Q40. - Algebra 1

Question

Find the following quotient.

$4÷\left(-\frac{2}{7}\right)$

Step-by-Step Solution

Answer

The quotient is $-14$.

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 $-\frac{2}{7}$

$-\frac{2}{7}.\left(-\frac{7}{2}\right)=1$

Hence, the reciprocal of $-\frac{2}{7}$ is $-\frac{7}{2}$.

Step 4. Find the quotient of the given numbers.

$\begin{array}{c}4÷\left(-\frac{2}{7}\right)=4\times \left(-\frac{7}{2}\right)\\ =-14\end{array}$