GCSE Maths Practice: sharing-in-a-ratio

Question 8 of 10

This question focuses on finding the smaller share when an amount is divided in a given ratio.

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\( \begin{array}{l}\text{£70 is shared between two people in the ratio } 2:5. \\ \text{How much does the person with the smaller share receive?}\end{array} \)

Choose one option:

Always check that the smaller and larger shares add up to the original total.

Finding the Smaller Share in a Ratio

Sharing an amount in a given ratio is a key GCSE Maths skill, and some questions specifically ask you to identify the smaller or larger share. These questions test whether you understand how ratios describe relative sizes rather than fixed values.

What Does a Ratio Show?

A ratio compares quantities by showing how many equal parts each share receives. In a ratio such as 2:5, one person receives 2 equal parts while the other receives 5 equal parts. The total amount must first be divided into these equal parts before individual shares can be found.

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 represents the smaller share.
  4. Multiply the value of one part by that number.

Worked Example 1

£84 is shared between two people in the ratio 3:4. How much does the smaller share receive?

  • Total parts = 3 + 4 = 7
  • One part = £84 ÷ 7 = £12
  • Smaller share = 3 × £12 = £36

Worked Example 2

56 points are shared between two teams in the ratio 1:7. How many points does the smaller team receive?

  • Total parts = 1 + 7 = 8
  • One part = 56 ÷ 8 = 7
  • Smaller share = 1 × 7 = 7 points

Common Mistakes to Avoid

  • Choosing the wrong part: Always identify which number in the ratio represents the smaller share.
  • Dividing by one ratio number: You must divide by the total number of parts.
  • Skipping the check: Adding both shares together should give the original total.

Real-Life Applications

Finding smaller or larger shares is common in real life. Examples include splitting money unequally, sharing time between tasks, dividing rewards in competitions, or allocating resources based on responsibility or effort.

Frequently Asked Questions

Q: Does the smaller share always come first?
Not always. The order of the ratio tells you which share is which, so read the question carefully.

Q: Can ratios be simplified first?
Yes. Simplifying a ratio does not change which share is larger or smaller.

Study Tip

Circle the smaller number in the ratio before you start calculating. This helps you stay focused on the correct share.

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