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Absolute Value



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The absolute value of a number describes the distance of the number on the number line from 0. It does not consider which direction from 0 the number lies. The absolute value of a number is always positive.


The absolute value of 3 is 3 which means that its distance from 0 is 3 units
 
The absolute value of  −3 is also 3 which means that its distance from 0 is 3 units
 
The symbol for absolute value is two straight lines || (called bars) surrounding the number or expression for which you wish to indicate absolute value.

For example:
| 6 | = 6 which means the absolute value of 6 is 6.
| 6 | = 6 which means the absolute value of -6 is 6.

| 3 7 | = | 4 | = 4

| 6 + 3(5) | = | 6 15 | = | 9 | = 9



Have a look at the following videos for more examples on absolute values:

It is important to note that the absolute value bars do NOT work in the same way as parentheses. Recall that − (−5) = (−1) × (−5) = +5.

However, for the absolute value it is done by removing the absolute bar and then performing the sign operation.
−| −5 | = −(+5) = (−1) × (+5) = −5

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