Yurp! :D

There's no lack of one, just misunderstanding in this thread. Math is hard facts, not multiple answers.

What canwll said, basically the problem wouldn't involve multiplying the denominator unless there were some sort of parenthesis to contain the 3 in the denominator and not the the numerator. Otherwise, the 3 is looked at as a whole separate number. As canwll showed, it's 3, not 1/3.

(6/2)*(1+2)=9 or (6/2)*3=9...........18/2=9.............9=9

6/(2*(1+2))=1 or (6/2)*(1/(1+2))=1.........6/(2*3)=1...........6/6=1

There's only one answer and it's 9. Without the parenthesis, at least.

ahahahahahahaa... Man, that's a good one.

Ever heard of Heisenberg's Uncertainy Principle? That you cannot know both the location and velocity of an atomic particle at the same time? Or what about the "Schodinger's Cat" paradox, which states that the cat is both alive and dead at the same time? It can't be both, because maths is hard facts, not multiple answers, right?

Even moving away from physics and into pure maths, x = 5 mod 6. What's x? Well, it's 5. It's also 11, and 16, and 365. In fact, it's 6n + 5, but without any information about n, you can't get a more accurate answer.

That's what's going on here. This is EXACTLY like a function with multiple possible values. Take a quadratic equation, like x^2 + 2x -3 = 0. "x" is both 3 and -1, right? You can't get one specific answer until you are given more information, like x>0. With this lovely equation, 6/2*(1+2) is both 1 and 9 unless more information about the order in which the multiplication and division should be done is given. Once the extra parentheses are added, the answer would be clear.

If anyone responds to this post with "but but but we were taught in school that you do PEMDAS" or "We were taught in school that if you have multiplication and divison in the same equation you just work from left to right", I am just going to ignore you, or assume that you're just completely incapable of reading seeing as I've explained this 5 times before.

THERE IS NO STANDARD CONVENTION FOR THE ORDER OF EVALUATION OF OPERATIONS. THEY ARE MADE UP IN ORDER TO MAKE IT EASIER TO TEACH THE SUBJECT. It just so happens that most of you tend to have been taught one of two common methods. This thread is all the evidence anyone should need to prove this is the case. If you want more, there's currently a facebook poll with about 2 MILLION votes, and about 200k difference between the two.

If anyone wants to argue this, I'm happy to do so, so long as you have an argument other than "look at these links" or "this is what my maths teacher said". I taught maths for 6 months, and the amount of white lies I had to say in order to avoid topics that were confusing the students was slightly soul-destroying. If anyone wants to disagree with me on the principle that you feel that you are right and I am wrong just because, please go and study maths - specifically Group Theory and Real Analysis - for a few years, and then get back to me.

/end rant

I wasn't trying to offend you. When I said multiple answers, I didn't mean a problem can't have two solutions. I meant that you can't go about problems like the one this thread is about in two different ways and get two wildly different answers, because one is technically incorrect. What I mean is, you can't pick and choose how you solve a problem and then call it the correct answer. There are certain guidelines to follow by, otherwise it is incorrect.

Sorry for the misunderstanding, but I still stand by 9 being the only answer. Even if you do multiplication first, this thread has proven the answer is still 9. It's not a matter of how you do the order of operations, it's a matter of multiplying correctly.

And the parenthesis or lack of makes no difference, as the problem stands (and with the parenthesis it currently has), the solution reads as 9. Thats why if you copy & paste it directly into Google it'll give you 9.

It only works out as 9 doing the multiplication first if you assume that there are parentheses around the (6/2).

In order to get any one, unique answer, you have to add one set of parentheses:

(6/2)*(1+2) = 9
6/(2*(1+2)) = 1

There are your two choices. I will add that Google gives the 9 answer because calculators, indeed all computer programs, are designed to evaluate from left to right in the absence of proper syntax, similar to how you can figure out what someone is saying even if they have atrocious spelling. Doesn't make their spelling any more correct, though. I will also point out that if you put the equation into Google, it adds a pair of parentheses in the position it is assuming you mean due to your incorrect syntax:

http://i.imgur.com/pXNeO.png

if you break the equation down into a, b and c, to represent the parts which there is argument about, it's a lot easier to see what's going on. In the following, a=6, b=2, and c=(1+2):

a/b*c = ... ?

Now, one interesting thing worth noting is that Canwllcorfe, among others, has chosen to see this as (a*c)/b, which is interesting as it totally changes the order. It is however equivalent to (a/b)*c, which is one solution to the problem, so it's fine as an answer, but it just goes to show that "left to right" isn't always even correct, as you can manipulate such an ambiguous statement to have the inverse order of operations.

Your choice, however, boils down to (a/b)*c or a/(b*c). If you substitute back in the values, you will (hopefully) note that this equals 9 and 1 respectively.

Do you still feel that the "parentheses or lack thereof makes no difference"?

I just add up the number of empties in my bin the following morning to deduce whether I have had a good night or not.

Yes, because the parenthesis you showed that Google had on them are unneccessary. They only make it easier for people to see how the process is. Lack of parentheses implies that it's a 6/2 fraction.

That's what I was thinking. I mean, I know the inclusion of another pair of parentheses would certainly alleviate any real confusion, but I don't think they're necessary. I certainly didn't look at the problem and read it as 6/(2*(1+2)), because those parentheses aren't there. So I figure, by default, it should be (6/2)*(1+3). It also seems, to me anyway, more logical.

EDIT: But do note that I'm just explaining my mindset. You could be completely right Moonlit (in that, ironically, there is no definite answer).

I do agree that maths are not cold, hard facts that never change and are designed to only ever have specific answers. What a lot of people may be forgetting is that convention is set to arrive at a particular point consistently, to achieve a particular goal. If you desire to arrive at another point consistently, the convention must be altered, but it doesn't invalidate the outcome. Maths serves a purpose based on your application of it.
I say all that to say, while I'm not educated very much in this department, it seems logical to me that what you're saying is correct.
(I could be off, but I was just trying to verbalize my general take on what you ultimately meant.)

I had no idea this would turn into a huge discussion. This is madness.