In my algebra b ook it says if a is less than 0, the absolute value of a is negative. But I thought absolute value was always positive! Is this a goof or is there some truth to this?
if that is what it says, then you are indeed looking at a misprint.
e.g.
a = -5, so a is less than 0
but │-5│ = +5
the amount of rainfall every year goes down and up, so I think its misleading
It is true that the amount of rainfall can vary from year to year, and it can go up and down. However, the concept of absolute value remains the same. The absolute value of a number is always its distance from 0 on the number line, which is a positive value.
So, if we measure the amount of rainfall as a negative value when it is below the average and a positive value when it is above the average, we can still calculate the absolute value using the same formula:
| amount of rainfall | = distance from 0 on the number line
For example, if the amount of rainfall in Year 1 is -50 mm (below average) and the amount of rainfall in Year 2 is 100 mm (above average), we can calculate the absolute values as:
| -50 | = 50
| 100 | = 100
In both cases, the distances from 0 on the number line are positive values.
There seems to be some confusion here. In mathematics, the absolute value of a number is always non-negative, meaning it is either positive or zero. It cannot be negative.
The statement in your algebra book is incorrect. If a is less than 0, the absolute value of a is positive. The absolute value of a negative number is the opposite of that number but positive. For example, the absolute value of -3 is 3.
To double-check this, you can use the definition of absolute value. The absolute value of a number is the distance of that number from zero on the number line. Since distance is always positive, the absolute value is always positive. Therefore, if you encounter situations where the absolute value is claimed to be negative, it is likely an error or a misunderstanding.