Chapter 0.5, Problem 17E

To determine

The simplified value of the expression $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)$ .

Answer to Problem 17E

The simplified value of the expression $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)$ is $-\frac{1}{2}$ .

Explanation of Solution

Given information:

The expression $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)$ .

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 $\left(\right),\times \text{ or }\cdot$ .

Product of a negative and a positive real number is always negative.

Calculation:

Consider the expression $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)$ .

It can be simplified as,

  $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)=-\frac{1\cdot 3}{2\cdot 3}$

Striking off the common terms, we get,

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

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,

  $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)=-\frac{1}{2}$

Thus, the simplified value of the expression $\frac{3}{2}\cdot \left(-\frac{1}{3}\right)$ is $-\frac{1}{2}$ .