Complex fractions
Objective. Simplify fractions containing fractional numerators or denominators.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A complex fraction is one where the numerator, denominator, or both contain fractions themselves, such as (1/2)/(3/4). To simplify a complex fraction, rewrite the division as multiplication by the reciprocal of the denominator fraction. For example, (1/2) ÷ (3/4) becomes (1/2) × (4/3) = 4/6 = 2/3. When the numerator or denominator is a sum of fractions, combine it into a single fraction first using a common denominator before dividing. This topic draws together fraction addition and division skills into one streamlined process.
Worked example
Simplify the complex fraction (2/3 + 1/6) ÷ (5/9).
- 1Combine the numerator over a common denominator: 2/3 = 4/6, so 4/6 + 1/6 = 5/6.
- 2The expression is now (5/6) ÷ (5/9).
- 3Multiply by the reciprocal: 5/6 × 9/5.
- 4Cancel the 5s: 1/6 × 9/1 = 9/6 = 3/2.
Answer: 3/2
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes try to cross-cancel or divide numerators and denominators directly across the complex fraction without first converting to a single division. Always rewrite as 'numerator fraction ÷ denominator fraction' before using the reciprocal rule.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.