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Fractions
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GCSE MATHS PRACTICE
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Build your maths confidence, spot common mistakes, and understand the method behind each answer. Build your skills in fractions and percentages.
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4 areas · 20 training modules
Percentage
Practise percentages of amounts, percentage change and finding the original value.
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GCSE · PERCENTAGES
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Four areas · 20 modules. Learn the method, diagnose mistakes and build lasting mastery.
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These 20 core skills are relevant to both papers. Higher learners also study this content.
GCSE · PERCENTAGES
Basics & Conversions
Learning, Practice, Quiz and a delayed Mastery Check. Enter numerical answers without % or currency symbols.
GCSE · PERCENTAGES
Percentage Calculations
Learning, Practice, Quiz and a delayed Mastery Check. Enter numerical answers without % or currency symbols.
GCSE · PERCENTAGES
Percentage Change
Learning, Practice, Quiz and a delayed Mastery Check. Enter numerical answers without % or currency symbols.
GCSE · PERCENTAGES
Repeated Change & Applications
Learning, Practice, Quiz and a delayed Mastery Check. Enter numerical answers without % or currency symbols.
GCSE · FRACTIONS
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FRACTIONS · CALCULATIONS
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FRACTIONS · FOUNDATIONS
Foundations
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FRACTIONS · CONVERSIONS & CONNECTIONS
Conversions & Connections
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FRACTIONS · APPLICATIONS
Applications
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FRACTION ADDITION
Learn it step by step
Use these four rules every time you add fractions.
1
Read the fraction
The numerator is the number on top. The denominator is the number on the bottom. The denominator tells you the size of each part.
37
3 parts out of 7 equal parts
2
Same denominator: add the top numbers
When the denominators are already the same, keep that denominator. Only add the numerators.
29 + 49 = 2 + 49
= 69
= 23 simplify by ÷3
Do not add the denominators: 2/9 + 4/9 is not 6/18.
3
Different denominators: make them match first
You cannot add fractions until their parts are the same size. Find a common denominator, then multiply the top and bottom of each fraction by the same number.
How to find the lowest common multiple (LCM)
Use factor trees first. For 12 and 18, split each number until every end number is prime.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Use every prime factor needed: 2 × 2 × 3 × 3 = 36. So the LCM of 12 and 18 is 36.
Shortcut: short division
Divide both numbers by prime numbers until both reach 1. Multiply the divisors on the left.
21218
369
223
311
2 × 3 × 2 × 3 = 36
34 + 16 common denominator: 12
= 3 × 34 × 3 + 1 × 26 × 2
= 912 + 212
= 1112
4
Check whether the answer can be simplified
If the top and bottom share a factor, divide both by it. If the numerator is larger than the denominator, write the answer as a mixed number when needed.
812 = 23 divide top and bottom by 4
94 = 214 9 ÷ 4 = 2 remainder 1
1
Improper fractions: the top number is larger
An improper fraction is still a fraction. Add it in the usual way; then turn the final answer into a mixed number if asked.
117 + 57 = 167
= 227 16 ÷ 7 = 2 remainder 2
1
Mixed numbers: add wholes and fractions
Add the whole numbers together. Then add the fractional parts. If the fractional answer is improper, exchange it for one whole.
235 + 145 = 3 + 75
= 3 + 125
= 425
Before you submit
- Are the denominators the same?
- Did you add only the numerators?
- Did you simplify the final answer?
FRACTIONS · ADDITION
Fraction Addition
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Fraction Addition
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Foundation · Core method
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FRACTIONS · SUBTRACTION
Fraction Subtraction
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FRACTIONS · MULTIPLICATION
Fraction Multiplication
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FRACTIONS · DIVISION
Fraction Division
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FRACTIONS · EXAM SKILLS
Mixed Fraction Challenge
The operation is not given. Read each situation and decide what calculation is needed.
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