48÷2(9+3) = ?

This 48/2(9+3) could be either

1) (48)/(2(12)) = 48/24 = 2

.

2) (48/2)(9+3) = 24(12) = 288

No. There is an unambiguous order of preference. Brackets, Indices, then Multiplication and Division, then Addition and Subtraction.
If the precedence is equal, i.e. Multiplication and Division, then you go left to right.

Always.
There is no debate.

I don't know what you call 17 pages of, well, debate then.

Personally, I would say 2 since:
48/2(9+3)
= 48/(2*12)
= 48/24
= 2

Knowing the more complicated stuff in maths doesn't mean you know the easier stuff.

One of my lecturers knows a hell of a lot about real variable theory but that doesn't mean he can answer any of my quantum questions.

Yes, because using a big font isn't needlessly irritating or anything.

The reason it "could" be equal to either depends on whether the (9+3) is on the numerator or denominator. If this problem were to be interpreted by a computer, then because computers follow BIDMAS pretty much accurately, what they'll see is:

48÷2×(9+3)

And because of the lack of bracket around 2×(9+3), the computer will interpret this as "take 48, divide it by 2, and then multiply what you get by 9+3", giving the answer 288. This is because, as far as a computer is concerned, "÷2" is the same as "×(1/2)" and then all the multiplications are done sequentially, so you get 48×(1/2)×(9+3).

However, because we're humans, we might think that the (9+3) lies on the denominator of the fraction, in which case what we do is "take 48, work out 2×(9+3) and then divide 48 by that", giving the answer 2. Alternatively, we might think in the same way as the computer, which is how this whole silly debate started.

Personally I think the notation is ambiguous. It's unclear whether the 9+3 should be on the numerator or denominator, and whatever the implicit prescribed rules for this sort of thing are, you could forgive anyone for making a notational error.

However these threads do illustrate why LaTeX is a good idea; far too often people don't make it clear what's on a numerator or denominator, e.g. when people write, say, 1+x/3+x, they might have meant $\frac{1+x}{3+x}$ or $1 + \frac{x}{3} + x$ or a number of other things, and whether they got the notation right or wrong makes no difference to what they meant. So I think future reference to this thread for such people is probably the only good thing to come out of all this.

Sigh. The maths forum is usually so nice.

My calculator says 2 though other people say they get 288 though

There are strong arguments for both answers. I would argue that there is a slightly better argument for 2 just because I haven't seen the ÷ sign being used for an amazingly long time in any question I've come across for the past 3 years. It's bad notation. Perhaps this is just because using ÷ is ambiguous whereas have 48 ALL OVER 2(9+3) has only one answer, which is 2.

However, as the question is written I think the answer is 288. How confusing.

Ultimately calculators are programmed by people, and if people have programmed it so that a sequence of multiplications after a ÷ sign should be calculated first and then divided by, then it'll say 2. [And alternatively, if it's programmed as per my post, then it'll say 288.]

Oh, my calculator says 2
fx-991ES plus

Surely the lack of multiplication sign between 2 and (9+3) means 2(9+3) should be treated as 1 number, for they are coefficients, so the answer must be 2.

Don't know why anyone would think anything bar 2.

I would argue that there is a slightly better argument for 2 just because I haven't seen the ÷ sign being used for an amazingly long time in any question I've come across for the past 3 years. It's bad notation.