# Absolute Value

### Absolute Value means ...

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

"6" is 6 away from zero,

and "−6" is **also** 6 away from zero.

So the absolute value of 6 is **6**,

and the absolute value of −6 is also **6**

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**

### Try It Yourself

### 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 *(8−3 = 5)*

|3−8| = 5 *(3−8 = −5, and |−5| = 5)*

### More Examples

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

|−3×6| = 18

Because −3×6 = −18, and **|−18| = 18**

−|5−2| = −3

Because **5−2 = 3 **and then the first minus gets us** −3**

−|2−5| = −3

Because **2−5 = −3 **, **|−3| = 3**, and then the first minus gets us** −3**

−|−12| = −12

Because **|−12| = 12 **and then the first minus gets us** −12**

Learn more at Absolute Value in Algebra