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### 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!
```
Associated Topics:
High School Basic Algebra

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