Question

Find the following quotient.

$\frac{3}{7}÷\left(-\frac{1}{5}\right)$

Short answer

The quotient is $-\frac{15}{7}$.

Step-by-step solution

Step 1. Formula Used.

The division of two fractions is given by multiplying the first fraction by the reciprocal of the second fraction.

$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

Step 2. Definition of reciprocal.

The product of any number and its reciprocal is 1.

Step 3. Find the reciprocal of the given number.

Reciprocal of$-\frac{1}{5}$

$-\frac{1}{5}·\left(-5\right)=1$

Hence, the reciprocal of $-\frac{1}{5}$is –5.

Step 4. Find the quotient of the given numbers.

Now by the definition of the quotient of two fractions:

$\begin{array}{c}\frac{3}{7}÷\left(-\frac{1}{5}\right)=\frac{3}{7}\times \left(-5\right)\\ =-\frac{15}{7}\end{array}$