GCSE MATHS • HIGHER TIER
Multiplying Fractions Made Simple
Learn how to multiply fractions, cancel common factors, work with whole numbers and mixed numbers, and find fractions of amounts.
Clear method
Exam practice
Worked proofs
Multiplying Fractions in Four Moves
1
Convert
Convert whole or mixed numbers into fractions when needed.
2
Cancel
Cancel common factors before multiplying where possible.
3
Multiply
Multiply numerator by numerator and denominator by denominator.
4
Simplify
Simplify the final fraction and convert improper fractions if needed.
What You’ll Learn
Understand Fraction Multiplication
Recognise multiplication as finding a fraction of a fraction.
Use the Golden Rule
Multiply the numerators and denominators directly.
Cancel Common Factors
Simplify before multiplying to keep numbers smaller.
Multiply Whole and Mixed Numbers
Convert them into suitable fraction forms first.
Find Fractions of Amounts
Use multiplication to calculate fractions of quantities.
The Golden Rule
To multiply fractions:
1. Multiply the numerators.
2. Multiply the denominators.
3. Then simplify if possible.
Visual Fraction Model
1/2 × 3/4
3/4 is shaded. Take half of the shaded region.
Result = 3/8
Worked Proof: Multiplying Fractions
Why Cancelling Helps
Cancelling before multiplying keeps numbers smaller and reduces mistakes.
Multiplying Fractions by Whole Numbers
Write the whole number as a fraction over 1.
Example: 3 × 2/5
3 = 3/1
3/1 × 2/5 = 6/5 = 1 1/5
More Worked Examples
1
1/2 × 3/4
Numerators: 1 × 3 = 3
Denominators: 2 × 4 = 8
2
2/3 × 4/5
2 × 4 = 8
3 × 5 = 15
3
Simplifying Before Multiplying
3/8 × 4/9
Cancel common factors:
3 and 9 divide by 3.
4 and 8 divide by 4
3 and 9 divide by 3.
4 and 8 divide by 4
4
Multiplying Fractions by Whole Numbers
3 × 2/5
3 = 3/1
- Common GCSE Mistakes
- Wrong denominator operation: Multiply denominators instead of adding them.
- Unsimplified answer: Reduce the final fraction where possible.
- Mixed number not converted: Change it to an improper fraction first.
- Missed cancellation: Cancel common factors before multiplying when helpful.
- Exam Tips
- No common denominator needed: Multiply fractions directly.
- Cancel first: Keep numbers smaller and reduce errors.
- Whole numbers go over 1: Convert them before multiplying.
- Convert mixed numbers first: Use improper fractions for multiplication.
- Simplify at the end: Check the final form carefully.
Skills Used in Multiplying Fractions
Fractions
Simplifying Fractions
Improper Fractions
Mixed Numbers
Fractions of Amounts
Ratio
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 Multiplying Fractions Tutorial
Step-by-step walkthroughs of Multiplying Fractions with clear methods and exam tips.
Frequently Asked Questions
Multiply the numerators together, multiply the denominators together, then simplify.
No. A common denominator is not needed for multiplication.
Cancelling means dividing common factors before multiplying to make the calculation simpler.
Write the whole number as a fraction over 1, then multiply.
Convert mixed numbers into improper fractions first.
Multiply the fraction by the amount, writing the amount over 1 if useful.
