Sheet № 125 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
Question:
Find 3/8 of 56.
Answer:
200 girls study French.
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?
§Formulas to memorise
Fraction of an amount = (numerator / denominator) × amount
Divide the amount by the denominator first, then multiply by the numerator
Worked example
Find 3/8 of 56.
Working:
⚠ 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.