What is the value of the expression (2/3 - 5/6) divided by 3/4?

Jan 3, 2017

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

Explanation:

We'll first sort out the first part by equalizing denominators:

$\left(\frac{2}{3} \times \frac{2}{2}\right) - \frac{5}{6} = \frac{4}{6} - \frac{5}{6} = - \frac{1}{6}$

Dividing by a fraction is the same as multiplying by its inverse:

$= - \frac{1}{6} \times \frac{4}{3} = - \frac{4}{18} = - \frac{\cancel{2} \times 2}{\cancel{2} \times 9} = - \frac{2}{9}$