GCSE MATHS • HIGHER TIER
Comparing Fractions Made Simple
Learn how to compare fractions using numerators, denominators, equivalent fractions, decimals, percentages, mixed numbers and number lines.
Clear method
Exam practice
Worked proofs
Comparing Fractions in Four Moves
1
Check
Check whether the fractions share a denominator or numerator.
2
Convert
Use equivalent fractions, decimals or percentages when needed.
3
Compare
Compare the values using the clearest method.
4
Decide
State which fraction is larger, smaller or equal.
What You’ll Learn
Compare Same Denominators
Compare numerators when denominators are the same.
Compare Same Numerators
Use the smaller denominator to identify the larger fraction.
Use Equivalent Fractions
Find a common denominator to compare unlike fractions.
Use Decimals and Percentages
Convert fractions into other forms for comparison.
Compare Mixed Numbers
Compare whole-number parts before fractional parts.
Key Rules
Introduction
Comparing fractions is a fundamental GCSE Maths skill. Students need to decide which fraction is larger, smaller or whether two fractions are equal. This skill appears in fraction questions, probability, ratio and problem-solving.
What Does Comparing Fractions Mean?
Comparing fractions means deciding which fraction has the greater value. For example, is 1/2 larger or smaller than 3/4?
Worked Proof: Comparing Fractions
Visual Fraction Model
- 1/2 → ■■□□
- 3/4 → ■■■□
- The second diagram has more shaded area, so 3/4 is larger.
More Worked Examples
1
Fraction Wall Visual
1/2 = 4/8
3/4 = 6/8
2
Comparing Fractions Using Decimals
Convert fractions into decimals.
1/2 = 0.5
3/4 = 0.75
3/4 = 0.75
3
Comparing Fractions Using Percentages
1/2 = 50%
3/4 = 75%
4
Using Number Lines
Number lines help visualise fraction size.
0 ---- 1/4 ---- 1/2 ---- 3/4 ---- 1
- Common GCSE Mistakes
- Numerators only: Do not compare numerators when denominators differ.
- Missing ÷ 360: Convert the angle into a fraction of 360°.
- Wrong angle: Use the central angle.
- Arc vs sector: Do not confuse arc length with sector area.
- Exam Tips
- Write the formula first: Use the arc length formula before substituting.
- Check radius or diameter: Use the correct circle measurement.
- Keep π exact: Leave π unless a decimal is requested.
Skills Used in Comparing Fractions
Equivalent Fractions
Common Denominators
Decimals
Percentages
Mixed Numbers
Number Lines
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 Comparing Fractions Tutorial
Step-by-step walkthroughs of Comparing Fractions with clear methods and exam tips.
Frequently Asked Questions
Compare the numerators. The fraction with the larger numerator is larger.
The fraction with the smaller denominator is larger.
Convert them to equivalent fractions with a common denominator, then compare the numerators.
Yes. Convert each fraction to a decimal and compare the decimal values.
Yes. Convert each fraction to a percentage and compare the percentages.
Compare the whole-number parts first, then compare the fractional parts if necessary.
