Question

Simplify the following:

$\frac{2}{3}+\frac{-5}{12}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To simplify, convert the given fractions into equivalent fractions, having the same denominators.

LCM of $3$ and $12$ is $12$.

So,

$\Rightarrow \frac{2\times 4}{3\times 4}=\frac{8}{12}$ and

$\frac{-5\times 1}{12\times 1}=\frac{-5}{12}$

Step 2: Adding $\frac{8}{12}$ and $\frac{-5}{12}$

$\frac{8}{12}+\frac{-5}{12}$

$$\begin{gathered} =\frac{8-5}{12} \\ =\frac{3}{12} \\ =\frac{\cancel{3}}{{\displaystyle \underset{4}{\cancel{12}}}} \\ =\frac{1}{4} \end{gathered}$$

Hence, $\frac{4}{5}+\frac{3}{8}=\frac{1}{4}$.