Question

Simplify$-\frac{3}{8}÷\left(-\frac{3}{10}\right)$

Short answer

On simplifying the given expression, we get

$-\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{5}{4}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Theexpressiongivenis}\\ -\frac{3}{8}÷\left(-\frac{3}{10}\right)\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Rewrite the expression 

$\begin{array}{l}\text{Todivide,multiplythefirstfractionbythereciprocalofthesecond.}\\ \Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=-\frac{3}{8}\times \left(-\frac{10}{3}\right)\\ \text{Determinethesignoftheproduct,andthenmultiply}\\ \Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{3\times 10}{8\times 3}\left[\text{Signofproduct,}\left(-\right)\left(-\right)=\left(+\right)\right]\\ \Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{30}{24}\end{array}$

Step 3. Simplify the fraction

$\begin{array}{l}\Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{30}{24}\\ \Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{\cancel{6}\times 5}{\cancel{6}\times 4}\\ \Rightarrow -\frac{3}{8}÷\left(-\frac{3}{10}\right)=\frac{5}{4}\end{array}$