Absolute Value Definition

In this section, we think about the absolute value definition. What exactly is absolute value? How do we find the absolute value of a number? The absolute value of a number is the distance between the number and 0 on the number line. This means that two numbers such as: 2, and -2 will have the same absolute value. In each case, they are 2 units away from zero on the number line. For practical purposes, to find the absolute value of a positive number, it stays the same.
Example 1: Find the absolute value of 8
8 is a positive number, so the absolute value of 8 is just 8. Again, 8 is 8 units away from zero on the number line.
|8| = 8
To find the absolute value of a negative number, we simply change the sign or find the opposite of the number.
Example 2: Find the absolute value of -11
-11 is a negative number, so the absolute value of -11 is 11. We change the sign of -11 to +11. Again, -11 is 11 units away from zero on the number line.
|-11| = 11
Lastly, we will tackle some simplification problems that relate our last section on opposites to our current section on absolute value.
Example 3: Simplify -|-5|
First, find the absolute value of -5, which is 5
-(5), now we are left with the opposite of 5 or -5 as the answer.
-|-5| = -5