GCSE Maths Practice: sharing-in-a-ratio

Question 10 of 10

This question tests your ability to share a total amount between three people using a given ratio.

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\( \begin{array}{l}\text{£100 is shared between Amir, Sara and Leo in the ratio } 2:3:5. \\ \text{How much does Amir receive?}\end{array} \)

Choose one option:

After calculating all shares, add them together to check they equal the original total.

Sharing an Amount Between Three People Using Ratios

Sharing a total amount between more than two people using a ratio is a key GCSE Maths skill. These questions test your ability to understand ratios, divide totals accurately, and apply multiplication correctly. Although three-part ratios may look harder than two-part ratios, the method is exactly the same.

Understanding Three-Part Ratios

A ratio such as 2:3:5 shows how a total is divided between three people. The numbers in the ratio tell us how many equal parts each person receives. They do not represent money values. Instead, they show the relative size of each share.

Consistent Step-by-Step 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. Multiply the value of one part by each person’s number in the ratio.

Worked Example 1

£90 is shared between Anna, Ben and Carl in the ratio 1:2:3. How much does Ben receive?

  • Total parts = 1 + 2 + 3 = 6
  • One part = £90 ÷ 6 = £15
  • Ben receives 2 × £15 = £30

Worked Example 2

60 points are shared between three teams in the ratio 2:4:4. How many points does the first team receive?

  • Total parts = 2 + 4 + 4 = 10
  • One part = 60 ÷ 10 = 6
  • First team receives 2 × 6 = 12 points

Common Mistakes Students Make

  • Forgetting to add all parts: In three-part ratios, missing one number leads to incorrect answers.
  • Using the ratio numbers as money: Always calculate the value of one part first.
  • Skipping the final check: The total of all shares must equal the original amount.

Real-Life Applications

Three-part ratios appear in many real-life situations, such as splitting money between siblings, sharing tasks in a group project, dividing time between activities, or allocating resources in competitions. Being confident with ratios helps ensure fair and accurate decisions.

Frequently Asked Questions

Q: Can I simplify a three-part ratio?
Yes. If all numbers share a common factor, simplifying makes calculations easier without changing the result.

Q: Is the method different from two-part ratios?
No. The only difference is that you add more numbers when finding the total parts.

Study Tip

Always write the total number of parts clearly before dividing. This prevents errors, especially in three-part ratio questions.

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