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It's not ambiguous regardless of the task at hand if it's published in an American Physical Society journal, and I haven't seen you acknowledge that the answer is unambiguously 2 in those journals, where multiplication is done before division.
Masterjaden
reply to post by 3mperorConstantinE
Yeah I guess I started nuking it too. There is no way to get 2 from that without additional parentheses or without assuming it is
48
-------
2(9+3)
It is just straight up non ambiguous without considering it relative to the task at hand.
Arbitrageur
reply to post by Korg Trinity
Thank you for understanding the point of the thread that so many missed. This was the point, and the reason I titled the thread the way I did:
"Why you can't trust your calculator, or What is 48/2(9+3)?"
Arbitrageur
t's not ambiguous regardless of the task at hand if it's published in an American Physical Society journal, and I haven't seen you acknowledge that the answer is unambiguously 2 in those journals, where multiplication is done before division.
Masterjaden
reply to post by 3mperorConstantinE
As to whether or not you can insert imaginary numbers into an equation, if there are no variables in an equation, you can't insert ANYTHING.
You solve it as is.
Jaden
The programs would be hard to change, but some students already misinterpret the PEMDAS mnemonic and think the fact that M comes before D implies that multiplication comes before division, though that's not the intent of educators. But if they changed the intent to give multiplication a higher priority, they wouldn't even need to change the mnemonic. Well there are variants like BEDMAS and BOMDAS where the M and D are sometimes interchanged so they aren't all consistent.
mbkennel
It's unfortunate that programming languages didn't follow this, they all treat multiplication and division at the same precedence level in which case they go left to right.
I think Fortran was responsible for the original sin, and nobody corrected it later.
So in conclusion, we can't say that either 2 or 288 is the wrong answer. However if you're following prominent physics textbooks or reading journals from the American Physical Society, if you said the answer is 2, you would be right, because of the conventions followed in those sources.
…changed in 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind stronger than explicit multiplication).
There is another interpretation which is pretty common that states the answer is 2, based on the implied multiplication having priority over explicit multiplication issue mentioned in the quote above regarding a change in 2013 in Wolfram Alpha. I couldn't find much documentation on this, but one reason it's not even an issue at the American Physical Society is, they don't even use multiplication signs for multiplication, rather they are used only for vector products so all multiplication is the "implied" type:
48/2(9+3) - implied
48/2x(9+3) - explicit
You are repeating stuff I already said, but you appear to be mixing up Wolfram Alpha and APS. APS is not "Wolfram Alpha, etc". I wasn't citing the guidelines from Wolfram Alpha and APS as the same, because they aren't, but here you seem to be lumping them together with "etc" which I did not do and is either a misunderstanding, misdirection, or something like that.
3mperorConstantinE
What the sources such as Wolfram et al. are talking about is:
2x/2x = 2*x/2*x = 2(x)/2(x)
Arbitrageur
You are repeating stuff I already said, but you appear to be mixing up Wolfram Alpha and APS. APS is not "Wolfram Alpha, etc". I wasn't citing the guidelines from Wolfram Alpha and APS as the same, because they aren't, but here you seem to be lumping them together with "etc" which I did not do and is either a misunderstanding, misdirection, or something like that.
3mperorConstantinE
What the sources such as Wolfram et al. are talking about is:
2x/2x = 2*x/2*x = 2(x)/2(x)
Maybe you can clarify what you mean by referring to this without discussing Wolfram Aplha:
Physical Review Style and Notation Guide (pdf) p21
Are you saying following that would give you 288?
To prevent cases where operands would be associated with two operators, or no operator at all, operators with the same precedence must have the same associativity.
Use the solidus (/) or negative exponents for fractions in running text, and in displayed equations when this does not reduce clarity. When the extent of a denominator is ambiguous, use appropriate bracketing to ensure clarity.
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?
3mperorConstantinE
reply to post by Arbitrageur
While yes, by convention the multiplication is performed first, here in the specific case, there are some overriding conditions:
From the link I gave above, after noting that both division and multiplication are left-associative:
To prevent cases where operands would be associated with two operators, or no operator at all, operators with the same precedence must have the same associativity.
This means that you cannot do the multiplication first in this equation
The APS refers to ambiguous denominators, here:
Right. I can't argue with that, since that was sort of the point of this thread.
Use the solidus (/) or negative exponents for fractions in running text, and in displayed equations when this does not reduce clarity. When the extent of a denominator is ambiguous, use appropriate bracketing to ensure clarity.
This Berkeley mathematician agrees with you on that point, as that's pretty much what he said:
luciddream
I would say this question is asked in a bad way. If i was a teacher i would give check mark to both.