GCSE Maths Practice: sharing-in-a-ratio

Question 5 of 10

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

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\( \begin{array}{l}\text{£84 is divided in the ratio } 4:3. \\ \text{What is the larger share?}\end{array} \)

Choose one option:

After finding both shares, add them together to confirm they equal the original total.

Finding the Larger Share When an Amount Is Divided in a Ratio

Some GCSE Maths ratio questions ask you to find the larger share rather than the smaller one. These questions test whether you can correctly interpret the ratio and identify which number represents the larger portion before carrying out the calculation.

Understanding Larger and Smaller Shares

In a ratio such as 4:3, the first number represents the larger share because it has more equal parts. However, this is not always obvious unless you read the ratio carefully. The total amount must be split into equal parts first, and only then can you decide which share is larger.

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. Identify which number in the ratio represents the larger share.
  4. Multiply the value of one part by that number.

Worked Example 1

£70 is divided in the ratio 5:2. What is the larger share?

  • Total parts = 5 + 2 = 7
  • One part = £70 ÷ 7 = £10
  • Larger share = 5 × £10 = £50

Worked Example 2

63 points are divided between two teams in the ratio 6:3. How many points does the larger team receive?

  • Total parts = 6 + 3 = 9
  • One part = 63 ÷ 9 = 7
  • Larger share = 6 × 7 = 42 points

Common Mistakes to Avoid

  • Choosing the wrong share: Always identify which ratio number is larger before calculating.
  • Dividing by only one ratio number: You must divide by the total number of parts.
  • Not checking the total: The larger and smaller shares should add back up to the original amount.

Real-Life Applications

Finding the larger share is common when dividing money, allocating resources, sharing time, or distributing rewards based on contribution. Ratio skills ensure that the distribution matches the intended proportions.

Frequently Asked Questions

Q: Does the larger share always come first?
No. The larger share is the one with the greater number in the ratio, regardless of position.

Q: Can the ratio be simplified first?
Yes. Simplifying a ratio makes calculations easier and does not change which share is larger.

Study Tip

Circle the larger number in the ratio before starting your calculations. This helps you stay focused on the correct share.

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