GCSE Maths Practice: sharing-in-a-ratio

Question 5 of 10

This question tests your ability to identify and calculate the smaller share when an amount is divided in a given ratio.

‹ ›

\( \begin{array}{l}\text{£132 is shared between two people in the ratio } 4:7. \\ \text{How much is the smaller share?}\end{array} \)

Choose one option:

After calculating both shares, check that they add up to the original total.

Finding the Smaller Share in a Two-Part Ratio (GCSE Higher)

At GCSE Higher level, ratio questions often test whether you can correctly interpret wording such as smaller share or larger share rather than simply calculating both values. A ratio like 4:7 is deliberately chosen to avoid symmetry and to check that you understand how ratios compare quantities.

Understanding What the Ratio Represents

A ratio compares quantities by showing how many equal parts each share receives. In the ratio 4:7, one person receives 4 equal parts and the other receives 7 equal parts. This does not tell you the values directly — you must first calculate the value of one part.

Identifying the Smaller Share

The smaller share always corresponds to the smaller number in the ratio. However, you cannot simply choose the smaller number and multiply by the total. You must first divide the total amount by the sum of the ratio numbers to find the unit value.

Efficient Higher-Tier 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. Identify which number in the ratio represents the smaller share.
  4. Multiply the value of one part by that number.

Worked Example 1

£165 is shared between two people in the ratio 5:6. How much is the smaller share?

  • Total parts = 5 + 6 = 11
  • One part = £165 ÷ 11 = £15
  • Smaller share = 5 × £15 = £75

Worked Example 2

198 points are divided between two teams in the ratio 3:8. How many points does the smaller team receive?

  • Total parts = 3 + 8 = 11
  • One part = 198 ÷ 11 = 18
  • Smaller share = 3 × 18 = 54 points

Common Higher-Tier Errors

  • Choosing the wrong share: Always identify the smaller number in the ratio.
  • Dividing by one ratio number: You must divide by the total number of parts.
  • Skipping the final check: The smaller and larger shares should add back to the original total.

Exam Technique

Underline the phrase smaller share in the question and circle the smaller ratio number before you begin calculations. This reduces careless mistakes.

Real-Life Applications

Finding the smaller share is useful in budgeting, splitting profits unequally, allocating time between tasks, or distributing resources based on contribution. Ratio skills are essential for making fair and accurate decisions.

Frequently Asked Questions

Q: Can the ratio be simplified first?
Yes. Simplifying ratios can make calculations easier but does not change which share is smaller.

Q: Will totals always divide exactly?
At Higher tier, you may encounter decimals or fractions, so careful arithmetic is important.

Study Tip

Always write the unit value clearly before multiplying. This keeps your working organised and reduces errors.

Related Quizzes