# Evaluating Absolute Value Expressions

Updated on September 8, 2012

Absolute value expressions can be used to find the maximum and minimum temperatures of electronic devices, find the normal range of body temperatures, conduct time studies, and determine the accuracy of measurements.

So, what exactly is absolute value? The absolute value of a real number a , denoted by |a | and read “the absolute value of a ” is geometrically the distance that the number a is from 0 (zero) on the real number line.

The Definition of Absolute Value

If a is a real number, then the absolute value of a is

a │ = {a , if a≥ 0 and –a , if a < 0

Key Points:

(1) –a is read as the opposite of a and not as negative a.

(2) Real numbers a and –a are opposites meaning that each is the same distance from 0 on the real number line; just in opposite directions.

The first part of the definition means that the absolute value of a non-negative number is itself. Therefore, |¾|= ¾.

The second part of the definition means that the absolute value of a negative number is the opposite of the number. For example, |-¾| = -(-¾) = ¾. (The opposite of negative ¾ is positive ¾.)

Absolute value of real numbers is always positive or zero, with zero being the only number whose absolute value is 0. Therefore, |0| = 0.

Set I:Evaluate the following absolute value expressions.

1)|-23.6|

2)|11|

3)|0|

4)|-¾|

Evaluating Opposite Absolute Values

Whenever the opposite sign is outside of the vertical absolute value bars, the answer is the opposite of the absolute value. Since absolute value is always positive or zero, the opposite must be negative. For example, -|35| = -35. (The opposite of the absolute value of 35 is -35 because the absolute value of 35 is positive 35.) Keep in mind, this answer is not interpreted as negative absolute value, but as the opposite of the absolute value.

Set II:Evaluate the following absolute value expressions:

1.-|4.09|

2.-|-43|

3.-|-25|

4.-|½|

1)23.6

2)11

3)0

4)3/4

1)-4.09

2)-43

3)-25

4)-½

## Review Quiz - Decide whether each statement is true or false.

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