GCSE MATHS • HIGHER TIER
Dividing Fractions Made Simple
Learn how to divide fractions using Keep, Change, Flip, work with reciprocals, whole numbers and mixed numbers, and simplify final answers.
Clear method
Exam practice
Worked proofs
Dividing Fractions in Four Moves
1
Keep
Keep the first fraction exactly as it is.
2
Change
Change the division sign into multiplication.
3
Flip
Flip the second fraction to find its reciprocal.
4
Multiply
Multiply, simplify and convert the answer if needed.
What You’ll Learn
Understand Fraction Division
Understand what it means to divide one fraction by another.
Use Keep, Change, Flip
Apply the standard GCSE method confidently.
Understand Reciprocals
Recognise and use the reciprocal of a fraction.
Divide with Whole Numbers
Write whole numbers as fractions over 1 before dividing.
Divide Mixed Numbers
Convert mixed numbers into improper fractions before using the method.
The Golden Rule:
Keep, Change, Flip
1. Keep the first fraction.
2. Change division into multiplication.
3. Flip the second fraction upside down.
This is often called 'Keep, Change, Flip'.
Worked Proof: Arc Length
Why Does Keep, Change, Flip Work?
- Dividing Fractions by Whole Numbers
- Dividing Whole Numbers by Fractions
- Dividing Mixed Numbers
- 4. Multiply the circumference by this fraction. the angle.
- 5. Give the answer in exact or decimal form.
More Worked Examples
1
5/6 ÷ 3
5/6 × 1/3
2
4 ÷ 1/2
4/1 × 2/1
3
3 ÷ 3/4
3/1 × 4/3
4
1 1/2 ÷ 3/4
1 1/2 = 3/2
3/2 × 4/3
5
2 1/4 ÷ 1/2
2 1/4 = 9/4
9/4 × 2/1
6
Visual Diagram
3/5 ÷ 2/7
↓ Keep, Change, Flip : 3/5 × 7/2
↓ Multiply : 21/10
↓ Multiply : 21/10
- Common GCSE Mistakes
- Wrong fraction flipped: Only flip the second fraction.
- Division sign unchanged: Change ÷ into × before multiplying.
- Whole number not converted: Write whole numbers over 1 first.
- Mixed number not converted: Change it to an improper fraction first.
- Unsimplified answer: Simplify or convert the final result where needed.
- Exam Tips
- Say Keep, Change, Flip: It helps remember the correct order.
- Write whole numbers over 1: This avoids confusion.
- Convert mixed numbers first: Then apply the standard method.
- Cancel common factors: Simplify before multiplying when possible.
- Check the final form: Simplify and convert improper fractions if required.
Skills Used in Dividing Fractions
Reciprocals
Improper Fractions
Mixed Numbers
Multiplying Fractions
Simplifying Fractions
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 Dividing Fractions Tutorial
Step-by-step walkthroughs of Dividing Fractions with clear methods and exam tips.
Frequently Asked Questions
Keep the first fraction, change division to multiplication, and flip the second fraction.
A reciprocal is a fraction turned upside down, such as 3/4 becoming 4/3.
No. Keep the first fraction and flip only the second fraction.
Write the whole number over 1, then use Keep, Change, Flip.
Write the whole number over 1 and multiply by the reciprocal of the fraction.
Convert mixed numbers into improper fractions before dividing.
