Larfleeze said
*To Uranus
Jorick said
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. 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.
Jorick said
This problem and others like it are purposely written with shoddy notation to make two answers equally possible. The ÷ could mean a few different things (it is exactly the same as a / by the way, no difference in function even though it's a different symbol) and the 2 touching the parenthesis could mean two different things. You'll get one answer or the other depending on which interpretation you choose, but the other interpretations are just as valid. The order of operations is actually kind of irrelevant here, because it all comes down to how you interpret the shoddy notation. I could write this shit out in long form to explain all the various interpretations and why they're all valid, but I'll just give everyone the benefit of the doubt and assume they know basic algebra well enough (or have seen this stupid problem come up enough times) to get what I'm talking about.There is no one correct answer, which is the entire purpose of this problem. It's essentially a really successful trolling tool, nothing more. People expect that math problems will have one correct answer and all others are wrong, thus when there's disagreement on these kinds of problems people get all butthurt and defensive about their answer because they think it has to be the one true answer. This problem is not a test of math skills, it is a purposely broken problem intended to piss people off. The fact that people still argue about it to this very day is proof of how successful it is.