GCSE MATHS • HIGHER TIER
Fractions of an Amount Made Simple
Learn how to find fractions of quantities using the divide-then-multiply method, including money, lengths, quantities and whole-amount problems.
Clear method
Exam practice
Worked proofs
Fractions of an Amount in Four Moves
1
Identify
Identify the numerator, denominator and total amount.
2
Divide
Divide the amount by the denominator.
3
Multiply
Multiply the result by the numerator.
4
Check
Include the correct units and check the calculation.
What You’ll Learn
Understand Fractions of Amounts
Recognise that a fraction of an amount means taking part of a quantity.
Use Divide Then Multiply
Apply the standard method quickly and accurately.
Work with Real-Life Quantities
Find fractions of money, lengths, students and other quantities.
Use Multiplication
Recognise fraction-of-an-amount calculations as multiplication.
Find the Whole Amount
Work backwards when a fraction of a quantity is known.
The Golden Rule
To find a fraction of an amount:
- 1. Divide by the denominator.
- 2. Multiply by the numerator.
Memory Trick
Fraction of an Amount = Divide then Multiply
Worked Proof: Fractions of an Amount
Introduction
Finding a fraction of an amount is one of the most useful GCSE Maths skills. It appears in number, ratio, percentages, probability and real-life problem-solving questions. Students who master this topic can often gain straightforward marks in exams.
What Does 'Fraction of an Amount' Mean?
A fraction of an amount means taking part of a quantity. For example, finding 1/2 of 20 means finding half of 20.
Visual Example
- 1/2 of 20
- Half the objects are selected.
- Answer = 10
More Worked Examples
1
Visual Diagram
20 objects are split into 4 equal groups. Taking 3 groups gives:
3/4 of 20 = 15
2
Fractions of Money
Find 3/5 of £25.
25 ÷ 5 = 5
5 × 3 = 15
5 × 3 = 15
3
Fractions of Length
Find 2/3 of 30 cm.
30 ÷ 3 = 10
10 × 2 = 20 cm
10 × 2 = 20 cm
4
Fractions of Quantities
Find 4/7 of 56 students.
56 ÷ 7 = 8
8 × 4 = 32 students
8 × 4 = 32 students
- Common GCSE Mistakes
- Wrong order: Divide by the denominator before multiplying by the numerator.
- Wrong fraction number: Use the denominator for division and numerator for multiplication.
- Missing units: Include £, cm, students or other required units.
- Arithmetic errors: Check division and multiplication facts carefully.
- Exam Tips
- Remember divide then multiply: Use the denominator first.
- Write both steps: Clear working helps avoid mistakes.
- Check units: Include them in the final answer.
- Estimate first: Use a rough check to see whether the answer is sensible.
- Work backwards carefully: When finding the whole, undo the fraction step by step.
Skills Used in Fractions of an Amount
Fractions
Ratio
Percentages
Probability
Proportional Reasoning
Money
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Fractions of an Amount Tutorial
Step-by-step walkthroughs of Fractions of an Amount with clear methods and exam tips.
Frequently Asked Questions
Divide the amount by the denominator, then multiply by the numerator.
The denominator tells you how many equal parts the whole is divided into.
Divide the amount by 4, then multiply the result by 3.
Yes. A fraction of an amount can also be written as fraction × amount.
Work backwards from the known fractional amount to one part, then multiply to find the whole.
It appears in number, ratio, percentages, probability and real-life problem-solving.
