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

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Absolute value

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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).


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?


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. Image of the absolute value of x