Chapter 1.7, Problem 145ES

Tell whether each expression represents a positive number or a negative number when m and n are negative.

The following is a proof that a positive number times a negative number is negative. Provide a reason for each step. Assume that $a>0\text{ and }b>0$.

$\begin{array}{c}a\left(-b\right)+ab=a\left[-b+b\right]\\ =a\left(0\right)\\ =0\end{array}$

Therefore, $a\left(-b\right)$

is the opposite of $ab$.