GCSE Maths Practice: sharing-in-a-ratio

Question 1 of 10

This question tests your ability to share a total amount accurately using a given ratio.

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\( \begin{array}{l}\text{Select all options that correctly share £90 in the ratio } 1:2.\end{array} \)

Select all correct options:

After finding the shares, always add them together to check they equal the original total.

Understanding Sharing in a Ratio (GCSE Maths)

Sharing an amount in a given ratio is a key topic in GCSE Maths and appears frequently in exams, real-life problems, and financial situations. A ratio tells us how one quantity compares to another, and when we are asked to share something in a ratio, it means we divide a total into parts that follow that comparison.

What Does a Ratio Mean?

A ratio such as 1:2 means that for every 1 part given to the first person or group, 2 equal parts are given to the second. The actual size of each part depends on the total amount being shared. Importantly, the ratio does not tell us the values directly — it only tells us how many equal parts the total must be split into.

Step-by-Step Method

  1. Add 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 to find each share.

Worked Example 1

Share £60 in the ratio 2:1.

  • Total parts = 2 + 1 = 3
  • One part = £60 ÷ 3 = £20
  • Shares = £40 and £20

Worked Example 2

Share 24 sweets in the ratio 3:5.

  • Total parts = 3 + 5 = 8
  • One part = 24 ÷ 8 = 3
  • Shares = 9 sweets and 15 sweets

Common Mistakes to Avoid

  • Forgetting to add the ratio parts: Dividing by only one number in the ratio leads to incorrect answers.
  • Not checking the total: Always add the final shares together to ensure they match the original amount.
  • Mixing up order: The first number in the ratio always refers to the first share.

Real-Life Applications

Sharing in a ratio is used in many everyday situations. For example, dividing money between siblings, splitting profits in a business partnership, mixing ingredients in cooking, or allocating time between tasks. Understanding ratios helps ensure fairness and accuracy in these situations.

Frequently Asked Questions

Q: What if the total does not divide evenly?
A: At GCSE Foundation level, totals are usually chosen so each part is a whole number, but at higher levels you may get decimals or fractions.

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

Study Tip

Always write down the total number of parts before dividing. This simple step prevents most mistakes when sharing in a ratio.

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