GCSE Maths Practice: sharing-in-a-ratio

Question 6 of 10

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

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\( \begin{array}{l}\text{£144 is divided in the ratio } 3:2:1. \\ \text{What is the largest share?}\end{array} \)

Choose one option:

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

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

At GCSE Higher level, ratio questions often require careful interpretation of the wording rather than just calculation. When a question asks for the largest share, you must correctly identify which part of the ratio represents the greatest proportion and then apply the unit-value method accurately.

Understanding a Three-Part Ratio

A ratio such as 3:2:1 shows how a total is divided into three unequal shares. Each number represents how many equal parts that share receives. The size of each part depends on the total amount being shared.

Identifying the Largest Share

The largest share corresponds to the largest number in the ratio. However, you cannot find its value without first calculating the value of one part. Skipping this step is a common cause of errors at Higher tier.

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 largest number in the ratio.
  4. Multiply the value of one part by that number.

Worked Example 1

£180 is shared between three people in the ratio 5:3:2. What is the largest share?

  • Total parts = 5 + 3 + 2 = 10
  • One part = £180 ÷ 10 = £18
  • Largest share = 5 × £18 = £90

Worked Example 2

240 points are divided between three teams in the ratio 6:2:2. How many points does the team with the largest share receive?

  • Total parts = 6 + 2 + 2 = 10
  • One part = 240 ÷ 10 = 24
  • Largest share = 6 × 24 = 144 points

Common Higher-Tier Errors

  • Choosing the wrong ratio number: Always identify the largest number before calculating.
  • Incorrect unit value: A small division mistake affects all shares.
  • Not checking totals: All three shares should add up to the original total.

Exam Technique

Underline the phrase largest share and circle the largest ratio number before starting calculations. This reduces careless mistakes.

Real-Life Applications

Finding the largest share is useful when allocating budgets, dividing profits, sharing resources based on responsibility, or distributing rewards in competitions. Ratio skills support accurate and fair decision-making.

Frequently Asked Questions

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

Q: Will totals always divide exactly?
At Higher tier, some totals may result in 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.

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