Evaluating Absolute Values

Date: 02/05/99 at 17:00:33
From: Aaron Williams
Subject: Math Problem that is really hard!

How do you answer a question that looks like |-6 + 5| ?

Date: 02/11/99 at 11:24:05
From: Doctor Micah
Subject: Re: Math Problem that is really hard!

Hi Aaron,

Thanks for writing to Dr. Math. This is an interesting question.

First, I'm assuming you know how to do arithmetic with negative 
numbers. If you don't, you can read about it in the Dr. Math archives.  
Here is one URL that explains it:

   http://mathforum.org/dr.math/problems/mike3.19.96.html   

When an expression is surrounded by two vertical bars, as in your case, 
that means take the "absolute value" of the expression. The absolute 
value of a number is the distance of that number from zero. For 
example, |2| = 2 and | -3| = 3. A mathematical definition of absolute 
value is:
 
   |x| =  x if x >= 0
       = -x if x <  0

If this confuses you, don't worry. An easy way to take the absolute 
value of an expression is to just evaluate the expression, and then if 
it's negative, drop the minus sign. If it's positive, do nothing. For 
example,

Step 1: | -4 + 2 | = | -2 |  In this step, I evaluate the expression.
Step 2: | -2 | = 2           In this step, I take the absolute value.
                             Since -2 is negative, I drop the minus
                             sign.

Here's another example:

Step 1: | -4 - (-5) | = | -4 + 5 | = | 1 |     In this step I evaluate
                                               the expression.

Step 2: | 1 | = 1             In this step, I take the absolute value.
                              Since 1 is positive, |1| = 1.
 
It's important that you always remember to evaluate the expression 
BEFORE dropping any minus signs.

Now, it should be easy for you to evaluate | -6 + 5 |.

If you still can't get it, please feel free to write to Dr. Math again. 
We'll be happy to give more help.

Thanks for your question.

- Doctor Micah, The Math Forum
  http://mathforum.org/dr.math/