Question

Simplify $-\frac{1}{8}+\frac{7}{12}$

Short answer

On simplifying the given expression, we get

$-\frac{1}{8}+\frac{7}{12}=\frac{11}{24}$

Step-by-step solution

Step 1. Given information  

$\begin{array}{l}\text{Theexpressiongivenis}\\ -\frac{1}{8}+\frac{7}{12}=\frac{11}{24}\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Take the LCM 

$\begin{array}{l}\Rightarrow -\frac{1}{8}+\frac{7}{12}=\frac{\left(-1\times 12\right)+\left(7\times 8\right)}{8\times 12}\\ \Rightarrow -\frac{1}{8}+\frac{7}{12}=\frac{-12+56}{96}\\ \Rightarrow -\frac{1}{8}+\frac{7}{12}=-\frac{44}{96}\end{array}$

Step 3. Simplify the fraction  

$\begin{array}{l}\Rightarrow -\frac{1}{8}+\frac{7}{12}=-\frac{44}{96}\\ \Rightarrow -\frac{1}{8}+\frac{7}{12}=-\frac{\cancel{4}\times 11}{\cancel{4}\times 24}\\ \Rightarrow -\frac{1}{8}+\frac{7}{12}=\frac{11}{24}\end{array}$