# Absolute Value

### Absolute Value means ...

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

"6" is 6 away from zero, So the absolute value of 6 is |

More Examples:

- The absolute value of −9 is
**9** - The absolute 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).

### Absolute Value Symbol

To show that we want the absolute value of something, we put "|" marks either side (they are called "bars" and are found on the right side of a keyboard), like these examples:

|−5| = 5 | |7| = 7 |

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

### Subtract Either Way Around

And it doesn't matter which way around we do a subtraction, the absolute value will always be the same:

|8−3| = 5 | |3−8| = 5 |

(8−3 = 5) | (3−8 = −5, and |−5| = 5) |

### More Examples

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

|−3×6| = 18

(−3×6 = −18, and **|−18| = 18**)

−|5−2| = −3

(**5−2 = 3 **and then the
first minus gets you** −3**)

−|2−5| = −3

(**2−5 = −3 **, **|−3| = 3**, and then the
first minus gets you** −3**)

−|−12| = −12

(**|−12| = 12 **and then the
first minus gets you** −12**)

Learn more at Absolute Value in Algebra