# How do you simplify 1/2 + 2/3 + 3/4 ?

Aug 2, 2016

$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{23}{12} = 1 \frac{11}{12}$

#### Explanation:

To simplify $\frac{1}{2} + \frac{2}{3} + \frac{3}{4}$, we can add them if the denominators are common. Now as LCD of the denominators $2$, $3$ and $4$ is $12$

$\frac{1}{2} + \frac{2}{3} + \frac{3}{4}$

$= \left(\frac{1}{2} \times 1\right) + \left(\frac{2}{3} \times 1\right) + \left(\frac{3}{4} \times 1\right)$

= $\frac{1 \times 6}{2 \times 6} + \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3}$

= $\frac{6}{12} + \frac{8}{12} + \frac{9}{12}$

= $\frac{6 + 8 + 9}{12}$

= $\frac{23}{12}$ or $\left(\frac{12 + 11}{12}\right)$ or $\left(\frac{12}{12} + \frac{11}{12}\right)$ or $1 \frac{11}{12}$