Chapter 0, Problem 10POT

To determine

The simplified value of the expression $-81÷\left(-3\right)$ .

Answer to Problem 10POT

The simplified value of the expression $-81÷\left(-3\right)$ is $27$ .

Explanation of Solution

Given information:

The expression $-81÷\left(-3\right)$ .

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 two negative real numbers is always a positive real number.

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 $-81÷\left(-3\right)$ .

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,

  $\begin{array}{c}-81÷\left(-3\right)=-81\left(\frac{1}{-3}\right)\\ =\frac{-81}{-3}\end{array}$

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 $\left(\right),\times \text{ or }\cdot$ and product of two negative real numbers is always a positive real number.

Simplify it,

  $\begin{array}{c}-81÷\left(-3\right)=-81\left(\frac{1}{-3}\right)\\ =\frac{-81}{-3}\\ =\frac{81}{3}\\ =27\end{array}$

Thus, the simplified value of the expression $-81÷\left(-3\right)$ is $27$ .