Equivalent fractions

A fraction can be written in different ways and still mean the same thing.

Look at the shaded areas in these rectangles.

Diagram using rectangles to show equivalent fractions

Both rectangles have been divided up differently but have the same amount of shading.

The rectangle on the left has been divided into \({5}\) parts. \(3\) of these are shaded.

The rectangle on the right has been divided into \({10}\) parts. \(6\) of these are shaded.

So \(\frac{3}{5} = \frac{6}{{10}}\).

When fractions mean the same thing like this, we call them equivalent fractions.

You can produce lots of equivalent fractions by multiplying or dividing the top and bottom by the same number.

Flow diagram showing fractions being divided by 2, 3 then 4.

If you are asked to fill in a missing number, remember that the top and bottom must be multiplied or divided by the same number.

Question

What is the missing number?

\[\frac{4}{5} = \frac{?}{{15}}\]

Here, the denominator \(5\) is multiplied by \(3\) to get \(15\).

So you must multiply the numerator, \(4\), by \(3\):

\[\frac{4}{5} = \frac{{12}}{{15}}\]

The missing number is \(12\).