How to divide fractions - KS3 Maths

Key points

To divide a fraction by a fraction use the method. This means to turn the second fraction upside down and multiply.
Sometimes calculations can be simpler using fractions rather than their decimal equivalents.
Understanding improper fractions and mixed numbers conversions may help when dividing fractions. Knowing how to multiply fractions may also be useful.

How to divide by a fraction

To divide with fractions, it can be useful to think about how many times a fraction will fit into a number or another fraction.
For example, when dividing 5 by ½, you are asking how many halves there are in 5
This may help you to understand the reciprocal method.

Example: calculate 5 ÷ 1⁄2

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How many halves are there in 5?
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Dividing by ½ is the same as multiplying by 2. There are 10 halves in 5
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How many quarters are there in 2?
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Dividing by a quarter is the same as multiplying by 4. There are 8 quarters in 2

Reciprocal method

To divide a fraction by a fraction use the method.This means to turn the second fraction upside down and multiply.
the answer where necessary.

Example: calculate 10⁄3 ÷ 2⁄3

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Calculate 10⁄3 ÷ 2⁄3
$Calculate ten thirds divided by two thirds equals five. A fraction wall is used to model this.$
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The diagram shows that 2⁄3 fits into 10⁄3 five times.
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To divide these fractions use the reciprocal method. Turn the second fraction 2⁄3 upside down. Multiply 10⁄3 by 3⁄2. This is 30⁄6 which simplifies to 5
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To divide these fractions use the reciprocal method. Turn the second fraction 2⁄9 upside down. Multiply 5⁄3 by 9⁄2
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5⁄3 × 9⁄2 = 45⁄6. This simplifies to 15⁄2
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Remember that 2 is the same as 2⁄1. 2⁄1 × 4⁄1 = 8⁄1 = 8. Write the answer as simply as possible.

Work out 7⁄15 ÷ 3⁄4

Use the reciprocal method to divide by a fraction.Turn the second fraction upside down and multiply.

For any fraction, $ \frac{a}{b} $

$ ? ÷ \frac{a}{b} $ is the same as $ ? × \frac{b}{a} $

Question

Calculate $ \frac{7}{15} ÷ \frac{3}{4} $

Practise dividing fractions

Work out 2 1⁄4 ÷ 3⁄5

Hint: Understanding how to convert between mixed numbers and improper fractions can be useful when dividing fractions. It might be useful to have a pen and paper to help with your workings.

Dividing fractions quiz

Try practising dividing fractions with this quiz. You might need a pen and paper to solve these questions.

Real-world maths

Eco-marathon car — Image caption,
A competitor in the Eco-marathon.

Calculating average speed

Competitors in the Eco-marathon, a fuel economy competition, must have an average speed of at least 15 miles per hour (mph) to qualify.

Question

At one Eco-marathon race, the distance driven was 9 $ \frac{1}{2} $ miles, a car completed the race in 32 minutes.Was the average speed enough to qualify?