GCSE Maths Practice: sharing-in-a-ratio

Question 3 of 10

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

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\( \begin{array}{l}\text{Which of these show a correct sharing of £210 in the ratio } 7:3\text{?}\end{array} \)

Choose one option:

Check that both values follow the ratio and add back to the original total.

Sharing an Amount Using a 7:3 Ratio (GCSE Higher)

At GCSE Higher level, ratio questions often involve less familiar ratios and totals that require confident arithmetic. A ratio such as 7:3 is designed to test whether you can accurately find a unit value and then scale it correctly for each share.

Understanding the Structure of a 7:3 Ratio

The ratio 7:3 means that the total amount is divided into 10 equal parts. One share receives 7 of those parts, while the other receives 3. The ratio itself does not give the values — it only describes how the total is split.

Efficient Higher-Tier Method

  1. Add 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 unit value by each ratio number.

At Higher tier, you are expected to carry out these steps quickly and accurately, often mentally or with minimal written working.

Worked Example 1

£280 is shared in the ratio 7:1. What are the two shares?

  • Total parts = 7 + 1 = 8
  • One part = £280 ÷ 8 = £35
  • Shares = £245 and £35

Worked Example 2

180 points are divided between two teams in the ratio 9:3. How many points does each team receive?

  • Total parts = 9 + 3 = 12
  • One part = 180 ÷ 12 = 15
  • Shares = 135 points and 45 points

Common Higher-Tier Errors

  • Incorrect unit value: A small division error affects both shares.
  • Assuming symmetry: Equal-looking splits only work for 1:1 ratios.
  • Skipping the check: Both shares must add back to the original total.

Multiple-Choice Exam Strategy

In multiple-choice questions, eliminate options that do not add to the total first. Then check whether the remaining option follows the correct ratio by comparing the two values.

Real-Life Applications

Ratios like 7:3 are common in business profit sharing, budgeting, time allocation, and performance weighting. At higher levels, these ideas extend into percentages and algebraic ratios.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying 7:3 is not possible, but simplifying ratios where both numbers share a common factor often makes calculations faster.

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

Study Tip

Always find the unit value first and write it down clearly before calculating individual shares.

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