Cancelling fractions
Sometimes you can divide the top and bottom of a fraction by the same number. This is called cancelling down.
It is also called simplifying the fraction. You often have to write a fraction in its simplest form.
This means that you have to cancel it down until it cannot be cancelled down any more.
Example
If there are \({20}\) socks in a drawer and \({8}\) of them are red, \(\frac{8}{20}\) of the socks are red.
This isn't the simplest form of this fraction because both \({8}\) and \({20}\) can be divided by \({4}\).
This cancels to \(\frac{2}{5}\). We can't divide this any more, so this is the fraction in its simplest form.
Question
Write this fraction in its simplest form: \(\frac{{12}}{{16}}\)
Divide by \(4\).
You can do this in two stages.
Dividing top and bottom by \(2\) gives you \(\frac{6}{8}\).
Then dividing top and bottom by \(2\) again, you get \(\frac{3}{4}\).
If you had divided top and bottom originally by \(4\) you would have reached the answer more quickly.
When you have worked out a fraction question, you should always cancel the fraction down to the simplest form.
Question
What fraction of \({1}\) metre is \({}~38cm\) in its simplest form?
\({38}~cm\) as a fraction of \({100}~cm\) is:
\(\frac{38}{100}\)
Both numerator and denominator can be divided by \(2\) so we can cancel to the simplest form:
\(\frac{19}{50}\)
