In algebra, we follow three simple rules when we are multiplying integer numbers.  They are listed below

• If the two numbers are both positive, the answer is positive.
• If the two numbers are both negative, the answer is positive.
• If the two numbers have different signs, the answer is negative.

Example:  Find the product \(\left( { - 2} \right)\left( { - 12} \right)\)

Solution:  Here both of the numbers are negative.  So according to our rule above, the answer will be positive.  We simply multiply \(2 \times 12\). The answer is

\(\left( { - 2} \right)\left( { - 12} \right) = 2 \times 12 = 24\)

Example:  Find the product \(\left( { - 3} \right)\left( { - 1} \right)\)

Solution:  We have both signs negative.  Then the answer will be positive.  The answer is

\(\left( { - 3} \right)\left( { - 1} \right) = \left( 3 \right)\left( 1 \right) = 3\)

Now you may be asking yourself, “Why is the product of two negative numbers positive?”  This is a very good question.  I will attempt to give you a reason here.  For a formal proof, see the article entitled “Beginning Algebra – Dividing Integer Numbers” on this site.

Let’s think about it in terms of language.

Imagine that I told you to brush your teeth.  This is a positive statement telling you to do something.  There is no negatives in that statement, so the outcome is positive.

Now imagine that I told you “Do not brush your teeth.”  This involves one negative (not) and the answer is negative.

Finally, imagine that I told you “Do not not brush your teeth.”  In effect, I am telling you to brush your teeth!  The double negative yields a positive result!  Even in the English Language, two negatives make a positive!

Below you can download some free math worksheets and practice.