Working with Negative Numbers
What is a Negative Number?
Well, when you think about something that is negative, think about it as it’s the opposite of something. Every positive number has a negative number that’s its opposite.
Even when it comes to math—addition is the opposite of subtraction.
Multiplication is also the opposite of division.
So, ho does this apply to addition and subtraction?
Adding two positive numbers gives you a positive result.
(+) + (+) = +
3 + 2 = 5
Adding a negative number to a positive number is just like subtraction (you are really finding the difference between the two numbers).
(-) + (+) = You will find the difference and the number that’s the largest will have its sign be the sign of the answer.
- 2 + 3 = 1
When you start with a negative and subtract a positive number, you are moving left on the number line.
(-) - (+) = Move left on the number line
- 2 - 2 = - 4
When you subtract a negative number, you are doing the opposite of subtraction, so therefore you add.
-2 - (-3) =
- 2 + 3 = 1
This is just something you are going to have to practice over-and-over again because you will see this a lot in algebra.
More examples:
What about Multiplication and Division?
Multiplication and division are simple when it comes to working with negative numbers: if the signs are the same the answer is positive, if the signs are different the answer is negative.
So, if you know your multiplication and division facts, you will be able to easily figure out if the answer is negative or positive, when multiplying or dividing with negative numbers.
When you have a negative times a negative the answer will be positive.
- 8 * - 7 = 56
When you have a positive times a positive the answer will be positive.
8 * 7 = 56
When you have a negative times a positive the answer will be negative.
8 * - 7 = -56
NOTE: if you have an odd number of negative numbers to multiply or divide, the answer is going to be negative, but you should use the Order of Operations to help you find the right answer.
- 3 * - 4 * -3 = - 36