 7. How much does Ben get?

Reveal answer and marking guidance

Answer: Ben gets £49.

Marking: 2 + 7 = 9 parts; £63 ÷ 9 = £7; Ben has 7 parts, so 7 × £7 = £49.

Question 4

Share 90 minutes in the ratio 2 : 3 : 4.

Reveal answer and marking guidance

Answer: 20 minutes, 30 minutes and 40 minutes.

Marking: 2 + 3 + 4 = 9 parts; 90 ÷ 9 = 10; multiply 10 by each ratio part.

Question 5

Three people share £120 in the ratio 1 : 2 : 5. How much more does the largest share get than the smallest share?

Reveal answer and marking guidance

Answer: £60 more.

Marking: 1 + 2 + 5 = 8 parts; £120 ÷ 8 = £15; largest share = 5 × £15 = £75; smallest share = £15; difference = £60.

Question 6

A recipe uses flour : sugar : butter = 5 : 2 : 3. The total mass is 800 g. Find the mass of each ingredient.

Reveal answer and marking guidance

Answer: 400 g flour, 160 g sugar and 240 g butter.

Marking: Total parts = 5 + 2 + 3 = 10; one part = 800 g ÷ 10 = 80 g; multiply each part by 80 g.

Question 7

The ratio of adults to children on a coach is 2 : 5. There are 21 more children than adults. How many people are on the coach?

Reveal answer and marking guidance

Answer: 49 people.

Marking: The difference is 5 − 2 = 3 parts. 3 parts = 21, so 1 part = 7. Adults = 14 and children = 35, giving 49 people in total.

Question 8

Three clubs share £360 in the ratio drama : sport : music = 4 : 7 : 9. Sport and music spend £30 together. How much money is left between them?

Reveal answer and marking guidance

Answer: £258 is left between sport and music.

Marking: Total parts = 4 + 7 + 9 = 20, so 1 part = £360 ÷ 20 = £18. Sport and music originally get (7 + 9) × £18 = £288. After spending £30, £288 − £30 = £258 remains.

Question 9

Ali, Bea and Cai share some money in the ratio Ali : Bea : Cai = 2 : 3 : 7. Cai gets £45 more than Ali. How much money is shared altogether?

Reveal answer and marking guidance

Answer: £108.

Marking: Cai has 7 − 2 = 5 more parts than Ali. If 5 parts = £45, then 1 part = £9. The total is 2 + 3 + 7 = 12 parts, so 12 × £9 = £108.

Question 10

Paint is mixed in the ratio red : blue : yellow = 3 : 4 : 5. There are 18 litres more yellow paint than blue paint. How many litres of paint are mixed altogether?

Reveal answer and marking guidance

Answer: 216 litres.

Marking: Yellow is 5 − 4 = 1 part more than blue, so 1 part = 18 litres. Total parts = 3 + 4 + 5 = 12, so total paint = 12 × 18 = 216 litres.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For sharing into a ratio, marks usually come from adding the total parts, finding the value of one part, multiplying each share correctly, and checking that the shares add back to the original total with the right units. When the question gives a difference between two shares, link that difference to the matching difference in ratio parts before finding one part.

Common mistakes

  • Dividing by one ratio number: for 2 : 3, divide the total by 5 parts, not by 2 or 3.
  • Forgetting a part in a three-part ratio: for 2 : 3 : 5, the total is 10 parts.
  • Swapping the shares: keep names or categories in the same order as the ratio.
  • Stopping before the check: the final shares should add back to the original total.
  • Losing units: use £, g, kg, minutes or counters when the question gives units.

Extension challenge

A charity event raises £210. The money is shared between three causes in the ratio 4 : 5 : 6. The largest cause then donates £8 to the smallest cause. What is the new ratio of the three amounts?

Reveal answer

Answer: 32 : 35 : 38.

Total parts = 4 + 5 + 6 = 15. One part = £210 ÷ 15 = £14, so the original shares are £56, £70 and £84. After £8 moves from the largest to the smallest, the shares are £64, £70 and £76. The ratio 64 : 70 : 76 simplifies by dividing by 2 to give 32 : 35 : 38.

Exam-board guidance

Sharing a quantity in a given ratio is common across GCSE Maths specifications. It may be tested directly or inside worded problems involving money, measurements, recipes, groups and proportional reasoning.

AQA GCSE Maths

Show total parts, one part and each final share clearly. If a question gives a difference or one known share, match that value to the correct ratio parts before scaling up.

OCR GCSE Maths

Keep the ratio order matched to the wording, especially in three-part shares or questions asking for one named person's amount, the difference between shares, or a combined amount.

Pearson Edexcel GCSE Maths

Expect ratio sharing inside longer contexts. Identify whether you have the total, one share, a combined share, a remainder or a difference before deciding the first division.

Eduqas GCSE Maths

Write units on money or measures answers, and check each final share uses the same multiplier from the original ratio.

WJEC Wales

Sharing in a ratio may appear in practical numeracy settings, so finish with a unit-aware answer and a quick check that the shares total the original amount.

CCEA GCSE Maths

Write total parts, value of one part and final shares so method marks are visible in both calculator and non-calculator unit-style questions.

Next lesson

Next, connect ratio parts to fractions of a whole.