GCSE Maths Practice: sharing-in-a-ratio

Question 6 of 10

This question tests your ability to identify and calculate the correct share when the ratio is not written in size order.

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\( \begin{array}{l}\text{£80 is shared between Liam and Noah in the ratio } 5:3. \\ \text{How much does Noah receive?}\end{array} \)

Choose one option:

Check that both shares together add up to the original total.

Finding One Person’s Share When the Larger Ratio Comes First

In GCSE Maths, ratio questions do not always give the smaller share first. This type of question checks whether you can read the ratio carefully and match the correct number of parts to the correct person. Many mistakes happen when students assume the first person listed always receives the smaller share.

Understanding the Order of a Ratio

A ratio such as 5:3 means the first person receives 5 equal parts and the second person receives 3 equal parts. The order of names in the question matters, so it is important to match each name to the correct number in the ratio.

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 which number in the ratio belongs to the person named in the question.
  4. Multiply the value of one part by that number.

Worked Example 1

£72 is shared between Aisha and Ben in the ratio 4:2. How much does Ben receive?

  • Total parts = 4 + 2 = 6
  • One part = £72 ÷ 6 = £12
  • Ben receives 2 × £12 = £24

Worked Example 2

90 points are shared between two teams in the ratio 7:2. How many points does the second team receive?

  • Total parts = 7 + 2 = 9
  • One part = 90 ÷ 9 = 10
  • Second team receives 2 × 10 = 20 points

Common Mistakes to Avoid

  • Assuming the first person gets the smaller share: Always check the ratio numbers.
  • Dividing by the wrong value: You must divide by the total number of parts.
  • Not matching names correctly: The order of names must match the order of the ratio.

Real-Life Applications

This type of ratio problem appears when sharing money, dividing time between activities, allocating resources in a project, or sharing rewards based on contribution. Being able to interpret the order correctly ensures fair and accurate outcomes.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying a ratio like 10:6 to 5:3 can make calculations easier.

Q: How do I know which share to calculate?
Underline the name in the question and match it to the correct ratio number.

Study Tip

Write the ratio underneath the names before you start calculating. This helps prevent mixing up the shares.

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