GCSE MATHS • HIGHER TIER
Subtracting Fractions Made Simple
Learn how to subtract fractions with the same or different denominators, use common denominators and LCM, and work confidently with mixed numbers.
Clear method
Exam practice
Worked proofs
Subtracting Fractions in Four Moves
1
Check
Check whether the denominators are the same.
2
Convert
If needed, find a common denominator and write equivalent fractions.
3
Subtract
Subtract the numerators while keeping the common denominator.
4
Simplify
Simplify the final answer and convert improper fractions if needed.
What You’ll Learn
Same Denominators
Subtract numerators while keeping the denominator unchanged.
Different Denominators
Find a common denominator before subtracting.
Use the LCM
Find efficient common denominators for larger numbers.
Mixed Numbers
Subtract whole-number and fraction parts carefully.
Simplify Answers
Reduce final fractions to their simplest form.
Key Rules
Same denominator
If the denominators are the same, subtract the numerators only.
Different denominators
If the denominators are different, find a common denominator first.
Equivalent fractions
Rewrite each fraction as an equivalent fraction with the same denominator.
Simplify the answer
Always simplify the final fraction if possible.
Worked Proof: Subtracting Fractions
Step-by-Step Method
- Check whether the denominators are the same or different.
- If they are different, find a common denominator.
- Rewrite the fractions as equivalent fractions.
- Subtract the numerators and keep the denominator the same.
- Simplify the answer if possible.
More Worked Examples
1
Subtracting Fractions with Different Denominators
Find a common denominator before subtracting.
2
Visual Common Denominator Diagram
3/4 = 3/4
1/2 = 2/4<
3
Using the Lowest Common Multiple (LCM)
For larger denominators, find the LCM first.
5/6 - 1/4
LCM = 12
5/6 = 10/12
1/4 = 3/12
LCM = 12
5/6 = 10/12
1/4 = 3/12
4
Subtracting Mixed Numbers
Subtract whole numbers and fractions carefully.
3 2/5 - 1 1/5
Whole numbers: 3 - 1 = 2
Fractions: 2/5 - 1/5 = 1/5
Whole numbers: 3 - 1 = 2
Fractions: 2/5 - 1/5 = 1/5
- Common GCSE Mistakes
- Subtracting denominators: Keep the common denominator unchanged.
- No common denominator: Convert fractions before subtracting when denominators differ.
- Unsimplified answer: Reduce the final fraction where possible.
- Mixed-number errors: Handle whole numbers and fractional parts carefully.
- Exam Tips
- Check denominators first: Same denominators make subtraction direct.
- Use equivalent fractions: Create a common denominator when needed.
- Use the LCM: It can make larger denominator questions easier.
- Show conversions clearly: This helps prevent arithmetic errors.
- Simplify at the end: Always check the final fraction.
Skills Used in Subtracting Fractions
Equivalent Fractions
Common Denominators
Lowest Common Multiple
Simplifying Fractions
Mixed Numbers
Improper Fractions
Ratio
Algebra
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 Subtracting Fractions Tutorial
Step-by-step walkthroughs of Subtracting Fractions with clear methods and exam tips.
Frequently Asked Questions
Keep the denominator the same and subtract the numerators.
Find a common denominator, convert to equivalent fractions, then subtract the numerators.
It represents the size of each piece, which does not change when subtracting equal-sized parts.
The lowest common multiple can provide an efficient common denominator.
Subtract whole numbers and fractional parts carefully, converting where necessary.
Yes. Always simplify the final fraction where possible.