Algebraic Fractions
Algebraic fractions combine fraction skills with algebraic manipulation and are a step up from basic fractions. Students must simplify, add, subtract, multiply and divide fractions that contain variables, often needing to factorise first.
What You'll Learn
- Simplifying algebraic fractions by factorising and cancelling
- Adding and subtracting algebraic fractions
- Multiplying and dividing algebraic fractions
- Solving equations involving algebraic fractions
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Cancelling individual terms instead of factors (e.g., cancelling x from (x+1)/x)
Forgetting to find a common denominator when adding algebraic fractions
Not factorising fully before attempting to simplify
What Examiners Say About Algebraic Fractions
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
- Presentation●●●●●
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
- Common Mistake●●●●●
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Fractions
Fractions form the backbone of Cambridge IGCSE maths, appearing in nearly every paper. Students must be confident adding, subtracting, multiplying and dividing fractions, as well as converting between improper fractions and mixed numbers.
Factorising
Factorising is the reverse of expanding brackets and is essential for solving quadratics, simplifying expressions, and working with algebraic fractions. Students progress from single-bracket factorisation to double brackets and the difference of two squares.
Rearranging Formulae
Rearranging formulae requires students to change the subject of an equation, using the same inverse-operation skills as solving equations but with multiple variables. Harder questions involve subjects that appear twice or under roots and powers.
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