Equivalent fractions: expanding and simplifying

We expand a fraction by multiplying the numerator and the denominator by the same number, and we simplify by dividing both by the same number. Example: 2/3 = 4/6 and 6/8 = 3/4. The value of the fraction does not change.

Years 4–7 · Updated 9 November 2026

Watch Fox work it out on the board

Fox works one step at a time. Press play.

Expanding: more pieces, smaller pieces

We want to write the same fraction with a larger denominator.

Do we want 2/3 to have the denominator twelve? Three times four is twelve. So we multiply the numerator by four as well.

$\frac{2}{3}$ = (2 · 4)/(3 · 4) = $\frac{8}{12}$

The value does not change. We have multiplied by 4/4, and 4/4 is one whole.

Simplifying: fewer pieces, bigger pieces

We want to write the fraction with the smallest numbers possible.

$\frac{6}{8}$ = (6 ÷ 2)/(8 ÷ 2) = $\frac{3}{4}$

A fraction is in its simplest form when the numerator and the denominator have no common factor greater than one.

Finding a number to divide by

If both numbers …	you can divide by
are even	2
have a digit sum that is divisible by 3	3
end in 0 or 5	5
end in 0	10

We can simplify in several steps. The answer is the same.

$\frac{24}{36} = \frac{12}{18} = \frac{6}{9} = \frac{2}{3}$

Example

Example 1: expand $\frac{3}{5}$ so that the denominator is 20

We want to write 3/5 as twentieths, with the same value.

What must five be multiplied by to make twenty?
20 ÷ 5 = 4
We multiply the numerator and the denominator by four.
$\frac{3}{5}$ = (3 · 4)/(5 · 4)
Three times four is twelve. Five times four is twenty.
$\frac{3}{5} = \frac{12}{20}$

3/5 = 0.6 and 12/20 = 0.6. The same value.

Example 2: simplify $\frac{18}{24}$ as far as possible

We want to write 18/24 with the smallest numbers possible.

Both numbers are even. We divide by two.
$\frac{18}{24}$ = (18 ÷ 2)/(24 ÷ 2) = $\frac{9}{12}$
Nine and twelve are both in the three times table. We divide by three.
$\frac{9}{12}$ = (9 ÷ 3)/(12 ÷ 3) = $\frac{3}{4}$
Three and four have no common factor greater than one. We are done.
$\frac{18}{24} = \frac{3}{4}$

18 ÷ 24 = 0.75 and 3 ÷ 4 = 0.75. The same value.

Pitfalls

Changing the denominator but not the numerator: 2/3 expanded by two becomes 2/6.
2/6 is one third. Do the same to the numerator as to the denominator: 2/3 = 4/6.
Expanding by adding: (2 + 1)/(3 + 1) = 3/4.
Adding changes the value: 2/3 ≈ 0.667 but 3/4 = 0.75. We always expand by multiplying.
Stopping too early when simplifying: 12/18 = 6/9.
Check once more. Six and nine can both be divided by three: 6/9 = 2/3.

Practise on your own

0 of 4 correct

Expand $\frac{1}{4}$ so that the denominator is 12.
Your answer to task 1
Write $\frac{10}{15}$ in its simplest form.
Your answer to task 2
Write $\frac{36}{48}$ in its simplest form.
Your answer to task 3
Which fraction is larger, $\frac{3}{4}$ or $\frac{7}{10}$ ?
Your answer to task 4

Common questions

Does the value of a fraction change when you expand or simplify it?

No. Multiplying or dividing the numerator and the denominator by the same number is like multiplying or dividing by one whole.

What does simplest form mean?

The numerator and the denominator have no common factor greater than one. 3/4 is in its simplest form, but 6/8 is not.

Do you always have to simplify the answer?

An answer that has not been simplified has the same value. Many tasks still ask for the simplest form, so it is a good habit.

Can you simplify by any number you like?

No, it has to be a number that divides exactly into both the numerator and the denominator. 7/9, for example, cannot be simplified.

Keep practising with Somokai

Free to start. Hints and explanations when you get stuck.

Start practising for free

Found a mistake? Get in touch

Svenska