# Evaluating Absolute Value Expressions

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)–ais read as the opposite ofaand notas negativea.

(2) Real numbersaand–aare 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|

*Set I* *Answers* :

1)23.6

2)11

3)0

4)3/4

*Set II Answers:*

1)-4.09

2)-43

3)-25

4)-½

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