Learn how to multiply fractions – KS3 Maths

Key points

The of two fractions is calculated by multiplying the and multiplying the .
The word ‘of’ can be replaced by ‘multiplied by’ as it means the same thing. For example,\( \frac{1}{2} \)of\( \frac{1}{3} \)is the same as \( \frac{1}{2} \)multiplied by \( \frac{1}{3} \)
Sometimes the calculation can be simplified before multiplying.
must be converted to before multiplying.

How to multiply fractions

To multiply fractions:

Multiply the numerators.
Multiply the denominators.
Simplify the answer.

The answer may be simplified before calculation using the

Examples

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1⁄2 of 1⁄3 is the same as 1⁄2 multiplied by 1⁄3. Work out 1⁄2 of 1⁄3
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Diagrams can be drawn to illustrate this calculation. Draw a rectangle. Split the width into halves. Split the length into thirds. The rectangle is now split into 6 parts (sixths).
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1⁄2 of 1⁄3 is 1⁄6. The product of 1⁄2 and 1⁄3 is 1⁄6 (1⁄2 × 1⁄3 = 1⁄6)
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Multiplication can be processed in either order. 1⁄2 multiplied by 1⁄3 is the same as a 1⁄3 multiplied by 1⁄2. The rectangle can be used in either orientation. The answer is 1⁄6
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Work out 3⁄4 multiplied by 1⁄2
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To work out 3⁄4 × 1⁄2, draw a rectangle. Split the length into quarters and the width into halves. The rectangle is now split into 8 parts (eighths). 3⁄4 x 1⁄2 = 3⁄8
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To work out 4⁄5 × 3⁄8, multiply the numerators (4 x 3 = 12) and multiply the denominators (5 × 8 = 40). This gives the answer 12⁄40, which can be simplified to 3⁄10. This calculation can also be simplified before multiplying.
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The multiplication calculation can be simplified when both a numerator and a denominator have a HCF greater than 1. The HCF of 4 and 8 is 4
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Divide 4 and 8 by their HCF (4). The calculation has been simplified to 1⁄5 multiplied by 3⁄2
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1⁄5 × 3⁄2 gives the same answer as 4⁄5 × 3⁄8. The simplifying has been done first to make the calculation easier. 4⁄5 × 3⁄8 = 3⁄10

Question

Find the product of\( \frac{2}{9} \)and\( \frac{4}{5} \)

How to multiply mixed numbers

To multiply mixed numbers:

Rewrite the as . This is done by multiplying the integer by the denominator and adding the numerator.
If possible, simplify before calculating using the
Multiply the numerators.
Multiply the denominators.
Simplify the answer if possible.

Examples

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Multiply 3 1⁄4 by 1 1⁄2
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Convert each mixed number into an improper fraction. The calculation becomes 13⁄4 × 3⁄2
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Multiply the numerators and multiply the denominators.
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The improper fraction can be written as a mixed number. 39⁄8 is 4 7⁄8
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Multiply 2 7⁄10 by 4 1⁄6
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Convert each mixed number into an improper fraction. The calculation becomes 27⁄10 × 25⁄6. This can be simplified.
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The HCF of 27 and 6 is 3. The HCF of 10 and 25 is 5. Divide by these factors.
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The calculation has been simplified to 9⁄2 × 5⁄2
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9 x 5 = 45. 2 x 2 = 4. 45⁄4 is 11 1⁄4 as a mixed number.

Question

Find the product of \( 3\frac{1}{4} \) and \( 2\frac{2}{3} \)

Practise multiplying fractions

Try this quiz to practise multiplying fractions. You may need a pen and paper to solve some of these problems.

Quiz

Real-world maths

A strand of DNA. It has the shape of a double helix. — Image caption,
Multiplying fractions is useful in the study of genetics.

In genetics (the study of how genes and characteristics are passed down), multiplying by fractions can help track and predict the likelihood of features being passed onto a child, such as freckles or hair colour.

Half of a child’s genes come from one parent and half from another. When both parents carry the gene for a particular feature, they each have a chance of passing this on to the child.

By multiplying fractions, the chance of the child inheriting that feature can be worked out. For example, if both parents have\( \frac{1}{2} \)a chance of passing a feature on, the likelihood of inheriting is\( \frac{1}{4}\).