Question

Simplify$-\frac{3}{8}+\frac{5}{12}$

Short answer

On simplifying the given expression, we get

$-\frac{3}{8}+\frac{5}{12}=\frac{1}{24}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Theexpressiongivenis}\\ -\frac{3}{8}+\frac{5}{12}\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Take the LCM

$\begin{array}{l}\Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{\left(-3\times 12\right)+\left(5\times 8\right)}{8\times 12}\\ \Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{-36+40}{96}\\ \Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{4}{96}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{4}{96}\\ \Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{\cancel{4}}{\cancel{4}\times 24}\\ \Rightarrow -\frac{3}{8}+\frac{5}{12}=\frac{1}{24}\end{array}$