This topic summary covers Knowledge Organiser: Fraction Operations within Fraction Operations for GCSE Mathematics. Revise Fraction Operations in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 15 of 15 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Fraction Operations
Key Terms
- Common denominator: A shared denominator needed for adding/subtracting fractions
- LCM: Lowest Common Multiple — used to find the common denominator
- Reciprocal: A fraction flipped upside down (used in division)
- KFC method: Keep, Flip, Change — the method for dividing fractions
- Cancelling: Dividing numerator and denominator by a common factor before multiplying
Must-Know Facts
- Adding fractions with different denominators: find LCM first, then add numerators
- 1/2 + 1/3 = 3/6 + 2/6 = 5/6 (NOT 2/5)
- Multiplying fractions: top × top, bottom × bottom, then simplify
- Dividing fractions: Keep the first, Flip the second, Change ÷ to ×
- For mixed numbers: always convert to improper fractions before operating
- Multiplying proper fractions always gives a smaller answer
Key Formulas
- Add/subtract: a/b ± c/d — find common denominator first
- Multiply: a/b × c/d = ac/bd
- Divide: a/b ÷ c/d = a/b × d/c = ad/bc
- Mixed to improper: (whole × denom + numer) / denom
Common Mistakes
- Adding denominators: ½ + ⅓ ≠ 2/5 — always find a common denominator first
- Dividing fractions: Don't divide by the fraction — flip and multiply (KFC: Keep the first fraction, Flip the second, Change ÷ to ×)
- Mixed numbers: Convert to improper fractions before multiplying or dividing
- Not simplifying: Always check if the final answer can be simplified
- Multiplying mixed numbers directly: 2½ × 3 ≠ 6½ — convert to 5/2 × 3 = 15/2 = 7½
Practice questions for Fraction Operations
Which of these fractions is the largest? ⅔ ¾ ⅗ ⅝
Explain why you need a common denominator when adding fractions, but not when multiplying fractions.
Quick recall flashcards
Quick: 1/2 of 3/4
1/2 × 3/4 = 3/8
Half of anything: divide by 2
Or multiply by 1/2
Multiplying fractions
Top × Top, Bottom × Bottom
2/3 × 3/4 = 6/12 = 1/2
No need for common denominators!