Question

In your own words, state the rules for multiplying and dividing integers.

Short answer

The rules are explained in the solution.

Step-by-step solution

Step 1. Explain the multiplication of two numbers.

If we are multiplying two integers, the integers can be positive or negative, what would be the result after multiplication, is shown below as,

$$\begin{gathered} RuleResult \\ \left(+\right)\left(+\right)=+ \\ \left(-\right)\left(-\right)=+ \\ \left(+\right)\left(-\right)=- \\ \left(-\right)\left(+\right)=- \end{gathered}$$

For example:

$\begin{array}{rcl}5·3& =& 15\\ \left(-5\right)\left(-3\right)& =& 15\\ \left(-5\right)\left(3\right)& =& -15\\ \left(5\right)\left(-3\right)& =& -15\end{array}$

Step 2. Explain the division of two numbers.

If we are dividing two integers a andb, the integers can be positive or negative, what would be the result after division, is shown below as,

$\begin{array}{rcl}\frac{\left(+\right)}{\left(+\right)}& =& +\\ \frac{\left(-\right)}{\left(-\right)}& =& +\\ \frac{\left(-\right)}{\left(+\right)}& =& -\\ \frac{\left(+\right)}{\left(-\right)}& =& -\end{array}$

Let's suppose 5 and 15 are two integers. So,

$\begin{array}{rcl}\frac{\left(15\right)}{\left(5\right)}& =& 3\\ \frac{\left(-15\right)}{\left(-5\right)}& =& 3\\ \frac{\left(-15\right)}{\left(5\right)}& =& -3\\ \frac{\left(15\right)}{\left(-5\right)}& =& -3\end{array}$