GCSE Maths • Foundation & Higher
GCSE Fractions Revision Guide
Build confidence with equivalent fractions, simplifying, comparing, adding, subtracting, multiplying, dividing, mixed numbers and fractions of amounts with our comprehensive guide.
Clear explanations
Exam practice
Worked examples
What You'll Learn
x + y
Equivalent & Simplified Fractions
Identify equivalent fractions and simplify fractions by dividing the numerator and denominator by the same number.
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Compare Fractions
Compare fractions using common denominators, equivalent fractions, decimals, percentages and number lines.
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Add & Subtract Fractions
Use the same denominator or find a common denominator before adding or subtracting the numerators.
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Multiply & Divide Fractions
Multiply numerators and denominators, or use Keep, Change, Flip when dividing fractions.
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Use Mixed Numbers & Fractions of Amounts
Convert between mixed numbers and improper fractions, and find a fraction of a quantity by dividing and then multiplying.
Key Fraction Rules
Equivalent Fractions & Simplifying
Multiply or divide the numerator and denominator by the same number.
Adding and Subtracting
Multiply or divide the numerator and denominator by the same number.
Multiplying Fractions
Multiply the numerators, multiply the denominators and simplify the answer.
Dividing Fractions
Keep the first fraction, change division to multiplication and flip the second fraction.
Finding a Fraction of an Amount
Divide the amount by the denominator, then multiply by the numerator.
Fractions Lessons
Equivalent Fractions
Learn how fractions can have the same value even when they look different, and create equivalent fractions by multiplying the numerator and denominator by the same number.
Simplifying Fractions
Find the highest common factor and divide the numerator and denominator by it to leave a fraction in its simplest form.
Comparing Fractions
Decide which fraction is larger, smaller or equal by using common denominators, equivalent fractions, decimals, percentages or a number line.
Mixed Numbers and Improper Fractions
Replace variables with values, use brackets and follow BIDMAS.
Adding Fractions
Add fractions with the same denominator, different denominators and mixed numbers, then simplify the final answer.
Subtracting Fractions
Subtract fractions with the same or different denominators, work with mixed numbers and simplify answers correctly.
Multiplying Fractions
Multiply fractions without finding a common denominator, cancel common factors and convert mixed numbers before multiplying.
Dividing Fractions
Use Keep, Change, Flip to divide ordinary fractions, whole numbers and mixed numbers, then simplify the answer.
Fractions of an Amount
Find fractions of money, lengths and quantities using the divide-then-multiply method, and work backwards to find a whole amount.
Worked Examples
Example 1: Add Fractions with Different Denominators
3/4 + 5/6 = 1 7/12
Step 1: Find the lowest common multiple of 4 and 6.
LCM = 12
Write both fractions with denominator 12.
3/4 = 9/12
5/6 = 10/12
Step 3: Add the numerators.
9/12 + 10/12 = 19/12
Step 4: Convert the improper fraction. 19/12 = 1 7/12
LCM = 12
Write both fractions with denominator 12.
3/4 = 9/12
5/6 = 10/12
Step 3: Add the numerators.
9/12 + 10/12 = 19/12
Step 4: Convert the improper fraction. 19/12 = 1 7/12
Example 2: Multiply & Simplify Fractions
3/8 × 4/9 = 1/6
Step 1: Cancel common factors.
3 and 9 divide by 3.
4 and 8 divide by 4.
Step 2: Step 2: Multiply the simplified fractions.
1/2 × 1/3 = 1/6
3 and 9 divide by 3.
4 and 8 divide by 4.
Step 2: Step 2: Multiply the simplified fractions.
1/2 × 1/3 = 1/6
Example 3: Divide a Mixed Number by a Fraction
1 1/2 ÷ 3/4 = 2
Step 1: Convert the mixed number to an improper fraction.
1 1/2 = 3/2
Step 2: Keep, Change, Flip.
3/2 ÷ 3/4 = 3/2 × 4/3
Step 3: Multiply and simplify.
3/2 × 4/3 = 12/6 = 2
1 1/2 = 3/2
Step 2: Keep, Change, Flip.
3/2 ÷ 3/4 = 3/2 × 4/3
Step 3: Multiply and simplify.
3/2 × 4/3 = 12/6 = 2
- Common GCSE Mistakes
- Adding or subtracting the denominators instead of keeping or matching them.
- Forgetting to find a common denominator before adding or subtracting unlike fractions.
- Multiplying or dividing only the numerator or only the denominator when creating equivalent fractions.
- Looking only at numerators or only at denominators when comparing fractions.
- Forgetting to flip the second fraction when dividing, or flipping the wrong fraction.
- Failing to convert mixed numbers before multiplying or dividing.
- Not simplifying the final answer fully.
- Forgetting units in fractions-of-an-amount questions.
- Exam Tips
- Check whether a fraction can be simplified before giving your final answer.
- Use the highest common factor to simplify efficiently.
- Find a common denominator before adding, subtracting or comparing fractions with different denominators.
- Cancel common factors before multiplying to keep the numbers smaller.
- Convert mixed numbers to improper fractions before multiplying or dividing.
- For a fraction of an amount, divide by the denominator and multiply by the numerator.
- Include units when the question uses money, length or a measured quantity.
- Practise equivalent fractions and common denominators so that the methods become quicker and more accurate.
Ready to Practice?
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 Fractions Tutorial
Follow a clear, step-by-step explanation of equivalent fractions, simplifying, comparing, the four operations, mixed numbers and fractions of amounts.
- Equivalent fractions and simplifying
- Adding, subtracting, multiplying and dividing
- Mixed numbers, improper fractions and fractions of amounts
Continue Your GCSE Maths Revision
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Frequently Asked Questions
Equivalent fractions have the same value even though they look different. To create an equivalent fraction, multiply the numerator and denominator by the same number. For example, 1/2 = 2/4 = 3/6 = 4/8.
Find the highest common factor of the numerator and denominator, then divide both by that number. For example, the HCF of 18 and 24 is 6, so 18/24 simplifies to 3/4.
Find a common denominator and compare the equivalent fractions. You can also compare fractions by converting them to decimals or percentages. On a number line, the fraction further to the right is larger.
Find a common denominator, rewrite both fractions as equivalent fractions, then add or subtract the numerators. Keep the common denominator and simplify the final answer.
Multiply the numerators, multiply the denominators and simplify. A common denominator is not needed. You can cancel common factors before multiplying to make the calculation easier.
Use Keep, Change, Flip: keep the first fraction, change division to multiplication and flip the second fraction. Then multiply and simplify.
To convert a mixed number, multiply the whole number by the denominator, add the numerator and keep the same denominator. To convert an improper fraction, divide the numerator by the denominator; the quotient is the whole number and the remainder becomes the new numerator.
Divide the amount by the denominator, then multiply by the numerator. For example, 3/4 of 20 is 20 ÷ 4 × 3 = 15.
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