Definition of absolute value


Definition of absolute value: the absolute value of a number is the distance the number is from zero



Look at the following two graphs:

The first one shows 6 located at a distance of 6 units from zero.
We write |6| = 6


The second one shows -8 located at a distance of 8 units from zero.
We write |-8| = 8


You can see from this that the absolute value of a number is always positive with the exception of taking the absolute value of 0 (|0| = 0)

Therefore, do not write |5| = -5 or |4| = -4 please!


|6| means distance from 0 to 6


|-8| means distance from 0 to -8


For |-8| = 8, you could also argue that to get 8, you have to take the negative of -8 since - - 8 = 8


So, | - 8| = - - 8 = 8


This observation helps us to come up with a formal definition of absolute value


| x | = x if x is positive or zero, but -x if x is negative


This definition is important to understand before solving absolute value equations or absolute value inequalities


Calculate the absolute value of the following numerical expressions


1) 42 − 4 × 2


2) -5 + 5 × 2 − 15


3) -8 + 2 × 5


1)


| -8 + 2 × 5 | = | -8 + 10 |


| -8 + 2 × 5 | = | 2 |


| -8 + 2 × 5 | = 2


2)


| 42 − 4 × 2| = | 16 − 4 × 2|


| 42 − 4 × 2| = | 16 − 8|


| 42 − 4 × 2| = | 8 |


| 42 − 4 × 2| = 8


3)


|-5 + 5 × 2 − 15| = | -5 + 10 − 15 |


|(-5 + 5 × 2 − 15)| = | 5 − 15 |


|(-5 + 5 × 2 − 15)| = | -15 |


|(-5 + 5 × 2 − 15)| = 15








Recent Articles

  1. Bessy and Bob algebra word problem

    Jul 28, 17 02:38 PM

    Bessy has 6 times as much money as Bob, but when each earn $6. Bessy will have 3 times as much money as Bob. How much does each have before and after

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape








Recent Lessons

  1. Bessy and Bob algebra word problem

    Jul 28, 17 02:38 PM

    Bessy has 6 times as much money as Bob, but when each earn $6. Bessy will have 3 times as much money as Bob. How much does each have before and after

    Read More