Chapter 0.5, Problem 3E

To determine

The simplified value of the expression $42.3÷\left(-6\right)$ .

Answer to Problem 3E

The simplified value of the expression $42.3÷\left(-6\right)$ is $-7.05$ .

Explanation of Solution

Given information:

The expression $42.3÷\left(-6\right)$ .

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 $42.3÷\left(-6\right)$ .

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,

  $\begin{array}{c}42.3÷\left(-6\right)=42.3\left(\frac{1}{-6}\right)\\ =\frac{42.3}{-6}\end{array}$

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,

  $\begin{array}{c}42.3÷\left(-6\right)=42.3\left(\frac{1}{-6}\right)\\ =\frac{42.3}{-6}\\ =-\frac{42.3}{6}\\ =-7.05\end{array}$

Thus, the simplified value of the expression $42.3÷\left(-6\right)$ is $-7.05$ .