GCSE MATHS • HIGHER TIER
Equivalent Fractions Made Simple
Learn how to identify, create and compare equivalent fractions using multiplication, simplification, visual models, decimals and percentages.
Clear method
Exam practice
Worked proofs
Equivalent Fractions in Four Moves
1
Identify
Identify the fraction you are working with.
2
Multiply
Multiply the numerator and denominator by the same number.
3
Compare
Check that the new fraction represents the same value.
4
Simplify
Work backwards by dividing top and bottom by the same factor when simplifying.
What You’ll Learn
Understand Equivalence
Recognise fractions that have the same value even when they look different.
Create Equivalent Fractions
Multiply numerator and denominator by the same number.
Simplify Fractions
Use equivalence in reverse to reduce fractions.
Use Visual Models
Understand equivalence using fraction walls and shaded models.
Link Decimals and Percentages
Recognise that equivalent fractions have the same decimal value.
The Golden Rule :
Whatever you do to the numerator, you must also do to the denominator.
Introduction
Equivalent fractions are fractions that have the same value even though they look different. This GCSE guide explains how to identify, create and compare equivalent fractions using clear examples, diagrams and exam-style questions.
What Are Equivalent Fractions?
Fractions are equivalent when they represent the same proportion.
Visual Example
1/2 = 2/4 = 3/6 = 4/8
Worked Proof: Equivalent Fractions
Why Are Equivalent Fractions Important?
They are used when adding fractions, subtracting fractions, comparing fractions, solving ratio problems and working with percentages.
Visual Fraction Models
1/2
2/4
4/8
Each diagram represents exactly half of the whole.
How to Find Equivalent Fractions
Multiply the numerator and denominator by the same number.
1/2 × 2/2 = 2/4
1/2 × 3/3 = 3/6
1/2 × 4/4 = 4/8
More Worked Examples
1
Question: Find an equivalent fraction to 7/8 with denominator 40.
8 × 5 = 40
7 × 5 = 35
7 × 5 = 35
2
Equivalent Fractions and Simplifying
Equivalent fractions work in reverse when simplifying.
12/18 = 6/9 = 2/3
3
Using Fraction Walls
Fraction walls are a visual way to see equivalent fractions.
1/2 = 2/4 = 4/8 = 8/16
4
Equivalent Fractions and Decimals
1/2 = 0.5
2/4 = 0.5
4/8 = 0.5
4/8 = 0.5
- Common GCSE Mistakes
- Numerator only: Multiply or divide both numerator and denominator.
- Denominator only: Use the same operation on both parts of the fraction.
- Different multipliers: Use the same multiplier for top and bottom.
- Unsimplified answers: Reduce fractions fully when required.
- Exam Tips
- Use the same multiplier: Keep numerator and denominator in proportion.
- Check the target denominator: Work out the scale factor first.
- Work backwards to simplify: Divide top and bottom by a common factor.
- Use visual models if unsure: Fraction walls can confirm equivalence.
- Check the value: Equivalent fractions should represent the same amount.
Skills Used in Equivalent Fractions
Adding Fractions
Subtracting Fractions
Comparing Fractions
Percentages
Decimals
Simplifying Fractions
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 Equivalent Fractions Tutorial
Step-by-step walkthroughs of Equivalent Fractions with clear methods and exam tips.
Frequently Asked Questions
Equivalent fractions are different-looking fractions that represent the same value.
Multiply the numerator and denominator by the same number.
Yes. Dividing the numerator and denominator by the same common factor creates a simpler equivalent fraction.
Simplify them, convert them to a common denominator, or compare their decimal values.
Because they represent the same proportion of the whole.
They are used in adding, subtracting and comparing fractions, ratio, decimals and percentages.
