# What is the value of ((2/3-5/6)/(3/4))?

Jan 2, 2017

$\left(\frac{\frac{2}{3} - \frac{5}{6}}{\frac{3}{4}}\right) = - \frac{2}{9}$

#### Explanation:

$\left(\frac{\frac{2}{3} - \frac{5}{6}}{\frac{3}{4}}\right)$

The fractions in the numerator must have a common denominator. Determine the least common denominator (LCD) by determining the lowest multiple that each have in common.

$3 :$$3 , \textcolor{red}{6} , 9$
$6 :$$\textcolor{red}{6} , 12 , 18$

The LCD is $6$. Multiply $\frac{2}{3}$ by an equivalent fraction to obtain a denominator of $6$.

$\frac{\left(\frac{2}{3} \times \textcolor{red}{\frac{2}{2}}\right) - \left(\frac{5}{6}\right)}{\frac{3}{4}}$

Simplify.

$\frac{\left(\frac{4}{6} - \frac{5}{6}\right)}{\frac{3}{4}} =$

$\frac{- \frac{1}{6}}{\frac{3}{4}} =$

$- \frac{\frac{1}{6}}{\frac{3}{4}}$

When dividing by a fraction, invert and multiply.

$- \frac{1}{6} \times \frac{4}{3}$

Simplify.

$- \frac{4}{18}$

Simplify.

$- \frac{2}{9}$