GCSE Maths Practice: sharing-in-a-ratio

Question 2 of 10

This question focuses on sharing a total amount correctly using a given ratio.

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\( \begin{array}{l}\text{Which of the following show a correct sharing of £60 in the ratio } 1:2?\end{array} \)

Select all correct options:

Add the final shares together to confirm they equal the original total.

Sharing Money Using Ratios (GCSE Foundation)

Sharing amounts in a given ratio is an important GCSE Maths skill that combines understanding ratios with accurate division and multiplication. Questions like this often involve money, quantities, or objects, and test whether you can correctly interpret what a ratio is telling you.

What Does Sharing in a Ratio Mean?

A ratio compares two or more quantities. When you are asked to share something in a ratio such as 1:2, it means the total amount must be divided into parts that follow this relationship. The numbers in the ratio represent how many equal parts each person or group receives, not the actual amounts.

Clear Step-by-Step Method

  1. Add together the numbers in the ratio to find the total number of parts.
  2. Divide the total amount by the number of parts to find the value of one part.
  3. Multiply the value of one part by each number in the ratio.

Worked Example 1

Share £48 in the ratio 1:3.

  • Total parts = 1 + 3 = 4
  • One part = £48 ÷ 4 = £12
  • Shares = £12 and £36

Worked Example 2

Share 20 pens in the ratio 2:3.

  • Total parts = 2 + 3 = 5
  • One part = 20 ÷ 5 = 4
  • Shares = 8 pens and 12 pens

Common Mistakes Students Make

  • Dividing by the wrong number: Always divide by the total number of parts, not just one number from the ratio.
  • Forgetting the order: The first number in the ratio matches the first share.
  • Not checking the total: The final shares should always add back up to the original amount.

Why Ratios Matter in Real Life

Sharing in a ratio is used in many everyday situations, such as splitting money between people, sharing food fairly, dividing work time, or allocating resources in projects. Understanding ratios helps ensure fairness and accuracy, especially when totals are large.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying a ratio makes calculations easier and does not change the final shares.

Q: What if the total does not divide exactly?
At Foundation level, totals are usually chosen so each part is a whole number, but decimals may appear at higher levels.

Study Tip

Write down the number of parts before doing any calculations. This simple habit helps avoid most ratio mistakes.

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