Jonathan Groves
Posts:
2,068
From:
Kaplan University, Argosy University, Florida Institute of Technology
Registered:
8/18/05
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Different Orders of Operations Among Machines and Humans
Posted:
Feb 18, 2009 11:32 AM
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> We've seen in these (very helpful for me) discussions
> that things like a/bc
> and a/b(c) are handled differently by different
> pieces of technology. Indeed
> I would get nervous if I saw the expression a/bc
> somewhere.
Even among mathematicians (not computer algebra systems or calculators or the like), the expression a/bc can mean one of two things. PEMDAS says this is (a/b)c, but I think I have read somewhere that many (maybe most) mathematicians take this to mean a/(bc) since this source (I wish I knew what it was) says many (maybe most) mathematicians perform all multiplications before any divisions. Considering that I have heard from a few sources that some students outside the U.S. have learned it as PEDMAS (all divisions done before any multiplications; one here on Math Forum mentioned this recently), this source might have been discussing American mathematicians. So unless you're writing to mathematicians or students whom you know would not misinterpret a/bc by whatever convention you're using, it's probably best to use parentheses in all cases. I usually do myself so that the meaning, whether it is (a/b)c or a/(bc), is absolutely clear to myself and to my readers.
By the way, Eric Schecter on his common errors in undergrad mathematics under order of operations dicusses some of the differences in conventions among machines and humans; the link to his webpage is http://www.math.vanderbilt.edu/~schectex/commerrs/#Operations. He too recommends not writing a/bc or ab/cd (except dx/dy for the derivative, of course!) because of the different conventions. (He does have the "My Dear Aunt Sally" interpretation wrong, at least according to the way I learned it; I learned it as doing all multiplications and divisions in the order they occur so that a/bc is (a/b)c, not a/(bc). How many here have learned it according to the way Schecter describes it?
> Also, the infamous -3^2, which I still would like to
> ban as an ill-defined
> expression, or at least so confusing it's not worth
> the trouble.
Schecter, on his same webpage, says mathematicians generally see -3^2 as -(3^2) so that it's -9. As far as I know, I don't know any mathematicians or mathematics teachers do see this as (-3)^2=9.
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