# What is (3/4-2/3)+(1/2+1/3)?

Apr 6, 2018

$A n s w e r = \frac{11}{12}$

#### Explanation:

First we are gonna take L.C.M of $4$ and $3$ which is $12$ and then take L.C.M of $2$ and $3$ that is $6$.
$= \left(\frac{3}{4} - \frac{2}{3}\right) + \left(\frac{1}{2} + \frac{1}{3}\right)$
$= \left(\frac{3 \cdot 3}{4 \cdot 3} - \frac{2 \cdot 4}{3 \cdot 4}\right) + \left(\frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2}\right)$
$= \left(\frac{9 - 8}{12}\right) + \left(\frac{3 + 2}{6}\right)$
$= \frac{1}{12} + \frac{5}{6}$
Now what we are gonna do is taking L.C.M of $12$ and $6$ that is $12$
$= \frac{1}{12} + \frac{5 \cdot 2}{6 \cdot 2}$
$= \frac{1}{12} + \frac{10}{12}$
$= \frac{1 + 10}{12}$
$= \frac{11}{12}$