Chapter 0.5, Problem 33E

To determine

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

Answer to Problem 33E

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

Explanation of Solution

Given information:

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

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 $\frac{3}{2}÷\frac{1}{2}$ .

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,

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

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,

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

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