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There are two possible correct answers:
lordtez
The way the equation is presented is ambiguous.
Apparently you weren't exposed to physics journals which say that multiplication takes precedence over division. In that case, the parentheses to the right of the slash are not needed, so if you were taught that "the only way to express that everything after a / in a problem is part of the denominator, is to place it all in parens",then what you were taught is obviously incomplete. That's one way, but not the only way. The other way is if you publish in a journal which has a convention of multiplication before division in the publication guidelines, which makes the answer unambiguously "2" even without the parentheses after the /.
eNumbra
As I was taught, the only way to express that everything after a / in a problem is part of the denominator, is to place it all in parens, as such
48/(2(9+3))
3 Men check into a motel room. The room cost $30. Each man paid $10. The manager of the motel realized he overcharged the men for their room. The room should have been $25. He gave the bellboy $5 to give back to the men. The bellboy took the money, but on the way thought to himself, "$5 cannot be divided evenly by 3 people." The bellboy then pocketed $2 and decided to give the men $3 back, each man receiving $1. At this point the room cost each man $9.
$9 x 3 = $27
$27 + $2 (Bellboy pocketted) = $29.
What happened to the last dollar? They originally paid $30 for the room!
As I explained in the OP, the O stands for "Order", which is a way of saying exponent or power. If you were taught O meant off then I would scold your teacher.
Not so. If you give equal weight to multiplication and division, it's at best ambiguous, not 288. By getting 288 you're doing 48/2 before 2x(9+3) and there's no valid reason I can find that says you should.
Pilgrum
The way the problem is written IE 48/2(9+3), using the precedence rules giving equal weight to multiplication and division yields the answer 288.
I explained in the OP why order of operations doesn't solve the ambiguity, so you may want to read that explanation, and the source I cited.
Masterjaden
wrong. Order of operations requires that multiplication and division be done from left to right.
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction.
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