Absolute Value in Algebra
Absolute Value means …
… 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
Absolute Value Symbol
To show we want the absolute value we put “|” marks either side (called “bars”), like these examples:
||−5| = 5|||7| = 7|
Which says the absolute value of x equals:
- x when x is greater than zero
- 0 when x equals 0
- −x when x is less than zero (this “flips” the number back to positive)
So when a number is positive or zero we leave it alone, when it is negative we change it to positive using −x.
Example: what is |−17| ?
Well, it is less than zero, so we need to calculate “−x”:
− ( −17 ) = +17