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Chapter 2—Integers

2-3 Introducing Absolute Values

 When you complete the work for this section, you should be able to: Define the term, absolute value. Show the proper symbol for indicating an abolute-value function. Donstrate how to determine the absolute value of any signed integer.

 Definition The absolute value of an integer is its value without regard to the sign. Or to put it another way, the absolute value of an integer is its distance from the origin (zero) on the number line.

The absolute value of numbers is indicated by enclosing the numbers in a pair of vertical lines, | |.
For example, the absolute value of – 10 is written as | – 10 |.

Example 1

What is the absolute value of -5?

The distance between 0 and – 5 on the number line is 5 units. Therefore the absolute value of – 5 is equal to 5.

| – 5 |  = 5

Example 2

What is the absolute value of 3?

The distance between 0 and 3 on the number line is 3 units. Therefore the absolute value of 3 is equal to 3.

| 3 | = 3

Example 3

What is the absolute value of zero?

There no distance between 0 and 0 on the number line, therefore the absolute value of 0 is 0.

| 0 | = 0

Examples and Exercises

 Absolute Values Use these interactive examples and exercises to strengthen your understanding and build your skills:
 Thinking Mathematically See if you can explain this fact: The absolute value of an integer is equal or greater than the original value. Under what circumstances is the absolute value greater than the original value? Under what circumstances is the absolute value less than the original value?