GCSE Maths Practice: sharing-in-a-ratio

Question 2 of 10

This question tests your ability to share a total amount accurately using a three-part ratio.

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\( \begin{array}{l}\text{Which of the following correctly share £180 in the ratio } 2:3:5\text{?}\end{array} \)

Choose one option:

Always check that all three values together equal the original total.

Sharing an Amount Between Three Parts (GCSE Higher)

At GCSE Higher level, ratio questions often involve more than two shares and require careful organisation of working. Three-part ratios test whether you can correctly handle multiple values, avoid arithmetic slips, and check that all shares together form the original total.

Understanding a Three-Part Ratio

A ratio such as 2:3:5 shows how a quantity is divided into three unequal parts. Each number represents how many equal units that share receives. The key idea is that all parts must be the same size, even though each share may contain a different number of parts.

Efficient Higher-Tier Method

  1. Add all the ratio numbers 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 ratio number.

At Higher tier, you are expected to perform these steps fluently, often without writing full sentences for each stage.

Worked Example 1

£210 is shared in the ratio 3:4:7. What are the three shares?

  • Total parts = 3 + 4 + 7 = 14
  • One part = £210 ÷ 14 = £15
  • Shares = £45, £60 and £105

Worked Example 2

240 points are divided between three teams in the ratio 5:3:2. How many points does each team receive?

  • Total parts = 5 + 3 + 2 = 10
  • One part = 240 ÷ 10 = 24
  • Shares = 120, 72 and 48 points

Common Higher-Tier Errors

  • Missing a ratio number: Forgetting one part gives the wrong unit value.
  • Incorrect mental arithmetic: Small multiplication errors can affect all shares.
  • Not checking totals: All three values must add back to the original amount.

Multiple-Choice Exam Strategy

For multiple-choice questions, eliminate options that do not add up to the total first. Then check whether the remaining option matches the required ratio. This saves time and reduces careless errors.

Real-Life Applications

Three-part ratios appear in profit sharing, budgeting between departments, recipe scaling, and dividing workloads across teams. At higher levels, these ratios may be combined with percentages, fractions, or algebra.

Frequently Asked Questions

Q: Can I simplify a three-part ratio first?
Yes. Simplifying helps reduce calculations but does not change the final proportions.

Q: Is there always only one correct answer?
Yes. Only one option will both follow the ratio and sum to the correct total.

Study Tip

Write the unit value clearly before calculating individual shares. This keeps your working organised and accurate.

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