Chapter 0.5, Problem 31E

To determine

The quotient of the expression $\frac{2}{3}÷\frac{1}{3}$ .

Answer to Problem 31E

The quotient of the expression $\frac{2}{3}÷\frac{1}{3}$ is $2$ .

Explanation of Solution

Given information:

The expression $\frac{2}{3}÷\frac{1}{3}$ .

Formula used:

Product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Calculation:

Consider the expression $\frac{2}{3}÷\frac{1}{3}$ .

Recall that division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Apply it,

  $\begin{array}{c}\frac{2}{3}÷\frac{1}{3}=\frac{2}{3}\cdot \left(\frac{1}{\frac{1}{3}}\right)\\ =\frac{2}{3}\cdot \frac{3}{1}\end{array}$

Recall that product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Simplify it,

  $\begin{array}{c}\frac{2}{3}÷\frac{1}{3}=\frac{2}{3}\cdot \left(\frac{1}{\frac{1}{3}}\right)\\ =\frac{2}{3}\cdot \frac{3}{1}\\ =\frac{2}{1}\\ =2\end{array}$

Thus, the quotient of the expression $\frac{2}{3}÷\frac{1}{3}$ is $2$ .