Absolute Value Expression

Introduction for absolute value expression:

          In mathematics, the absolute value (or modulus) |a| of a real number a is a's numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and -3.Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternion, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.


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Example Problems for Simplifying Absolute Value Expression:

Example 1:

Simplify the absolute value expression -|-5|

Solution:

-|-5|  (evaluate the absolute value part)

= - (+5) (evaluate the sign)

= - 5

Example 2:

Simplify the absolute value expression - |3-5|

Solution:

= - |3-5|(evaluate the absolute value part)

= - |-2|( evaluate the absolute value part)

= - (+2) (evaluate the sign)

= - 2

 Example 3:

Simplify the absolute value expression - |3 - (5 * 4)|

Solution:

= - |3 - (5 * 4)| (evaluate the absolute value part)

= - |3 - 20)| (evaluate the absolute value part)

= - |-17| (evaluate the absolute value part)

= - (+17) (evaluate the sign)

= - 17

Example 4:

Simplify the absolute values expression - |3 - (5^2)|

Solution:

= - |3 - (5^2)| (evaluate the absolute value part)

= - |3 - (25)| (evaluate the absolute value part)

= - |- 22| (evaluate the absolute value part)

= - (+ 22) (evaluate the sign)

= -22

Example 5:

Simplify the absolute value expression - |3 - 3^2)|

Solution:

= - |3 - 3^2)| (evaluate the absolute value part)

= - |3 + 9)| (evaluate the absolute value part)

= - |12| (evaluate the absolute value part)

= - ( 12 ) (evaluate the sign)

= - 12

Practice Problems for Simplifying Absolute Value Expression:

Problem 1:

Simplify the absolute value expression -|-15|

Solution for the absolute value expression is: -15

Problem 2:

Simplify the absolute value expression -|25-15|

Solution for the absolute value expression is: -10

Problem 3:

Simplify the absolute value expression -|25 – (15*2)|

Solution for the absolute value expression is: -5

Problem 4:

Simplify the absolute value expression |-5^2|

Solution for the absolute value expression is: 25

Problem 5:

Simplify the absolute value expression -|-(-35* 2)|

Solution for the absolute value expression is: -70