Knowledge Organiser: Algebraic Fractions
Part of Algebraic Fractions · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Algebraic Fractions within Algebraic Fractions for GCSE Mathematics. Revise Algebraic Fractions in Algebra for GCSE Mathematics with 13 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
13 questions
Recall
12 flashcards
Knowledge Organiser: Algebraic Fractions
Key Terms
- Algebraic fraction: A fraction where the numerator or denominator contains a letter (e.g. (x+1)/x)
- Simplify: Cancel common factors in numerator and denominator
- Common denominator: A shared denominator needed to add or subtract fractions
- Factorise: Essential first step — factor top and bottom before cancelling
- Restriction: Values of x that make the denominator zero — must be excluded
Must-Know Facts
- To simplify: factorise numerator and denominator, cancel common factors
- NEVER cancel terms (adding) — only cancel factors (multiplying)
- To multiply: multiply numerators and multiply denominators, then simplify
- To divide: flip the second fraction (reciprocal) then multiply
- To add/subtract: find common denominator, adjust numerators, combine
- The denominator can NEVER be zero — this is undefined
Key Methods
- Simplify: factorise top and bottom, cancel common bracket/factor
- Multiply: (a/b) × (c/d) = ac/bd (simplify after)
- Divide: (a/b) ÷ (c/d) = (a/b) × (d/c)
- Add: find LCD, adjust each fraction, combine numerators
- Solving: multiply both sides by LCD to clear fractions
Key Formulas
- Simplify: factorise numerator and denominator, then cancel common factors
- Multiply: (a/b) × (c/d) = ac/bd
- Add: a/b + c/d = (ad + bc)/bd (use LCD)
- Equation with fractions: multiply every term by the LCD to eliminate fractions
Common Mistakes
- Cancelling terms not factors: Cannot cancel a term across a + or − sign — only cancel common bracket factors
- Adding numerators without common denominator: a/3 + b/5 ≠ (a+b)/8 — find LCD (15) first
- Dividing fractions: Flip the second fraction and multiply — do NOT divide numerators and denominators separately
- Not factorising before simplifying: Always try to factorise the numerator and denominator before cancelling
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Read this section alongside the surrounding pages in Algebraic Fractions. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Algebraic Fractions
Simplify 6x²/3x
Explain why you need a common denominator when adding algebraic fractions.
Quick Recall Flashcards
13 questions on Algebraic Fractions — practise free
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