GCSE Maths Practice: sharing-in-a-ratio

Question 9 of 10

This question checks your ability to share a total amount correctly using a given ratio.

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\( \begin{array}{l}\text{£60 is shared between Alice and Ben in the ratio } 2:3. \\ \text{How much does Alice receive?}\end{array} \)

Choose one option:

After finding each share, add them together to confirm they match the original total.

Sharing an Amount Between Two People Using Ratios

Sharing a total amount using a ratio is a fundamental GCSE Maths skill. These questions test whether you understand that a ratio describes how a total is divided into equal parts, rather than giving the actual values directly. Being confident with this process is essential for exam success and real-life problem solving.

What Does a Ratio Represent?

A ratio such as 2:3 compares two shares. It means that for every 2 equal parts given to the first person, 3 equal parts are given to the second. The size of each part depends on the total amount being shared.

Step-by-Step Method

  1. Add the numbers in the ratio to find the total number of parts.
  2. Divide the total amount by this number to find the value of one part.
  3. Multiply the value of one part by each person’s number in the ratio.

Worked Example 1

£50 is shared between Tom and Jack in the ratio 1:4. How much does Tom receive?

  • Total parts = 1 + 4 = 5
  • One part = £50 ÷ 5 = £10
  • Tom receives 1 × £10 = £10

Worked Example 2

45 tickets are shared between two teams in the ratio 3:6. How many tickets does the first team receive?

  • Total parts = 3 + 6 = 9
  • One part = 45 ÷ 9 = 5
  • First team receives 3 × 5 = 15 tickets

Common Mistakes to Avoid

  • Dividing by the wrong number: Always divide by the total number of parts, not just one number from the ratio.
  • Assuming ratios are amounts: The ratio shows proportions, not money values.
  • Not checking the total: Adding the final shares should always give the original amount.

Why Ratio Sharing Matters in Real Life

Ratio sharing is used when splitting money, sharing food, dividing time, or allocating points in games. Understanding ratios ensures fairness and accuracy in everyday decisions.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying ratios like 2:4 to 1:2 makes calculations easier and does not change the final shares.

Q: Does the order of the ratio matter?
Yes. The first number always corresponds to the first person mentioned.

Study Tip

Always write down the total number of parts before dividing. This small step prevents most ratio mistakes.

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