Multiply fractions
Objective. Multiply fractions and mixed numbers, cancelling before calculation.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Multiplying fractions means multiplying the numerators together and the denominators together, and the result is often simplified by cancelling common factors before working out the final product. Mixed numbers must first be converted to improper fractions. For example, ⅔ × ¾ cancels no common factors directly but multiplies to give 6/12, which simplifies to ½; cancelling earlier, the 3 in the numerator and the 3 in the denominator cancel first to give 2/1 × ¼ = 2/4 = ½. Cancelling before multiplying keeps the numbers smaller and easier to simplify.
Worked example
Work out 1⅓ × ⅔, cancelling before you multiply fractions.
- 1Convert the mixed number: 1⅓ = 4/3
- 2Write the multiplication: 4/3 × 2/3
- 3Multiply numerators and denominators: (4 × 2)/(3 × 3) = 8/9
- 4Check 8/9 cannot be simplified further, so it is the final answer
Answer: 8/9
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes find a common denominator before multiplying fractions, as if multiplying worked like addition, turning ½ × ⅓ into an unnecessary conversion instead of simply multiplying straight across to get 1/6.
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