GCSE Maths Practice: sharing-in-a-ratio

Question 4 of 10

This question tests your ability to find one person’s share when an amount is divided between three people using a ratio.

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\( \begin{array}{l}\text{£90 is shared between Ella, Tom and Zoe in the ratio } 2:1:2. \\ \text{How much does Tom receive?}\end{array} \)

Choose one option:

Add all three shares together to check that they equal the original total.

Finding One Person’s Share in a Three-Part Ratio

Some GCSE Maths ratio questions involve more than two people and ask you to find the share for just one person. These problems test whether you can correctly add all parts of the ratio, divide the total accurately, and match the correct part of the ratio to the named person.

Understanding Three-Part Ratios

A ratio such as 2:1:2 shows how a total is divided between three people. Each number represents how many equal parts that person receives. The actual value of each part depends on the total amount being shared.

Clear Step-by-Step Method

  1. Add all 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.
  4. Multiply the value of one part by that number.

Worked Example 1

£75 is shared between Anna, Ben and Cara in the ratio 3:1:1. How much does Ben receive?

  • Total parts = 3 + 1 + 1 = 5
  • One part = £75 ÷ 5 = £15
  • Ben receives 1 × £15 = £15

Worked Example 2

60 points are shared between three teams in the ratio 1:2:3. How many points does the second team receive?

  • Total parts = 1 + 2 + 3 = 6
  • One part = 60 ÷ 6 = 10
  • Second team receives 2 × 10 = 20 points

Common Mistakes to Avoid

  • Forgetting one part: In three-part ratios, missing a number leads to the wrong total.
  • Mixing up people: Always match the correct ratio number to the correct name.
  • Not checking totals: All three shares should add back up to the original amount.

Real-Life Applications

Three-part ratios are common when sharing money between siblings, dividing time across activities, allocating rewards in competitions, or splitting resources in group projects. Understanding these ratios helps ensure fairness and accuracy.

Frequently Asked Questions

Q: Does the middle number always mean the middle person?
Yes, the order of the names must match the order of the ratio.

Q: Can the ratio be simplified first?
Yes. Simplifying ratios makes calculations easier and does not change the final shares.

Study Tip

Underline the name you are finding the share for before starting. This helps you stay focused on the correct part of the ratio.

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