odd
odd = odd
even
odd = even
Positive and Negative Numbers
Positive and negative numbers are governed by rules similar to those that have to do with even and odd numbers. First, for their quick definitions:
Positive numbers are numbers that are greater than zero. Negative numbers are numbers that are less than zero. The number zero is neither positive nor negative.
Operations of Positive and Negative Numbers
The following rules define how positive and negative numbers operate under various operations.
Addition and Subtraction:
When adding and subtracting negative numbers, it helps to remember the following:
Adding a negative number is the same as subtracting its opposite. For example:
Subtracting a negative number is the same as adding its opposite. For example:
Multiplication:
positive
positive = positive
negative
negative = positive
positive
negative = negative
Division:
positive
positive = positive
negative
negative = positive
positive
negative = negative
The rules for multiplication and division are exactly the same since any division operation can be written as a form of multiplication:
a
b = a/b = a 
1/b.
Absolute Value
The absolute value of a number is the distance on a number line between that number and zero. Or, you could think of it as the positive “version” of every number. The absolute value of a positive number is that same number, and the absolute value of a negative number is the opposite of that number.
The absolute value of x is symbolized by |x|.
Solving an equation with an absolute value in it can be particularly tricky. As you will see, the answer is often ambiguous. Take a look at the following equation:
We can simplify the equation in order to isolate |x|:
Knowing that |x| = 2 means that x = 2 and x = –2 are both possible solutions to the problem. Keep this in mind; we’ll deal more with absolute values in equations later on in the Algebra chapter.
