# Question #89ec6

##### 1 Answer
Jan 18, 2018

Morgan has $\frac{23}{36}$ of a cake left

#### Explanation:

Morgan had $\frac{8}{9}$ of a cake and ate $\frac{1}{4}$ of it so essentially we have this expression:

$\frac{8}{9} - \frac{1}{4}$

To subtract fractions with different denominators we have find the least common denominator

If we list the multiples of $4$ and $9$

$4 : 4 , 8 , 12 , 16 , 24 , 28 , 32 , \textcolor{red}{36}$

$9 : 9 , 18 , 27 , \textcolor{red}{36} , 45$

$36$ is the least common denominator and so we'll have to manipulate each fraction such that both denominators are $36$

$\frac{8}{9} - \frac{1}{4} \implies \left[\frac{4}{4}\right] \cdot \frac{8}{9} - \frac{1}{4} \cdot \left[\frac{9}{9}\right] = \frac{32}{36} - \frac{9}{36}$

So we now have:

$\frac{32}{36} - \frac{9}{36} = \frac{23}{36}$

So she has $\frac{23}{36}$ of a cake left