Why you can't trust your calculator, or What is 48/2(9+3)?

reply to post by Arbitrageur


I should feel a bit proud. a bit!

thanks for posting that.

reply to post by Arbitrageur


Unrelated to the OP, I know, but has anyone noticed that on simple calculators, holding "÷" and "x", and then hitting "on", will shut down the calculator?

BTW I sent you a U2U.

Arbitrageur

 

That refers to "operators with the same precedence", and if APS specifies multiplication before division, then those two operators (multiplication and division) don't have the same precedence, right?

They have the same precedence. No real mathematician will ever tell you different. The are perfect-inverse operations, like addition and subtraction.

Right. I can't argue with that, since that was sort of the point of this thread.

Yes, but the exception was being taken to your statement that:

according to rules outlined in the APS style guide, "2" would be unambiguously correct

—where ^that is a far-fetched extrapolation based on the fact that they listed multiplication before division (multiplication everywhere? –overriding even the associativity of the operators??)

I can tell you that this situation NEVER comes up in reality. Which is precisely why the APS page doesn't go into detail about this kind of thing.
Essentially put: if you would write that 48/2(9+3) is unambiguously equal to 2, then you aren't going to be submitting any articles to the Physical Review journal for peer review, anyway.

I will also say, in answer to the question posed to the professor of Ring Theory at UCB, that if by some chance a question like that was given to students of mine…I would accept the following as correct answers: "288", "2", "n/a" (and even "42" and "wtf??!" for good measure). I, like the professor from Berkley, would do this due to the obvious ambiguity which exists — as demonstrated by the ongoing confusion.

Finally, keep in mind that there is no "ultimate answer" here to be issued by some "authority".
This particular debate has it's origins in school algebra texts from the early 1900's which would follow differing conventions for resolving this and related issues. Because of this, parenthetical clarity is on the onus of the author, and if not observed, they should not be surprised when people interpret their expressions and obtain different results~

Respectfully,
—E.

reply to post by Arbitrageur


Well, following PEMDAS, I would automatically say the answer is 2..... 288 wasn't even a consideration to me.

Two.

reply to post by Arbitrageur


I don't think this is confusing. It's not just the parenthesis that help to 'clarify' the expression, it defines it. And, it stands to reason that calculators (and all other electronics) change their software from one model to the other. Maybe in the 85 it read it one way and in the 86 it read it the other.

a reply to: Arbitrageur

NO NO NO NO The calculator saying 2 is wrong and it IS NOT AMBIGUOUS!!!! Starting with the equation 48 / 2 (9+3) = ?, we start with everything in parentheses. 9+3=12, so now we have 48/2*(12). Multiplying from left to right we get (48/2)*12, which equals 24*12, for a grand total of 288. EVERYONE THAT SAYS OTHERWISE IS WRONG ORDER OF OPERATIONS IS KING HERE seriously guys there's gonna be thousands of hating replies but know that order of operations states parentheses, then exponents, then multiplication and division from LEFT TO RIGHT then addition and subtraction from LEFT TO RIGHT. To get the other answer we have to add 2 extra parentheses like so: 48 / (2 (9+3)) = ? ASK ANY PROGRAMMER THEY EITHER BACK ME UP OR DON'T KNOW WHAT THEY'RE DOING 100% OF THE TIME.

a reply to: Draco314

There is no standard order of operations in programming languages.