GCSE MATHS • HIGHER TIER
Simplifying Fractions Made Simple
Learn how to simplify ordinary, improper, mixed-number and algebraic fractions using common factors and the highest common factor.
Clear method
Exam practice
Worked proofs
Simplifying Fractions in Four Moves
1
Identify
Identify the numerator and denominator.
2
Find
Find a common factor, ideally the highest common factor.
3
Divide
Divide the numerator and denominator by the same factor.
4
Check
Make sure no common factor greater than 1 remains.
What You’ll Learn
Understand Simplest Form
Recognise when a fraction has no common factors other than 1.
Find the HCF
Identify the highest common factor of the numerator and denominator.
Simplify Different Fraction Types
Simplify ordinary, improper, mixed-number, negative and algebraic fractions.
Use Prime Factors
Use prime factorisation for larger numbers.
Check Final Answers
Use prime factorisation for larger numbers.
Key Rules
Common factor
Divide the numerator and denominator by a common factor.
Same number
Always divide the numerator and denominator by the same number.
Use the HCF
Dividing both parts by the highest common factor (HCF) simplifies the fraction in one step.
Simplest form
A fraction is fully simplified when the numerator and denominator have no common factor except 1.
Worked Proof: Simplifying Fractions
Step-by-Step Method
- Find the numerator and denominator.
- Find the highest common factor (HCF) of both numbers.
- Divide the numerator by the HCF.
- Divide the denominator by the same HCF.
- Check that there are no common factors except 1. Write the fraction in its simplest form.
More Worked Examples
1
Prime Factor Method
For larger numbers, prime factorisation can help.
72 = 2 × 2 × 2 × 3 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
Common factors: 2 × 2 × 2 × 3 = 24
96 = 2 × 2 × 2 × 2 × 2 × 3
Common factors: 2 × 2 × 2 × 3 = 24
2
Improper Fractions and Mixed Numbers
Improper fractions can often simplify to whole numbers.
18/6 = 3
24/8 = 3
Mixed Number Example: 4 8/12
Simplify only the fractional part: 8/12 = 2/3
24/8 = 3
Mixed Number Example: 4 8/12
Simplify only the fractional part: 8/12 = 2/3
3
Negative Fractions
Negative fractions simplify in exactly the same way.
-12/18
HCF = 6
-12 ÷ 6 = -2
18 ÷ 6 = 3
HCF = 6
-12 ÷ 6 = -2
18 ÷ 6 = 3
4
Algebraic Fractions
Higher Tier students will meet algebraic fractions.
6x/12
Divide numerator and denominator by 6./br>
Divide numerator and denominator by 6./br>
- Common GCSE Mistakes
- One number only: Always divide both numerator and denominator.
- Not fully simplified: Continue until no common factor greater than 1 remains.
- Incorrect cancelling: Cancel common factors, not separate terms.
- No final check: Make sure the fraction is in simplest form.
- Exam Tips
- Find the HCF first: It usually simplifies the fraction in one step.
- Divide top and bottom equally: Use the same factor on both.
- Know your times tables: This makes common factors easier to spot.
- Check mixed numbers carefully: Simplify only the fractional part when appropriate.
- Always check again: Make sure the answer cannot simplify further.
Skills Used in Simplifying Fractions
Highest Common Factor
Multiplication Tables
Equivalent Fractions
Mixed Numbers
Improper Fractions
Algebraic Fractions
Ratio
Probability
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 Simplifying Fractions Tutorial
Step-by-step walkthroughs of Simplifying Fractions with clear methods and exam tips.
Frequently Asked Questions
It means writing an equivalent fraction whose numerator and denominator have no common factor greater than 1.
Find the highest common factor and divide both numerator and denominator by it.
GCSE mark schemes frequently expect fraction answers to be given in their simplest form.
Yes. For example, 18/6 simplifies to 3.
Simplify the fractional part while keeping the whole-number part unchanged.
Yes. Common numerical or algebraic factors can be cancelled when they are factors of the whole numerator and denominator.
