Absolute Value

Absolute Value means ...

... only how far a number is from zero:

absolute value 6 either way on number line

"6" is 6 abroad from zero,
and "−6" is also half-dozen abroad from zero.

And so the absolute value of six is 6,
and the absolute value of −vi is also 6

More Examples:

  • The absolute value of −9 is 9
  • The accented value of 3 is 3
  • The absolute value of 0 is 0
  • The absolute value of −156 is 156

No Negatives!

So in practice "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Accented Value Symbol

To bear witness that we want the accented value of something, nosotros put "|" marks either side (they are called "bars" and are constitute on the right side of a keyboard), like these examples:

Sometimes absolute value is also written as "abs()", so abs(−1) = one is the same as |−1| = 1

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images/absolute.js

Decrease Either Way Effectually

And information technology doesn't matter which way effectually nosotros do a subtraction, the accented value will always exist the aforementioned:

|8−iii| = 5 (8−3 = five)

|3−8| = v (iii−8 = −5, and |−5| = 5)

More Examples

Here are some more than examples of how to handle absolute values:

|−3×6| = xviii
Because −3×vi = −18, and |−xviii| = 18

−|five−2| = −3
Considering v−2 = 3 and so the first minus gets us −3

−|ii−5| = −3
Because two−5 = −iii , |−three| = 3, and then the first minus gets us −3

−|−12| = −12
Because |−12| = 12 and so the beginning minus gets usa −12

Learn more at Accented Value in Algebra

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