mbl said
lolno, there is a difference between obelus (÷) and solidus (/) and a single correct answer to this problem. This isn't some magical problem that has multiple possible correct answers depending on the reader's interpretation, it simply exploits the fact that people have failed to learn the difference between the two symbols (As obelus is generally pointless to use past basic arithmetic) and causes confusion.
In basic arithmetic, the difference between obelus and solidus is grouping. Obelus is simply the division operator, while solidus implies a fraction that contains everything unless it is encapsulated in parenthesis.
6÷2(1+2) implies (6/2)(1+2) which works out to 9
while 6/2(1+2) implies (6)/(2(1+2)) which works out to 1
Perhaps you were taught that there's a difference, but really, there's not. The obelus was used originally for all division operations, both simple division and to imply a fraction.
Some math conventions say that the obelus means only simple division, but others do not. For instance, the math classes I took at the community college I went to said that the obelus only meant simple division, but the math classes I took at Portland State University had textbooks that used it both ways (if I had a camera I'd take a picture and post it, but alas). Also, if you go look at the origins of the symbol being used in mathematics (it was originally used when translating texts to mark passages that might be corrupted), it seems to stem from a German algebra book from 1659, and in that book it uses the obelus both for simple division and to imply a fraction in which everything after it is in the denominator. It did not start as meaning just the one kind, and today it is still used interchangeably with the solidus. Hell, many calculators even use it interchangeably: the button for division functions shows an obelus, but then when you press the button it inputs a solidus. The general trend does seem to be that people are trying to move away from using the obelus for anything other than simple division with no grouping shenanigans, but it's not even close to being set in stone.
Also, even if you were to say the obelus can only mean the one thing, that still doesn't leave you with one solid answer. You can't just arbitrarily decide that the lack of a fraction bar means that it's (6/2)(1+2), because simple division does not in any way, shape, or form preclude that 2 from being modified before division. Specifically, the 2(1+2) part could either work out to be 2*3 or 6 depending on just what kind of multiplication you think is being implied by the two being right next to the parenthesis. Just as you can't arbitrarily input a set of parentheses because it changes the meaning of the problem, you can't arbitrarily insert a multiplication sign between the two and the parenthesis just because it's implied, just in the same way that you can't actually rewrite 2x+1 as 2*x+1 because that utterly changes the meaning of the expression (the first is irreducible, the second equals 3*x or x*3 and that's not at all the same). It could be that the intent is that there should indeed be a multiplication sign in there, but it could also be intended that you have to distribute the 2 into the parentheses (or perform the multiplication of 2(3) to remove the parentheses, not just remove them and replace them with a * after the addition is done, same result either way) before you're done with the first step of the order of operations.
See what I mean about it being crafted with purposely shoddy syntax? No context to make you aware of the intent of the shoddy syntax means no one correct answer is possible. The only way anyone can try to proclaim that there is only one true answer is by arbitrarily adding things to the problem or arbitrarily changing things to try to make the syntax not shoddy. Seriously, like I said, it's made expressly for the purpose of fucking with people and getting them to argue over the answers. It's not a matter of math skills or math knowledge, it's a shitty problem that does not have a correct answer because it's meant to not have one correct answer. End of story.
EDIT: And I'm done with trying to explain what's going on here. I'll just fuck off and let people argue pointlessly about it some more if they really feel like it.