# How do you simplify 3/4+(1/4-1/6)?

Nov 23, 2016

$\frac{5}{6}$

#### Explanation:

First we must find common denominators.

4 and 6 are not the same number, so we need to find the lowest common number that they both go into. 24 is the lowest number that they both fit into. So, we must multiply these fractions by $\frac{6}{6}$ and $\frac{4}{4}$ respectively, because $\frac{6}{6} \mathmr{and} \frac{4}{4}$ are both equal to 1 and doing this will make all of their denominators 24.

$\frac{3}{4} \cdot \frac{6}{6} + \left(\left(\frac{1}{4} \cdot \frac{6}{6}\right) - \left(\frac{1}{6} \cdot \frac{4}{4}\right)\right)$
$\frac{18}{24} + \left(\frac{6}{24} - \frac{4}{24}\right)$

Next it is a matter of PEMDAS, or specific order of operations. PEMDAS states that we must first solve what is inside the parentheses before we can do the outsides.
$\left(\frac{6}{24} - \frac{4}{24}\right) = \frac{2}{24}$
$\frac{18}{24} + \left(\frac{2}{24}\right)$
And now we can do the addition outside the parentheses.
$\frac{20}{24}$
All there is left to do is simplify. Both 20 and 24 are divisible by 4.
$\frac{5}{6}$