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A FRESH PAPER. ANOTHER CHANCE TO GROW.
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6 chaptersNumber, Algebra, Ratio, Geometry, Probability and Statistics
3 papersNon-calculator and calculator practice
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Fresh values and varied question selections. Some question types can recur. Original GCSE-style mocks, not official AQA papers.
PAPER 1 · NON-CALCULATORINTERACTIVE DEMO
123…25
Solve the equation
3x + 7 = 22
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One example, not a live exam. Answers in a full mock are marked after submission.
01 / THE CHALLENGE
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02 / THE INSIGHT
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03 / YOUR ROUTINE
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123
GCSE · 4 areas
Number
Arithmetic, powers and roots, fractions and decimals, standard form and accuracy.
⅟
4 areas · 34 training modules
Fractions
Foundations, calculations, conversions and applications with delayed mastery checks.
%
4 areas · 20 training modules
Percentage
Practise percentages of amounts, percentage change and finding the original value.
R
YOUR PROFILE
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0 / 53Fractions + Percentages · Foundation modules mastered
Four areas · 20 modules. Learn the method, diagnose mistakes and build lasting mastery.
Which paper are you studying for?
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 · NUMBER
Build your Number skills
Four areas. Each has Learning, Practice, a 15-question Quiz and a delayed Mastery Test.
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Your Foundation and Higher progress is saved separately.
NUMBER
Arithmetic & Place Value
Signed numbers, decimals, ordering and BIDMAS. Select your course below.
NUMBER
Factors, Powers & Roots
Primes, HCF, LCM, indices, roots and counting. Select your course below.
NUMBER
Fractions, Decimals & Percentages
Conversions, mixed numbers and calculations. Select your course below.
NUMBER
Standard Form & Accuracy
Rounding, estimation, bounds and units. Select your course below.
GCSE · FRACTIONS
Choose your next skill
Four areas. Learn the method, practise with feedback, then build lasting mastery.
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Foundation selected · Higher-only topics are hidden.
FRACTIONS · CALCULATIONS
Choose an operation
Choose a skill to learn the method, practise and test your understanding.
FRACTIONS · FOUNDATIONS
Foundations
Choose a skill for Learning, Practice, Quiz and a delayed Mastery Check.
FRACTIONS · CONVERSIONS & CONNECTIONS
Conversions & Connections
Choose a skill for Learning, Practice, Quiz and a delayed Mastery Check.
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.
373 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
= 23simplify 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 + 16common 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 = 23divide top and bottom by 4
94 = 2149 ÷ 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
= 22716 ÷ 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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Same Denominator
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1 Completed2 Secure3 Mastered
Number Quiz: 10 original questions + 5 adaptations from published AQA papers, with source links. Not endorsed by AQA.
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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.
Raise Maths