# How do you simplify the fraction 27/54?

Nov 15, 2016

$\frac{1}{2}$

#### Explanation:

To simplify the fraction consider the $\textcolor{b l u e}{\text{common factors}}$ of the numerator/denominator and $\textcolor{b l u e}{\text{cancel}}$ them.

That is 27 and 54 have a $\textcolor{b l u e}{\text{common factor}}$ of 27 and thus can be $\textcolor{b l u e}{\text{cancelled}}$ by dividing both by 27.

$\Rightarrow \frac{27}{54} = {\cancel{27}}^{1} / {\cancel{54}}^{2} = \frac{1}{2}$

A slightly longer approach is to cancel by the lowest common factor which is 3 and repeat the process.

$\Rightarrow \frac{27}{54} = {\cancel{27}}^{9} / {\cancel{54}}^{18} = \frac{9}{18}$

now cancel by 3 again.

$\Rightarrow \frac{9}{18} = {\cancel{9}}^{3} / {\cancel{18}}^{6} = \frac{3}{6}$

cancel by 3 again.

$\frac{3}{6} = {\cancel{3}}^{1} / {\cancel{6}}^{2} = \frac{1}{2} \leftarrow \text{ in simplest form}$

The fraction is said to be in $\textcolor{b l u e}{\text{simplest form}}$ when no other factor but 1 will divide into numerator/denominator.