Multiplying fractions

We multiply two fractions by multiplying the numerators together and the denominators together: 2/3 · 3/4 = 6/12 = 1/2. A whole number times a fraction: 3 · 2/5 = 6/5. We do not need a common denominator.

Years 6–9 · Updated 9 November 2026

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A whole number times a fraction

3 · 2/5 means that we take 2/5 three times.

3 · $\frac{2}{5} = \frac{2}{5} + \frac{2}{5} + \frac{2}{5} = \frac{6}{5}$

We multiply the numerator, which counts the pieces. The denominator stays the same, because the pieces are still fifths.

A fraction times a fraction

Half of a third is a sixth.

$\frac{1}{2} \cdot \frac{1}{3}$ = (1 · 1)/(2 · 3) = $\frac{1}{6}$

Divide a chocolate bar into three rows and four columns. It has 3 · 4 = 12 squares: the denominators are multiplied. We take two of the rows and three of the columns. That is 2 · 3 = 6 squares: the numerators are multiplied.

$\frac{2}{3} \cdot \frac{3}{4}$ = (2 · 3)/(3 · 4) = $\frac{6}{12} = \frac{1}{2}$

Why the answer can be smaller

"Of" means times. Multiplying by 2/3 is taking two thirds of something.

$\frac{2}{3} \cdot 12$ = (2 · 12)/3 = $\frac{24}{3} = 8$

Calculation	Means	Answer
2 · 10	two times ten	20, greater than 10
1 · 10	ten once	10, the same size
1/2 · 10	half of ten	5, less than 10
1/4 · 10	a quarter of ten	2.5, less than 10

If we multiply a positive number by a fraction between zero and one, the answer is smaller. That is a good check.

Example

Example 1: 4 · $\frac{2}{7}$

We want to know how much four times two sevenths is.

We take two sevenths four times.
4 · $\frac{2}{7} = \frac{2}{7} + \frac{2}{7} + \frac{2}{7} + \frac{2}{7}$
We multiply the numerator. The denominator stays the same.
4 · $\frac{2}{7}$ = (4 · 2)/7 = $\frac{8}{7}$
Seven sevenths is one whole, so 8/7 is one whole and one seventh.
$\frac{8}{7} = 1$ $\frac{1}{7}$

2/7 + 2/7 = 4/7, 4/7 + 2/7 = 6/7 and 6/7 + 2/7 = 8/7. The same answer.

Example 2: $\frac{2}{3} \cdot \frac{3}{4}$

We want to take two thirds of three quarters.

The numerators multiplied together: the squares we have.
2 · 3 = 6
The denominators multiplied together: the squares in the whole bar.
3 · 4 = 12
We have six squares out of twelve.
$\frac{2}{3} \cdot \frac{3}{4} = \frac{6}{12}$
Six and twelve can both be divided by six. We simplify.
$\frac{6}{12} = \frac{1}{2}$

One third of 3/4 is 1/4, and two of those make 2/4 = 1/2. The same answer, and less than 3/4.

Pitfalls

Multiplying both the numerator and the denominator by the whole number: 3 · 2/5 = 6/15.
6/15 = 2/5, so the value has not changed. Multiply the numerator: 3 · 2/5 = 6/5.
With a mixed number, multiplying the whole number but not the fraction: 2 1/2 · 2 = 4 1/2.
Rewrite it as a fraction first: 2 1/2 = 5/2 and 5/2 · 2 = 10/2 = 5.
Thinking that 1/2 · 8 = 4 is wrong because the answer got smaller.
Multiplying by 1/2 is taking half. Half of eight is four.

Practise on your own

0 of 4 correct

Work out 3 · $\frac{2}{7}$ .
Your answer to task 1
Work out $\frac{3}{4} \cdot 20$ .
Your answer to task 2
Work out $\frac{2}{5} \cdot \frac{3}{4}$ . Give your answer in its simplest form.
Your answer to task 3
Work out $\frac{5}{6} \cdot \frac{9}{10}$ . Try simplifying before you multiply. Give your answer in its simplest form.
Your answer to task 4

More walkthroughs with Fox

Common questions

Do you need a common denominator to multiply fractions?

No. A common denominator is needed for addition and subtraction. For multiplication we work out numerator times numerator and denominator times denominator directly.

Why does the answer get smaller when you multiply by a fraction?

Multiplying by a fraction less than one means taking a part, for example half. A part is smaller than the whole.

How do you multiply mixed numbers?

First rewrite them as fractions: 1 1/2 = 3/2. Then 1 1/2 · 2/3 = 3/2 · 2/3 = 6/6 = 1.

What does "of" mean in a fraction problem?

"Of" means times. 3/4 of 20 = 3/4 · 20 = 15.

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