Algebra/Chapter 1/Integers

Factoring and Divisibility

Algebra Chapter 1: Elementary Arithmetic Section 5: Integers

Fractions

1.5: Integers

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In this section, we begin to expand beyond the scope of whole numbers by exploring negative numbers.

Order and Absolute Value

The absolute value (or modulus) of a real number $a$, denoted by $|a|$ refers to its distance from zero on the real number line. This value is always taken to be nonnegative. For example, the illustration on the left shows the following:

$|-5|=5\ |3|=3$

The absolute value of -5 is 5 because it is 5 away from zero, and the absolute value of 3 is 3 because it is 3 away from zero. The absolute value of a positive number or zero is always itself. Conversely, the absolute value of a negative number is its opposite.

Likewise, the distance between two numbers on the number line can be thought of as the absolute value of the difference between them.