Signed (Negative and Positive) Numbers and Absolute Value

Did you know that the term for making a positive number negative is negate?

To negate a number is to change its sign to the opposite sign, so you can negate a positive number to a negative one or vice versa.

Let's review:

 If you start off with a positive number and put a minus sign to it, it becomes negative, like so:

Before      After
   5            -5

If you already have a negative number and put a minus sign to it, it becomes positive:

Before      After
   -5          --5

 We don't actually write it out as "--5" but as just plain old "5".  That's what negating is all about.

♫ You put the minus sign in, you take the plus sign out, you put the plus sign back and negate it all about...♪


If you aren't into negating, you can put a bar on each side of the number and make it an absolute value.
 
Absolute value gives you the positive value of a number, no matter whether the number was positive or negative beforehand.

Be careful with this, because anything outside the bar will affect the value of the number. The safe zone only exists inside the bars!

|5| =5


|-5| =5

-|5|= -5

-|-5|= -5

Also, if you put an absolute value bar around 0, it really doesn't do anything because 0 doesn't have a value so it's neither positive nor negative.

The book that I am using to review, Basic Math and Pre-Algebra for Dummies, shows and talks about number lines for adding and subtracting with negative numbers. Number lines are fine and dandy to use to help you until you get to multiplication and division. Then it's confusing as hell. If you must draw number lines keep in mind that you need to flip them for multiplication/division.


Adding and Subtracting Negative Numbers

A trick you can use for adding positive and negative numbers is to just put the positive number at the front:

-5 + 10         this becomes       10 - 5 = 5

-5 + 10 - 7         this becomes       10 -7 - 5 = 3 - 5 = -2

If all the numbers are negative just pretend they aren't and remember to add the - at the end:

-5 -5      this becomes      5 + 5 = 10      don't forget the minus     = -10


Multiplying and Dividing Negative Numbers

Just remember:

When two numbers have different signs, the result is negative
-5 * 5 = -25          10 / -5 = -2

When two numbers have the same signs, the result is positive
5 * 5 = 25       -5 * -5 = 25       10/5 = 2


Don't be a pessimist about this now. Practice makes perfect:

Basic Math & Pre Algebra Workbook For Dummies

Click here for some problems to practice on


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