# How do you simplify \frac{9}{10}\times \frac{1}{3}-\frac{2}{5}\times \frac{1}{11}?

Mar 7, 2018

$\textcolor{p u r p \le}{\frac{29}{110}}$

#### Explanation:

$\left(\left(\frac{9}{10}\right) \cdot \left(\frac{1}{3}\right)\right) - \left(\left(\frac{2}{5}\right) \cdot \left(\frac{1}{11}\right)\right)$

$\implies \left(\frac{9}{30}\right) - \left(\frac{2}{55}\right)$

Now we have to find the L C M of 30, 55.

$30 \implies 2 \cdot 3 \cdot \textcolor{b r o w n}{5}$

$55 \implies 11 \cdot \textcolor{b r o w n}{5}$

As $\textcolor{b r o w n}{5}$ is duplicated in both numbers 30 & 55,

$L C M o f \left(30 , 55\right) = 2 \cdot 3 \cdot 11 \cdot \textcolor{b r o w n}{5} = 330$

$\implies \left(\frac{9}{30}\right) - \left(\frac{2}{55}\right) = \frac{\left(9 \cdot 11\right) - \left(2 \cdot 6\right)}{330} = \frac{99 - 12}{330}$

$\implies {\cancel{87}}^{\textcolor{red}{29}} / {\cancel{330}}^{\textcolor{red}{110}} = \textcolor{p u r p \le}{\frac{29}{110}}$