It's not so much a need for extra perenthesis, but for a common standard in the order of operations.

So should we just not solve any equations that don't get the same answer using all orders of operations? The equations I'm presented with at school were written with the order of operations that I'm used to in mind, so that's the one I use. I assumed this one was too, which may or may not have been a mistake, but I went ahead and solved it the way I've been taught too. I suppose the best thing to do when one comes across an equation would be to somehow find out what order the person who wrote it had in mind, but in many cases that's impossible.

a) Parentheses. Exist. For a reason. That differential in terms of order exists for that exact reason, to specify the order of operations for that specific equation. Nowhere in the base axioms of multiplication does it say "by the way, if you have an ambiguous statement, do them in the order they come up. It's fine, for addition and multiplication on their own, as on the domain of natural numbers, rational numbers and real numbers, both are associative (the order in which the equation is evaluated doesn't matter) but when you start mixing operations, associativity isn't proven. Thus, you need parentheses in order to specify the order. Like I've been saying.

I know that you went ahead and solved it the way you'd been taught, but if you noticed, in my original post, which I then quoted as it was ignored, I stated that such "order conventions" shouldn't really be taught, as they lead to such ambiguities, where people assume they're both right, when the problem is that they've both been taught a convention that a) isn't standard and b) is a nasty shortcut in the first place. If people were taught to use parentheses properly from the start, we could avoid situations like this.

I agree that in a situation like that, you kinda have to guess for an answer. That, however, doesn't instantly mean that your guess is right. That's my point. I'm not saying sit on your hands and do nothing because you can't make a definite conclusion, I'm just saying that multiple answers can technically be correct as the statement is ambiguous, which you will note I stated at the start and and of my first post.

I understand what you're saying. I just think it didn't quite come across to me in your first post. This actually seems like a major flaw in education... the majority of people in this thread (including me) didn't even know other conventions existed. I wonder if most teachers are aware of this, and just choose to ignore it, or if it's possible they don't know either.

edit: think I'll ask my math teachers on monday.

To be honest, I'm four years into a maths degree, and it's never been directly addressed. The only reason I see things the way I do is because it's a direct result of the way Group Theory and Real Analysis proves everything else BOMDAS/PEMDAS and the order of operations are never defined nor proved. Therefore is has to be, and evidently is, based on a non-standard convention.

but since it is written out as 6/2 * (1+2) and not

the answer is "9"

if you want the answer to equal "1" then write it as

It seems like some of the things you've learned basically refute things taught in high schools. Would you say that's true?

edit: not really refute. But just off really really quick research it looks like group theory is concerned with having an expansive outlook such that one term can equal different things, depending on how you look at it. I feel like there should be some sort of hint in high school math that what we're learning is not the only applicable method.

That's some good reading the thread you did there, Neapolitan.

@Story: hmmm... kinda. In many ways, not so much refute, as expand. A lot of stuff that's taught in schools is over-simplified in order to make it easy enough to teach. Having had first hand experience teaching, I don't blame them nor the system, but it's arguable that the system could be improved without making the courses too difficult.

For what its worth, I got 1.

I'm boggled by the philosophy that addition/subtraction and multiplication/division are interchangeable. Order of operations is something artificially created to avoid these issues. So why boggle the issue by saying

These laws, for ease of things like international space travel, will be iron clad...except for these parts here. Do this however the **** ya want. That part I'm lost on.

its 1.

I don't know if that is sarcasm I am better at Math than English. (I did my best not reiterate any point already made.) tbh I only scan through it, but the problem besides what operation goes first is how it is written, I only addressed how it would look like if it was written on paper. IF one looked at the problem considering "/" as opposed to "_______" then I thought it would clear some things up. Using the former would yield nine, using the latter would yield "one."


a/b*(c+d) =
If the equation was this:

it would be a÷[b×(c+d)]


Burning Down is right QED