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Absolute Value

The absolute value of a number is its distance from zero on a number line. For instance, 4 and -4 have the same absolute value (4):

Math diagram

So, the absolute value of a positive number is just the number itself, and the absolute value of a negative number is its opposite. The absolute value of 0 is 0. Easy!

The absolute value of x is written | x |. So,

|4| = 4

|-4| = 4

|54221.997| = 54221.997

|(-1/4)| = 1/4

A Few Rules to Remember:

The absolute value of a product is the same as the product of the absolute values . For instance:

|(9)(-3)| = |9||-3| = (9)(3) = 27

|(-11)(-10)| = |-11||-10| = (11)(10) = 110

| x ³ y | = | x ³ || y|

The same goes for quotients .

|(10)/(-5)| = |10|/|-5| = 10/5 = 2

However, the same thing doesn't always work for addition and subtraction!

|-3 + 7| = |4| = 4, but

|-3| + |7| = 3 + 7 = 10

So be careful!

The Graph of the Absolute Value Function

The function y = | x | looks like this:

Math diagram