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

Jun 21, 2016

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

#### Explanation:

As GCD of the denominators $1$, $3$ and $4$ is $12$. Hence

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

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

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

= $\frac{12}{12} + \frac{3}{12} + \frac{8}{12}$

= $\frac{12 + 3 + 8}{12} = \frac{23}{12}$

We can also write it as $1 + \frac{3}{12} + \frac{8}{12} = 1 + \frac{3 + 8}{12} = 1 \frac{11}{12}$