2.3 Absolute Values

Absolute Values

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

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)