Fractions
Fractions run through the whole GCSE Maths paper, from adding and subtracting to converting between fractions, decimals and percentages. This guide walks each method with worked examples, then gives you exam-style questions to try.
📋 Key Rules & Methods
Adding & Subtracting Fractions
Rule: Fractions must have the SAME denominator to add or subtract.
Find the LCM of denominators, convert, then add/subtract numerators only.
Find the LCM of denominators, convert, then add/subtract numerators only.
Multiplying Fractions
Rule: Multiply numerators together, multiply denominators together.
Tip: Cancel common factors BEFORE multiplying to keep numbers small.
Tip: Cancel common factors BEFORE multiplying to keep numbers small.
Dividing Fractions (KFC)
KFC Method:
Keep the first fraction
Flip the second fraction (reciprocal)
Change to multiplication
Keep the first fraction
Flip the second fraction (reciprocal)
Change to multiplication
✏️ Worked Examples
Example 1: Adding Fractions
Calculate: ²⁄₃ + ¾
LCM of 3 and 4 = 12
²⁄₃ = ⁸⁄₁₂ and ¾ = ⁹⁄₁₂
⁸⁄₁₂ + ⁹⁄₁₂ = ¹⁷⁄₁₂ = 1⁵⁄₁₂
Answer: 1⁵⁄₁₂
Example 2: Dividing Fractions
Calculate: ³⁄₄ ÷ ²⁄₅
Keep: ³⁄₄
Flip: ²⁄₅ becomes ⁵⁄₂
Change: ³⁄₄ × ⁵⁄₂ = ¹⁵⁄₈ = 1⁷⁄₈
Answer: 1⁷⁄₈
📝 Practice Questions
Q1
Calculate: ½ + ⅓Q2
Calculate: ¾ - ²⁄₅Q3
Calculate: ²⁄₃ × ⁴⁄₅Q4
Calculate: ⁵⁄₆ ÷ ²⁄₃Q5
Convert ³⁄₈ to a decimalQ6
Convert 0.35 to a fraction in simplest formAnswers
Q1: ⁵⁄₆ | Q2: ⁷⁄₂₀ | Q3: ⁸⁄₁₅ | Q4: 1¼ | Q5: 0.375 | Q6: ⁷⁄₂₀
⚠️ Common Mistakes
Mistake: Adding denominators when adding fractions
Wrong: ½ + ⅓ = ²⁄₅ ❌
Correct: ½ + ⅓ = ³⁄₆ + ²⁄₆ = ⁵⁄₆ ✓
Wrong: ½ + ⅓ = ²⁄₅ ❌
Correct: ½ + ⅓ = ³⁄₆ + ²⁄₆ = ⁵⁄₆ ✓
Mistake: Forgetting to simplify
Always check if your answer can be simplified!
Always check if your answer can be simplified!