Absolute Value Sign

Date: 07/08/2003 at 12:23:56
From: Nick
Subject: I need help in evaluating an absolute expression

I understand how an absolute value works but when combined with order 
of operation and signs I get confused. Please help me out if you can.

   -|8-3|+|3+(-8)|

   -|8-3|+|3+(-8)|
   =5+5
   =10

Date: 07/08/2003 at 13:00:36
From: Doctor Peterson
Subject: Re: I need help in evaluating an absolute expression

Hi, Nick.

The key is to take one step at a time, working from the inside out. 
An expression like

  -|5|

means that you FIRST find the absolute value of 5, and THEN negate 
that. That's because the - operator has to work on a number, and to 
get that number you have to evaluate |5| first.

Your only error is that -|8-3| is negative, not positive, since 8-3 
evaluates to 5, and |5| is 5, and its negative is -5.

Incidentally, you can think of the absolute value sign as both an 
operation and a grouping symbol: it functions as parentheses, forcing 
you to evaluate what's inside first; then it does its own work; and 
then the result can be used by operations outside.

If you have any further questions, feel free to write back.

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

Date: 07/08/2003 at 14:23:01
From: Nick
Subject: Thank you (I need help in evaluating an absolute expression)

Just a short note saying thank you....I knew there was 
something simple I was missing!