# Absolute Value Bars & OoOp

Where is the absolute values bars in the mathematical order of operations. If possible please provide a direct quote from a book. None of my university books has the information printed (too basic I guess) and the person I am debating with won’t believe me unless I can get a quote from a book, but he has agreed that if I can get a quote from somebody here it will be okay (he comes to this message board too).

-2|3-4-5| = -12 or +12? The debate rages on!

> -2|3-4-5| = -12 or +12?

I can’t figure out any reasonable way in which you can get +12 from this. If you wanted to quibble over anything, it would be over the order of the subtractions:

(3-4)-5 = -6
3-(4-5) = 4

But, in any case, the first order is standard. So now the question is how to interpret the following:

-2|-6|

It doesn’t matter whether you interpret this as this:

-(2|-6|) = -(2(6))

or as this:

(-2)|-6| = (-2)(6)

because in either case the answer is -12. So how can you get +12? Is the claim being made that absolute value bars suck all the numbers next to them inside them, so that you get:

-2|-6| = |(-2)(-6)| = |12| = 12

If that’s the question, the answer is no, absolute value bars don’t suck numbers inside them, anymore than parentheses suck numbers inside them. You have to do everything inside the bars first, then apply the absolute value to the resulting number, and only then do stuff outside the bars.

(Although qualifications are generally irrelevant on the SDMB, if the person you’re debating with asks, you can tell him that I have a master’s degree in math and work as a mathematician.)

-2|3-4-5| = -12 or +12? The debate rages on!

The absolute value marks take the precedence of parentheses. So:
[list=a][li]“3-4-5” is evaluated (left to right), giving -6[/li][li]Absolute value is next, resulting in +6[/li][li]Multiply by -2, final result is -12[/list=a][/li]
Also, writing this in computerese:

-2*ABS(3-4-5)

returns -12.

The only way I see that someone might get +12 is if they multiplied -2 by -6 before evaluating absolute value. This is wrong because the -2 is outside of the AV bars.

The best literary reference I could find doesn’t quite expalin what you want. I checked my Mathematics Dictionary (4th ed.) by James & James. It’s most detailed reference to absolute value is:

|x| + |y| >= |x + y|

Basically, the expression inside the AV bars is “absolute valued” before any outside operations.

If it helps, tell your friend that I have a BS in Mathematics & Computer Science. (And yes, I do.)

OK, now we need a PhD in Mathematics to verify what the MS and BS said.

I concur with AWB, and I have a Ph.D. in mathematics (thus upstaging his simple B.S.)

The absolute value symbols are used to represent the function ABS(x)… as such, it works just as sin(x) or f(x). There’s no confusion between f(-2x) and -2f(x), nor is there any confusion between -2*|x| and |-2*x|

Thinking of it this way will also help you understand why it takes the same order of precedence of parenthesis: it’s just a short hand for ABS(x).

Yes, I say it is -12.

My wife is heading back to school and needs to take a proficiency exam. One question on the exam is -2|3-4-5|. They have the answer as being +12. I went to the college and said that this is dead wrong the answer is -12 (-2 x |3-4-5| = -2 x |-6| = -2 x 6 = -12). The “professor” says that the -2 is subject to the absolute value bars because multiplication is a higher order of operation (i.e. multiply then abs). I say, and I am glad to have the support that it is absolute value then multiply.

Hey bernard, are you sure you want your wife going to that school?

I concur with tomndebb. Seriously, she may want to look somewhere else.

BTW: Bachelor of Aerospace Engineering, but I had to take some math classes

*Bernard sed: The “professor” says that the -2 is subject to the absolute value bars because multiplication is a higher order of operation (i.e. multiply then abs). *

BUZZ Wrong! Zing the “professor” again!

Absolute value is a unary operator, i.e., it only has one operand (the value between the |'s, 3-4-5). Multiplication is a binary operator, needing two operands (-2 and |-6|). And unary operators have a higher order of precedence than binary ones.