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