# Question 659dc

Feb 28, 2017

$\frac{12}{8} = \frac{3}{2}$

#### Explanation:

To add 2 fractions we require the $\textcolor{b l u e}{\text{denominators}}$ to be the same value.

In this case they are, both 8

We can therefore $\textcolor{b l u e}{\text{add the numerators}}$ while leaving the denominator as it is.

$\Rightarrow \frac{5}{8} + \frac{7}{8}$

$= \frac{5 + 7}{8}$

$= \frac{12}{8}$

We can $\textcolor{b l u e}{\text{simplify}}$ the fraction by dividing the numerator/denominator by the $\textcolor{b l u e}{\text{highest common factor}}$ of 12 and 8, which is 4

rArr12/8=(12÷4)/(8÷4)=3/2larrcolor(red)" in simplest form"#

This process is normally done using $\textcolor{b l u e}{\text{cancelling}}$

$\Rightarrow \frac{12}{8} = {\cancel{12}}^{3} / {\cancel{8}}^{2} = \frac{3}{2} \leftarrow \textcolor{red}{\text{ in simplest form}}$

A fraction is in $\textcolor{b l u e}{\text{simplest form}}$ when no other factor but 1 divides into the numerator/denominator.