Chapter 0.5, Problem 6E

To determine

The simplified value of the expression $108÷\left(-0.9\right)$ .

Answer to Problem 6E

The simplified value of the expression $108÷\left(-0.9\right)$ is $-120$ .

Explanation of Solution

Given information:

The expression $108÷\left(-0.9\right)$ .

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

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 $108÷\left(-0.9\right)$ .

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,

  $\begin{array}{c}108÷\left(-0.9\right)=108\left(\frac{1}{-0.9}\right)\\ =\frac{108}{-0.9}\end{array}$

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,

  $\begin{array}{c}108÷\left(-0.9\right)=108\left(\frac{1}{-0.9}\right)\\ =\frac{108}{-0.9}\\ =-\frac{108}{0.9}\\ =-120\end{array}$

Thus, the simplified value of the expression $108÷\left(-0.9\right)$ is $-120$ .