Q41. - Algebra 1

Question

Find the following quotient.

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

Step-by-Step Solution

Answer

The product is $\frac{5}{18}$.

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.

First, simplify the mixed fraction into important per fraction and then find its reciprocal 

$-1\frac{1}{5}=-\frac{1\times 5+1}{5}=-\frac{6}{5}$

Reciprocal of $-\frac{6}{5}$

$-\frac{6}{5}\times -\frac{5}{6}=1$ 

Hence, reciprocal of $-\frac{6}{5}$ is $-\frac{5}{6}$.

Step 4. Find the quotient of the given numbers.

By using the formula of the division of two fractions.

$$\begin{gathered} -\frac{1}{3}÷\left(-1\frac{1}{5}\right)=-\frac{1}{3}÷\left(-\frac{6}{5}\right) \\ =-\frac{1}{3}\times \left(-\frac{5}{6}\right) \left[\mathrm{productofsamesignispositive}\right] \\ =\left(\frac{1}{3}\times \frac{5}{6}\right) \\ =\frac{1\times 5}{3\times 6} \\ =\frac{5}{18} \end{gathered}$$