Prealgebra for Two-Year Colleges/Appendix (procedures)/Absolute value

Absolute value
The absolute value of a number is found by applying a simple rule: If you see a negative sign in front of the number, change it to a plus sign. If you see a plus sign, leave it alone. So, for example, the absolute value of -17 is +17. The absolute value of +36 is +36.

Another way to understand the absolute value of a number is to think about the number line:



The absolute value of a number is the distance from zero to that number on the number line.

The absolute value of x is usually written as |x|. On calculators and computers it is sometimes written as abs (x).

Questions:

1. Calculate the absolute value of the following numbers:
 * a. -5
 * b. 9
 * c. -3.8
 * d. -139,462
 * e. 5/8

2. What is the absolute value of zero? Explain.

3. Calculate the following:


 * a. |27|
 * b. |-1.9|
 * c. |3 - 7|
 * d. |3 - 0.5|
 * e. abs (-6)

4. Draw a graph of abs(x) from -5 to +5. Can abs(x) ever be less than zero? How can you see that from your graph?

Answers:

1. a. 5 b. 9 c. 3.8 d. 139,462 e. 5/8

2. Zero, because zero is exactly zero away from zero on the number line.

3. a. 27 b. 1.9 c. |3-7| = |-4| = 4 d. |3-0.5| = |2.5| = 2.5 e. 6

4. [[Media:Absolute value.svg|Image of the absolute value of x]]