GCSE Maths Practice: sharing-in-a-ratio

Question 3 of 10

This question checks your understanding of how to share a total amount using a given ratio.

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\( \begin{array}{l}\text{Which of these correctly share £120 in the ratio } 2:4?\end{array} \)

Select all correct options:

Always add your final shares together to confirm they match the original total.

Sharing an Amount Using Ratios (GCSE Foundation)

Sharing amounts in a given ratio is a core GCSE Maths skill that helps students understand fairness, proportional thinking, and real-world problem solving. These questions often involve money, quantities, or objects and require careful interpretation of the ratio before carrying out calculations.

What Does a Ratio Tell Us?

A ratio compares quantities by showing how many equal parts each share receives. For example, a ratio of 2:4 does not mean £2 and £4. Instead, it means one share gets 2 equal parts and the other gets 4 equal parts. The actual value of each part depends entirely on the total amount being shared.

Reliable 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 number in the ratio to find each share.

Worked Example 1

Share £90 in the ratio 1:2.

  • Total parts = 1 + 2 = 3
  • One part = £90 ÷ 3 = £30
  • Shares = £30 and £60

Worked Example 2

Share 36 apples in the ratio 3:3.

  • Total parts = 3 + 3 = 6
  • One part = 36 ÷ 6 = 6
  • Shares = 18 apples and 18 apples

Common Mistakes to Watch Out For

  • Dividing by one ratio number: Always divide by the total number of parts, not just one value.
  • Assuming ratios are values: Ratios describe relationships, not actual amounts.
  • Forgetting to check: The final shares must always add back up to the original total.

Real-Life Uses of Ratio Sharing

Ratio sharing is used in many everyday situations, such as splitting money between friends, dividing ingredients in recipes, allocating time between tasks, or sharing rewards in games. Understanding ratios ensures fair and accurate distribution in all these contexts.

Frequently Asked Questions

Q: Can ratios be simplified before sharing?
Yes. A ratio like 2:4 can be simplified to 1:2, which often makes calculations easier.

Q: What if the total doesn’t divide evenly?
At GCSE Foundation level, totals usually divide exactly, but decimals or fractions may appear at higher levels.

Study Tip

Write the total number of parts clearly before calculating. This small step prevents most ratio-sharing errors.

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