In physics and mathematics, the **absolute value** of a real number (x) is the distance that x is from zero on the number line. Since the distances are not negative, the absolute value is not negative either. For example: *|8| = 8 (the absolute value of 8 is 8) and |-8| = 8 (absolute value of -8 is 8)*. This represents that both 8 and -8 are 8 units away from zero.

In mathematics, there is a definition of absolute value that is expressed:

**|x| = {x, if x ≥ 0**

** {-x, if x < 0**

This definition is explained as follows:

Regarding the absolute value notation, the number is always written between vertical bars:

In addition, the absolute value can be applied in different calculations:

**Calculation in which the trade is between the bars**. If all the numbers are inside the bars, the operation is first solved and then the absolute value is assigned to the result. For example:

*|-10 -7| = |-17| =***17****Calculation in which there is only one number between the bars**. In this case, the absolute value of the number between the bars is first determined, and then the operation is solved. For example:

*|-2| – 5 =***two**–5 = -3

## Absolute Value Properties

The absolute value has different properties, the most important are:

## Absolute Value Examples

- |-107| =
**107**(absolute value of -107 is 107) - |2.34353| =
**2.34353**(the absolute value of 2.34353 is 2.34353) - |⅛| =
**⅛**(the absolute value of ⅛ is ⅛) - |43| =
**43**(absolute value of 43 is 43) - |-¼| =
**¼**(the absolute value of -¼ is ¼) - |-5| =
**5**(absolute value of -5 is 5) - |-32,789| =
**32,789**(absolute value of -32,789 is 32,789) - |78| =
**78**(the absolute value of 78 is 78) - |-1½| =
**1½**(the absolute value of -1½ is 1½) - |-984.32| =
**984.32**(absolute value of -984.32 is 984.32) - |24| =
**24**(the absolute value of 24 is 24) - |-476| =
**476**(absolute value of -476 is 476) - |139.2| =
**139.2**(absolute value of 139.2 is 139.2) - |12⅙| =
**12⅙**(the absolute value of 12⅙ is 12⅙) - |-32⅔| =
**32⅔**(the absolute value of -32⅔ is 32⅔) - |7,333| =
**7,333**(the absolute value of 7,333 is 7,333) - |-2.13| =
**2.13**(absolute value of -2.13 is 2.13) - |-19| =
**19**(absolute value of -19 is 19) - |-6.5| =
**6.5**(absolute value of -6.5 is 6.5) - |-⅝| =
**⅝**(absolute value of -⅝ is ⅝)

## Examples of absolute value in operations

- |45 + 17| –12 = |62| – 12 =
**62**– 12 = 50 - |119 – 200| = |-81| =
**81** - 200 * |-2| = 200 *
**two**= 400 - |49 / -7| = |-7| =
**7** - 356 + |-100| = 356 +
**100**= 456 - |3 – 3| = |0| =
**0** - |200| – 50 =
**200**– 50 = 150 - |-3| *80 =
**3***80 = 240 - |-350| / 10 =
**350**/ 10 = 35 - |-2*15| + 7 = |-30| + 7 =
**30**+7 = 37

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