So, what do you say the answer is Hodgman.
The question I am left with is, "when does the order of operations apply?

I said in that post that changing it to "2b" makes no difference to the answer (so it's still 9). "2b" is just shorthand for "2?b". So do the shorthand expansion first, then resolve the order of ooperations as usual, which means the division comes before the multiply.

Wikipedia says that "2b" used to be shorthand for "(2?b)", so if reading some old editions of a math textbook you'd want to take care and resolve the ambiguity / find out if they're using old conventions...
But if someone wrote that equation today, the right thing to do is to assume they're not using archaic shorthand.

[edit]
If guess the right answer is to show your working using every possible convention and interpretation of the question...

im glad I always reinforce operations with "unnecessary" parenthesis, cause I got that wrong (1)

shit, my mom got it right >.<*

On my head, I solve the entire right side at a single move, I feel like "eliminate the parenthesis", but since I dont depict it step by step, I feel the parenthesis is still there after doing the sum..with still dont justify the error since 6/2(3) is still nine... I suppose >.>

since 2*(1+2) can be either 2*3 or 2*1 + 2*2, to me its not even the "inside" the parenthesis that matter, its the 2*(whatever) that I feel like eliminating..

I wonder since when I got that shit in my head, cause I aced most math tests on school.. I swear u_u;

edit

after reading all the posts.. I feel much better >.> fuck the dude who wrote the equation.. But I agree the more correct is 9, as depicted by Bacterius, 6/2(1+2) != 6/(2(1+2)).

After reading wikipedia, it appears that some universities did actually used to teach that "implied multiplication" has higher precedence than explicit multiplications/divisions... which would mean that both of the above result in 1 (or the top line is false)...
But there seems to have been a shift where this is now a non-standard way of reading/writing formulae... so to get 1 as the answer from the OP's equation, you've got to be using archaic interpretations of it, instead of the now common way of interpreting it.

It has been two decades since I was at university.

Both interpretations are very logical. Proving one right does not prove the other wrong. There are people from all part of the world and in different disciplines, their convention or in this case more of instinction will differ.

The problem is no one has the authority to universally decide which interpretation is "right", it is just a short ASCII string with no context at all. If you are a math teacher you can probably force the interpretation in your class if they want your grade. If you design your own programming language or calculator you can specify how this should be parsed by your grammar. If your are a journal editor you can write a guideline or probably best reject the paper and tell them to get an equation editor. But none of this hold across all field. If International Mathematical Union passed some resolution regarding this, maybe people will respect it, but remember what happened when they say Pluto is not a planet.

Judging from the poll, I would say there is no "now common way of interpreting it". 80% is not common enough. If your project have a simple but important expression that only 80%, or 20% qualified worker that can get it right by instinct, you are going to loss money, lives, and have a bad time.

Conventions regarding these less used subjects evolve very slow because we shun them. Sane usage will produce same result for both interpretation so we normally don't have to debate over it. I think the "more common way of interpreting it" is "Don't do this". Make your expression/program easy to do right and hard to do wrong. I personally add parenthesis whenever in doubt, split complex expressions into smaller steps, and even add a link in the comment to the actual human-readable equation. I've wrote an C++ compiler and don't even remember the operator precedence, I consider those knowledge dangerous to rely upon.

This expression is just like the gold white/black blue dress. People are crazy about it because they think "this is so simple how could you get it WRONG". In the end it was just a badly taken photo.

Your answer is correct, but mine is MORE correct[citation needed].

Both interpretations are very logical. Proving one right does not prove the other wrong.

Resistance is futile. You will be assimilated.


L. Spiro

writing 3 / 4 is different form 3 (over) 4. The evaluation order is brackets 1st then operator priority ((* /) (+ -)) and after that left to right.

6/2(1+2) != 6 (over) 2 (1+2) so => 6 / 2 * 3, / and * have equal priority so we go left to right =? 3 * 3 = 9

if the task was

6 ( over ) 2(1+2) => 6 (over) 2*3 => 6 (over) 6 = 1

x / y != x (over) y

If the exceptions are used by the majority, are they really the exception?

This is the kind of thinking that leads to non-existent words being added to the dictionary, such as “ain’t” and “snuck”.

Just because it is common it does not mean it is correct.

I literally almost complimented my American coworker Tuesday for using “sneaked” instead of “snuck”. It’s bad enough that we’ve been degraded to this, but to actually reward the wrong-doers by making their mistakes official would only serve to make it worse.

If only 1 of your dogs craps on your carpet, you punish him or her and clean the mess.

If all 10 of your dogs crap on your carpet, do you punish them all, or do you just leave the mess?

L. Spiro

Nonsense. That is how language evolves.

Not all additions are created equal though. While "snuck" is a more natural and fluid way of saying "sneaked", expressions such as "axed" instead of "asked" add nothing. Ultimately it's up to how people use language, especially a language as mongrel as English, which freely borrows from other languages.

It's one thing to demand clarity of language in formal documents (engineering documentation, scientific papers), but I ain't going to lose much sleep just because a few new words snuck into the dictionary.

Nonsense. That is how language evolves.

[snip]

It's one thing to demand clarity of language in formal documents (engineering documentation, scientific papers), but I ain't going to lose much sleep just because a few new words snuck into the dictionary.

.

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

L. Spiro, you should realize that dictionaries are NOT style guides. They are documentation of language and how it is being used. Seriously, go to a library and flip through a paper copy of the complete Oxford English Dictionary. (Not a little single volume quick reference, but an actual full dictionary detailing word history.)

If a large group of people consistently uses a different set of words than you do, and they can all communicate clearly with each other, then they are no more wrong for speaking that way than you are for not speaking in German, or French. Other people may have no desire to speak with such people, but strictly speaking they're as correct as you are if other people are able to comprehend them reliably.