GCSE Maths Practice: sharing-in-a-ratio

Question 4 of 10

This question tests your ability to identify and calculate the smallest share in a three-part ratio.

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\( \begin{array}{l}\text{£105 is shared between three people in the ratio } 7:5:3. \\ \text{How much does the person receiving the smallest share get?}\end{array} \)

Choose one option:

After finding all three shares, check that they add up to the original total.

Finding the Smallest Share in a Three-Part Ratio (GCSE Higher)

At GCSE Higher level, ratio questions often test more than just calculation. You are expected to interpret the wording carefully, identify which part of the ratio is being asked for, and apply the unit-value method accurately. Questions that ask for the smallest share are designed to check your understanding of how ratios compare quantities.

Understanding Three-Part Ratios

A three-part ratio such as 7:5:3 shows how a total amount is divided between three people or groups. Each number represents how many equal parts that share receives. The actual value of each part depends on the total amount being shared.

Identifying the Smallest Share

In any ratio, the smallest share is represented by the smallest number. However, you must still calculate the value of one part before multiplying. Simply choosing the smallest number without calculating can lead to mistakes, especially when totals are unfamiliar.

Efficient Higher-Tier Method

  1. Add all 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 the smallest number in the ratio.
  4. Multiply the value of one part by this number.

Worked Example 1

£180 is shared between three people in the ratio 8:4:2. How much does the smallest share receive?

  • Total parts = 8 + 4 + 2 = 14
  • One part = £180 ÷ 14 ≈ £12.86
  • Smallest share = 2 × £12.86 ≈ £25.72

Worked Example 2

150 points are divided between three teams in the ratio 6:3:1. How many points does the smallest team receive?

  • Total parts = 6 + 3 + 1 = 10
  • One part = 150 ÷ 10 = 15
  • Smallest share = 1 × 15 = 15 points

Common Higher-Tier Errors

  • Skipping the unit value: Always calculate one part before multiplying.
  • Choosing the wrong share: Make sure you identify the smallest ratio number.
  • Not checking totals: All shares together should equal the original amount.

Exam Technique

When asked for the smallest share, underline the phrase in the question and circle the smallest ratio number before you begin. This reduces the risk of choosing the wrong value.

Real-Life Applications

Identifying the smallest share is useful in situations such as budgeting, allocating limited resources, dividing time between tasks, or sharing rewards unequally based on contribution.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying ratios makes calculations easier and does not change which share is smallest.

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

Study Tip

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

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