# How do you simplify 7/8 + 11/14 -5/6?

May 2, 2018

$\frac{139}{168}$

#### Explanation:

In order to add or subtract fractions you have to have the same denominator:

Let's use prime factors to find the $L C M$. It is not an obvious one.

$\text{ } 8 = 2 \times 2 \times 2$
$\text{ } 6 = 2 \textcolor{w h i t e}{x . \times \times} \times 3$
$\text{ } 14 = \underline{2 \textcolor{w h i t e}{x . \times \times \times x} \times 7}$
$L C M = 2 \times 2 \times 2 \times 3 \times 7 = 168$

$\frac{7}{8} + \frac{11}{14} - \frac{5}{6}$

$\left(\frac{7}{8} \times \frac{21}{21}\right) + \left(\frac{11}{14} \times \frac{12}{12}\right) - \left(\frac{5}{6} \times \frac{28}{28}\right)$

$= \frac{147 + 132 - 140}{168}$

$= \frac{139}{168}$