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# Identify and order absolute values

Use a number line to find absolute value and then order absolute values from least to greatest.   Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• An absolute value always makes a number positive. Is there a way to make a number always negative?
• imagine a function like this:
abs(x)
it will always give the positive value of x,
if you put a minus in front of it, it will always be negative:
-abs(x)

If you plot the two functions you will see that they mirror each other through the x-axis. When two functions mirror each other like that, they are said to be conjugate.
For example, when x=2, abs(x) will give 2, so:
(x,y)=(2,2)
the conjugate of two is (the second term is flipped):
(x,y)=(2,-2)
and this is also what you would expect from:
-abs(2)= -(+2) = -2
so that:
(x,y)=(2,-2)
• Why is the absolute value of a number always positive?
• As meanderingly said, absolute value basically represents the distance a number is from zero on the number line. If you can imagine, nobody would say "My car went negative thirty miles today," so you wouldn't use negative "distances" on the number line either. That's why absolute values are always positive.

I hope this helps!
• Does l-1l = 1?
• Yes, the absolute value of any negative number is the positive of that number.
• Smallest to largest order, is that ascending or descending order ?
• Smallest to largest is ascending order, because the numbers are ascending, or rising.
• What happens if the number is -|-3|?
• Learn to "read" the expression given as looking for the OPPOSITE of the absolute value of -3.
therefore the answer is -3 since the absolute value of -3 is 3, thus the opposite of 3 is -3
• When do you use the absolute value rule?
• Is there a -0?
• -0 is the same as just 0. It's the only number which doesn't change when you put a negative sign in front, and that's because it's the only number which is neither negative nor positive.
• Why can't there be negative distances?
• even if you walk backwards, you still went somewhere...a negative distance would imply that you are traveling into yourself or (others think) backwards in time...it doesn't make sense. so its always positive and left in terms of absolute value within equations. It might be taken for granted and your "just suppose to know" this, but it needs to be positive. If you go somewhere, you go somewhere and travel some positive distance.