Sharing in a Ratio –

Sharing in a ratio is one of the most frequently tested skills in GCSE Maths. Whether you are splitting money between friends, dividing ingredients for a recipe, or working out how much paint to mix, the method is always the same. This guide covers every variation you will meet in the exam — sharing with a total given, sharing with a difference given, and finding a single share.

What Is Sharing in a Ratio?

When you share an amount in a ratio, you divide it into unequal parts according to the ratio provided. The ratio tells you how many parts each person or quantity receives relative to the others.

For example, sharing £200 in the ratio 3 : 2 means splitting the money into 5 equal parts, then giving 3 parts to one person and 2 parts to another. The key insight is that the ratio describes the relative size of each share, not the actual amounts.

There are three main types of sharing problems you will encounter at GCSE. The most common gives you the total amount and asks you to find each share. The second type gives you the difference between two shares and asks you to find the total or individual amounts. The third type gives you the value of one share and asks you to find the others.

Key Formulas

Step-by-Step Method

1. Add the parts of the ratio together to find the total number of parts.
2. Divide the given amount by the total parts to find the value of one part.
3. Multiply each number in the ratio by the value of one part to find each share.
4. Check your answers add up to the original total.

Worked Example 1 — Foundation Level

Question: Share £360 between Amy and Ben in the ratio 4 : 5.

Working: Total parts = 4 + 5 = 9. Value of one part = £360 ÷ 9 = £40. Amy receives 4 × £40 = £160. Ben receives 5 × £40 = £200. Check: £160 + £200 = £360 ✓

Answer: Amy gets £160 and Ben gets £200.

Worked Example 2 — Higher Level

Question: Three friends share some prize money in the ratio 2 : 3 : 7. The largest share is £84 more than the smallest share. Find the total prize money.

Working: The difference between the largest and smallest parts is 7 − 2 = 5 parts. 5 parts = £84, so 1 part = £84 ÷ 5 = £16.80. Total parts = 2 + 3 + 7 = 12. Total prize money = 12 × £16.80 = £201.60. Check: Shares are £33.60, £50.40, £117.60. Largest − Smallest = £117.60 − £33.60 = £84 ✓

Answer: The total prize money is £201.60.

Worked Example 3 — Exam Style

Question: Tom and Lisa share sweets in the ratio 5 : 3. Tom receives 30 sweets. How many sweets does Lisa receive?

Working: Tom's 5 parts = 30 sweets, so 1 part = 30 ÷ 5 = 6 sweets. Lisa gets 3 parts = 3 × 6 = 18 sweets.

Answer: Lisa receives 18 sweets.

Common Mistakes

• Dividing by a ratio part instead of the total. If the ratio is 3 : 5 and you are given the total, divide by 8 (the sum), not by 3 or by 5.
• Mixing up the order. "Alice to Bob in the ratio 2 : 7" means Alice gets 2 parts. Read the names and the numbers in the same order.
• Forgetting to check. Always verify your shares add up to the total. This catches arithmetic slips before they cost you marks.

Exam Tips

• Write "Total parts = ..." as your first line of working. Examiners look for this and award a method mark.
• When given a difference, find the difference in parts first, then calculate one part from there.
• If one share is given directly, divide that share by its number of parts to find the value of one part immediately.
• Questions sometimes express ratios using fractions (e.g., ½ : ⅓). Multiply both sides by the LCM to clear fractions before sharing.

Practice Questions

Q1 (Foundation): Share £540 between two charities in the ratio 2 : 7.

Q2 (Foundation): Divide 72 marbles among three children in the ratio 1 : 3 : 5.

Q3 (Higher): Sam and Jake share money in the ratio 4 : 9. Jake receives £35 more than Sam. How much does each person receive?

Practise sharing in a ratio questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Ratio Basics and Sharing
• Ratio Problem Solving
• Percentages

Summary

• To share in a ratio, add the parts, find the value of one part, then multiply.
• When given the total, divide the total by the sum of parts.
• When given the difference between shares, find the difference in parts first.
• When given one share directly, divide it by its number of parts.
• Ratios involving fractions or decimals should be simplified first by clearing the fractions.
• Always check that your shares add up to the original amount.
• Read the order of names carefully — the first name corresponds to the first number in the ratio.