GCSE Maths Practice: sharing-in-a-ratio

Question 7 of 10

This question tests your ability to find one person’s share when an amount is divided in a given ratio.

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\( \begin{array}{l}\text{£72 is shared between Eva and Mia in the ratio } 1:2. \\ \text{How much does Mia receive?}\end{array} \)

Choose one option:

After calculating the share, check that both parts together equal the original total.

Finding One Person’s Share in a Ratio

Sharing an amount in a given ratio is a core GCSE Maths skill. In many questions, you are asked to find how much one specific person receives rather than all shares. This requires careful reading of the ratio and accurate use of division and multiplication.

Understanding a 1:2 Ratio

A ratio of 1:2 means the total is split into three equal parts. One person receives 1 part, while the other receives 2 parts. The ratio does not give the values directly; instead, it shows the relative sizes of the shares.

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. Identify how many parts the named person receives.
  4. Multiply the value of one part by that number.

Worked Example 1

£45 is shared between two people in the ratio 1:4. How much does the second person receive?

  • Total parts = 1 + 4 = 5
  • One part = £45 ÷ 5 = £9
  • Second person receives 4 × £9 = £36

Worked Example 2

60 points are shared between two teams in the ratio 2:3. How many points does the second team receive?

  • Total parts = 2 + 3 = 5
  • One part = 60 ÷ 5 = 12
  • Second team receives 3 × 12 = 36 points

Common Mistakes to Avoid

  • Forgetting to add the ratio numbers: Always find the total number of parts first.
  • Mixing up the people: Make sure you match the correct ratio number to the correct person.
  • Not checking your answer: Adding both shares together should give the original total.

Why This Skill Is Important

Sharing amounts in ratios is used in everyday situations such as dividing money, sharing prizes, allocating time, or splitting tasks. Being confident with ratios helps ensure fairness and accuracy in real-life decisions.

Frequently Asked Questions

Q: Does the order of names matter?
Yes. The first name corresponds to the first number in the ratio.

Q: Can ratios be simplified first?
Yes. Simplifying ratios makes calculations easier without changing the final result.

Study Tip

Underline the name of the person you are finding the share for before starting calculations. This helps prevent mixing up the parts.

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