# How do you simplify 5/6+8/9 ?

Feb 10, 2017

See the entire simplification process below:

#### Explanation:

First, we need to get each fraction over a common denominator in order to be able to add the fractions. In this case the lowest common denominator is $18$. To get each fraction over this common denominator we must multiply it by the appropriate form of $1$:

$\left(\frac{5}{6} \times \frac{3}{3}\right) + \left(\frac{8}{9} \times \frac{2}{2}\right) \to \frac{15}{18} + \frac{16}{18}$

We can now add the two fractions:

$\frac{15}{18} + \frac{16}{18} \to \frac{15 + 16}{18} \to \frac{31}{18}$

Feb 10, 2017

$\textcolor{g r e e n}{\frac{31}{18}}$ or $\textcolor{g r e e n}{1 \frac{13}{18}}$

#### Explanation:

If we note that the LCM (Least Common Multiple) of the denominators $6$ and $9$
is $18$,
Then $\frac{5}{6} = \frac{5}{6} \times \frac{3}{3} = \frac{15}{18}$

and $\frac{8}{9} = \frac{8}{9} \times \frac{2}{2} = \frac{16}{18}$

So $\frac{5}{6} + \frac{8}{9}$ is the same as $\frac{15}{18} + \frac{16}{18}$

$15$ eighteenths $+ 16$eighteenths $= 31$ eighteenths
$\textcolor{w h i t e}{\text{XXX}}$($15$ of anything plus $16$ of the same thing
$\textcolor{w h i t e}{\text{XXXX}}$equals $31$ of that thing)

We would normally write $31$ eighteenths as
$\textcolor{w h i t e}{\text{XXX}} \frac{31}{18}$
or
we could write it as a mixed fraction:
$\textcolor{w h i t e}{\text{XXX}} 1 \frac{13}{18}$