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# Absolute Value Definition

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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

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

Absolute Value Definition Resources:

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Khan Academy - Video Learn Zillion - Video Virtual Nerd - Video Text Lessons:

Khan Academy - Text Lesson Math is Fun - Text Lesson PurpleMath - Text Lesson Worksheets:

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