Dividing fractions

We divide by a fraction by multiplying by the fraction turned upside down: 2/3 ÷ 4/9 = 2/3 · 9/4 = 18/12 = 3/2. Check: 3/2 · 4/9 = 12/18 = 2/3, which is what we started with.

Years 6–9 · Updated 9 November 2026

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What division means

12 ÷ 3 asks: how many threes fit into twelve? The same question works with fractions.

We want to know how many halves fit into three.

3 ÷ $\frac{1}{2} = ?$

Each whole holds two halves. Three wholes hold 3 · 2 = 6 halves.

3 ÷ $\frac{1}{2} = 6$

Small pieces fit in many times, so the answer is greater than three.

Why we flip the fraction

How many times does 3/4 fit into three wholes?

Three wholes are 3 · 4 = 12 quarters. We multiply by the denominator.
Twelve quarters are enough for 12 ÷ 3 = 4 groups of three. We divide by the numerator.
Times four and divided by three is the same as times 4/3.

3 ÷ $\frac{3}{4} = 3 \cdot \frac{4}{3} = \frac{12}{3} = 4$

The fraction turned upside down is called the reciprocal.

The rule step by step

Write whole numbers and mixed numbers as fractions: 5 = 5/1 and 1 1/2 = 3/2.
Keep the first fraction.
Change ÷ to · and flip the fraction we are dividing by.
Multiply, and simplify if you can.
Check: the answer times the fraction we divided by should give what we started with.

Example

Example 1: $\frac{2}{3} \div \frac{4}{9}$

We want to know how many times 4/9 fits into 2/3.

We keep 2/3, change ÷ to · and flip 4/9.
$\frac{2}{3} \div \frac{4}{9} = \frac{2}{3} \cdot \frac{9}{4}$
Numerator times numerator, denominator times denominator.
(2 · 9)/(3 · 4) = $\frac{18}{12}$
Eighteen and twelve can both be divided by six.
$\frac{18}{12} = \frac{3}{2}$
So 4/9 fits in one and a half times.
$\frac{3}{2} = 1$ $\frac{1}{2}$

3/2 · 4/9 = 12/18 = 2/3. We are back at 2/3, so the answer is correct.

Example 2: $\frac{5}{6}$ litre of juice shared equally between 5 glasses

We want to know how much juice each glass gets: 5/6 ÷ 5.

Five is 5/1. Flipped, it becomes 1/5.
$\frac{5}{6} \div 5 = \frac{5}{6} \cdot \frac{1}{5}$
Dividing by five is taking one fifth. We multiply.
(5 · 1)/(6 · 5) = $\frac{5}{30}$
Five and thirty can both be divided by five.
$\frac{5}{30} = \frac{1}{6}$

5 · 1/6 = 5/6 litre, which is all the juice. Each glass gets 1/6 litre.

Pitfalls

Flipping the first fraction: 2/3 ÷ 4/9 becomes 3/2 · 4/9.
Flip the fraction after the division sign. The first one stays as it is: 2/3 · 9/4.
Thinking that dividing by 1/2 is like dividing by 2: 3 ÷ 1/2 = 1.5.
Dividing by a half is counting halves. Six halves fit into three wholes, so 3 ÷ 1/2 = 6.
Forgetting to flip a whole number: 3/4 ÷ 3 = 3/4 · 3 = 9/4.
Write 3 = 3/1 and flip it: 3/4 ÷ 3 = 3/4 · 1/3 = 3/12 = 1/4. If we share into three parts, the answer should be smaller.

Practise on your own

0 of 4 correct

Work out 2 ÷ $\frac{1}{3}$ .
Your answer to task 1
Work out $\frac{3}{5} \div 3$ . Give your answer in its simplest form.
Your answer to task 2
Work out $\frac{3}{4} \div \frac{3}{8}$ .
Your answer to task 3
Work out $\frac{5}{6} \div \frac{2}{3}$ . Give your answer as a fraction in its simplest form.
Your answer to task 4

Common questions

Why does the answer get bigger when you divide by a fraction?

Dividing by a fraction less than one asks how many small pieces fit. More pieces fit than wholes, so the answer is bigger.

What is a reciprocal?

The fraction turned upside down. The reciprocal of 4/9 is 9/4, and 4/9 · 9/4 = 36/36 = 1.

How do you divide mixed numbers?

Rewrite them as fractions first. How many 1/4 litre glasses fit into 1 1/2 litres? 3/2 ÷ 1/4 = 3/2 · 4/1 = 12/2 = 6 glasses.

Can you divide numerator by numerator and denominator by denominator?

Yes, when they divide exactly: 6/8 ÷ 2/4 = (6 ÷ 2)/(8 ÷ 4) = 3/2. Otherwise flip and multiply is safer.

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