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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):

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 as |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

|x³y| = |x³||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: