Q38. - Algebra 1

Question

Find the following quotient.

$-1\frac{1}{3}÷\frac{2}{3}$

Step-by-Step Solution

Answer

The quotient is –2.

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 $\frac{2}{3}$

$\frac{2}{3}·\frac{3}{2}=1$

Hence the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Step 4. Find the quotient of the given numbers.

First, convert mixed fraction into an improper fraction and then calculate the quotient of two fractions:

$-1\frac{1}{3}=-\frac{1\times 3+1}{3}=-\frac{4}{3}$

So, then given quotient becomes

$$\begin{gathered} -1\frac{1}{3}÷\frac{2}{3}=-\frac{4}{3}÷\frac{2}{3} \\ =-\frac{4}{3}\times \frac{3}{2} \\ =-2 \end{gathered}$$