GCSE Maths • Higher Tier
GCSE Algebraic Fractions Revision Guide
Build confidence with simplifying algebraic fractions, factorising expressions, using index laws, clearing denominators and solving algebraic fraction equations with this Higher Tier GCSE guide.
Foundation
Exam practice
Worked examples
What You'll Learn
Recognise Algebraic Fractions
Understand fractions that contain algebraic expressions in the numerator, denominator or both.
Simplify Using Common Factors
Simplify algebraic fractions by identifying and cancelling common factors.
Factorise Before Cancelling
Factorise expressions first so that common factors become visible and can be cancelled correctly.
Use Index Laws
Apply index laws when dividing powers of the same variable, such as x³ ÷ x² = x.
Solve Algebraic Fraction Equations
Remove fractions, isolate the variable and check solutions by substitution.
Key Algebraic Fraction Rules
Factorise first
Factorise the numerator and denominator where possible before looking for common factors.
Cancel factors, not terms
Only common factors can be cancelled. Terms that are being added or subtracted cannot be cancelled.
Use index laws
When dividing powers with the same base, subtract the powers; for example, x³ ÷ x² = x.
Clear the denominator
To solve an algebraic fraction equation, multiply both sides by the denominator. If there are different denominators, use their lowest common multiple and multiply every term.
Check the result
Check that a simplified fraction cannot be reduced further, and check an equation solution by substituting it into the original equation.
Algebraic Lessons
Simplifying Algebraic Fractions
Identify matching variables and combine coefficients correctly.
Solving Algebraic Fractions
Multiply every term inside a bracket and simplify.
Example 1: Add Fractions with Different Denominators
Example 2: Multiply & Simplify Fractions
Example 3: Divide a Mixed Number by a Fraction
- 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.
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
