In algebra, we follow three simple rules when we are multiplying integer numbers. They are listed below
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.
Find each product.
This free worksheet contains 10 assignments each with 24 questions with answers.
Example of one question:
Watch bellow how to solve this example:
Find each product.
This free worksheet contains 10 assignments each with 24 questions with answers.
Example of one question:
Watch bellow how to solve this example:
Find each product.
This free worksheet contains 10 assignments each with 24 questions with answers.
Example of one question:
Watch bellow how to solve this example: