Simplifying fractions

Before taking a look at simplifying algebraic fractions, let's remind ourselves how to simplify numerical fractions.

Sometimes the top and bottom of a fraction can be divided by the same number. This is called cancelling down. It is also called simplifying the fraction. Fractions often have to be written in their simplest terms. This means they have to be cancelled down until they cannot be cancelled down any more.

To do this, look for fractions where the numerator (top number) and the denominator (bottom number) are both multiples of the same times table. This tells you their common factor, which you use to divide the top and bottom number, in order to simplify or cancel down the fraction as required.

Example

Write this fraction in its simplest form: \frac{{12}}{{16}}

Answer

Here, notice that the top and bottom numbers are both in the 4 times table (common factor 4), therefore divide both numbers by 4.

\frac{{12}}{{16}} = \frac{3}{4}

If you noticed that 12 and 16 were both in the 2 times table (common factor 2), you would get the answer:

\frac{{12}}{{16}} = \frac{6}{8}

But this is still not cancelled down to its simplest form as 6 and 8 are both in the 2 times table again.

This means that this fraction needs to be simplified further by again dividing the top and bottom numbers by 2.

\frac{{12}}{{16}} = \frac{6}{8} = \frac{3}{4}

So, it is better to choose the highest common factor to divide, as that means that the fraction can be simplified in just one step.