GCSE Maths Practice: sharing-in-a-ratio

Question 8 of 10

This question tests your ability to find the smaller share in a ratio when decimal values are involved.

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\( \begin{array}{l}\text{£260 is shared between two people in the ratio } 5:3. \\ \text{What is the smaller share?}\end{array} \)

Choose one option:

Always check that both shares add back up to the original total.

Sharing an Amount in a Ratio with Decimals (GCSE Higher)

At GCSE Higher level, ratio questions often move beyond whole-number answers and introduce decimal values. These questions are designed to test both your understanding of ratio and your confidence with decimal arithmetic. When totals do not divide evenly into whole numbers, accuracy becomes especially important.

Understanding Why Decimals Appear

A ratio such as 5:3 tells you how a total is split into equal parts. If the total amount is not a multiple of the sum of the ratio numbers, the value of one part will be a decimal. This does not make the method any different — it simply means you must calculate carefully.

Identifying the Smaller Share

The smaller share corresponds to the smaller number in the ratio. In a 5:3 ratio, the smaller share is linked to the number 3. However, you must still find the value of one part before multiplying. Guessing or rounding too early can lead to incorrect answers.

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. Identify the smaller number in the ratio.
  4. Multiply the unit value by this number.

At Higher tier, it is expected that you can work confidently with decimals at each stage.

Worked Example 1

£150 is shared between two people in the ratio 4:2. What is the smaller share?

  • Total parts = 4 + 2 = 6
  • One part = £150 ÷ 6 = £25
  • Smaller share = 2 × £25 = £50

Worked Example 2

£275 is divided in the ratio 3:5. How much is the smaller share?

  • Total parts = 3 + 5 = 8
  • One part = £275 ÷ 8 = £34.375
  • Smaller share = 3 × £34.375 = £103.125

Common Higher-Tier Errors

  • Rounding too early: Keep decimals until the final step.
  • Choosing the wrong share: Always identify the smaller ratio number first.
  • Arithmetic slips: Decimal multiplication must be done carefully.

Exam Technique

Write the unit value clearly before multiplying. If working with decimals, keep at least two decimal places until the final answer, unless the question states otherwise.

Real-Life Applications

Decimal ratio sharing appears in finance, profit splitting, budgeting, wages, and cost allocation. Being confident with these calculations is essential for real-world problem solving.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying ratios can reduce calculations but will not change the final proportions.

Q: Should I round my answer?
Only round if the question specifically asks you to. Otherwise, give the exact value.

Study Tip

When decimals appear, slow down slightly and double-check each step. Accuracy matters more than speed at Higher tier.

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