# What is the simplified value of 2/9 + 1/2 - 7/8 + 5/6 ?

May 5, 2016

$\frac{2}{9} + \frac{1}{2} - \frac{7}{8} + \frac{5}{6} = \frac{49}{72}$

#### Explanation:

To simplify $\frac{2}{9} + \frac{1}{2} - \frac{7}{8} + \frac{5}{6}$, we should first make all denominators equal. For this, we ought to know Least Common Denominator (LCD) of $\left\{9 , 2 , 8 , 6\right\}$, which is $72$.

Hence, $\frac{2}{9} + \frac{1}{2} - \frac{7}{8} + \frac{5}{6}$

= $\frac{2 \times 8}{9 \times 8} + \frac{1 \times 36}{2 \times 36} - \frac{7 \times 9}{8 \times 9} + \frac{5 \times 12}{6 \times 12}$

= $\frac{16}{72} + \frac{36}{72} - \frac{63}{72} + \frac{60}{72}$

= $\frac{16 + 36 - 63 + 60}{72}$

= $\frac{49}{72}$