Fractions of Amounts –

Finding a fraction of an amount is one of the most practical GCSE Maths skills. It appears in money problems, measurement contexts, and multi-step questions across Foundation and Higher papers. Once you master this technique, you can apply it to ratio sharing, probability, and data interpretation.

What Is a Fraction of an Amount?

Finding a fraction of an amount means working out what a given fraction of a total quantity is. For example, finding 3/5 of 40 means splitting 40 into 5 equal parts and then taking 3 of those parts.

This skill connects directly to percentages and ratio — once you can find a fraction of an amount, you can tackle a wide range of real-world problems including discounts, sharing quantities, and interpreting data.

The method works with any amount — whole numbers, decimals, or even algebraic expressions at Higher tier.

Key Formulas

Step-by-Step Method

1. Divide the amount by the denominator of the fraction.
2. Multiply the result by the numerator.
3. Check your answer makes sense — it should be less than the original amount for proper fractions and more for improper fractions.

Worked Example 1 — Foundation Level

Question: Find 3/8 of 56.

Working:

Step 1 — Divide 56 by 8: 56 ÷ 8 = 7.

Step 2 — Multiply by 3: 7 × 3 = 21.

Answer: 21

Worked Example 2 — Higher Level

Question: A school has 1,260 students. 5/9 of the students are girls. 2/7 of the girls study French. How many girls study French?

Working:

Step 1 — Find 5/9 of 1,260: 1,260 ÷ 9 = 140, then 140 × 5 = 700 girls.

Step 2 — Find 2/7 of 700: 700 ÷ 7 = 100, then 100 × 2 = 200.

Answer: 200 girls study French.

Worked Example 3 — Exam Style

Question: Jake earns £2,400 per month. He spends 1/3 on rent, 1/4 on bills, and saves the rest. How much does Jake save each month?

Working:

Step 1 — Rent: 2,400 ÷ 3 = £800.

Step 2 — Bills: 2,400 ÷ 4 = £600.

Step 3 — Total spent: 800 + 600 = £1,400.

Step 4 — Savings: 2,400 − 1,400 = £1,000.

Answer: Jake saves £1,000 per month.

Common Mistakes

• Multiplying by the denominator instead of dividing. Always divide by the bottom number first, then multiply by the top number.
• Dividing by the numerator instead of the denominator. Remember: the denominator tells you how many equal parts to split into.
• Not reading multi-step problems carefully. Some questions ask for a fraction of a fraction — you must apply each step in order.

Exam Tips

• On non-calculator papers, choose whether to divide first or multiply first based on which gives easier arithmetic.
• If the amount does not divide evenly by the denominator, express your answer as a fraction or decimal as appropriate.
• Always re-read the question to check exactly what value you need to find the fraction of.
• Show your division and multiplication steps separately to earn method marks even if the final answer is wrong.

Practice Questions

Q1 (Foundation): Find 2/5 of 65.

Q2 (Foundation): A bag contains 72 sweets. 5/8 of the sweets are red. How many red sweets are there?

Q3 (Higher): A factory produces 4,500 items. 2/5 are defective. Of the defective items, 3/4 can be repaired. How many defective items cannot be repaired?

Practise fractions of amounts questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Fractions
• Percentage of an Amount
• Ratio Basics and Sharing

Summary

• To find a fraction of an amount, divide by the denominator then multiply by the numerator.
• This method works for whole numbers, money, and measurements.
• Multi-step problems may require finding a fraction of a fraction — apply each step in sequence.
• Always check that your answer is smaller than the original for proper fractions.
• Show every step of your working to secure method marks on exam papers.