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

9.

Well, that seems to be the general consensus here.

Yeah I just read the title, did the problem, got 9.

Or 1 (if you do it the way you were taught your entire life, and the way that everyone you have ever interacted with in any mathematical environment have always done it).

You seem to be missing the entire point about the differing orders of operations that we have encountered here. You are giving division precedence over multiplication, while telling me that I am wrong for giving multiplication precedence over division. It's like a retarded dog chasing his tail here (No insult intended). As MoonlitSunshine has stated numerous times, we apparently need more parameters since there are opposing orders of operations at hand.

Read: http://www.musicbanter.com/games-lis...ml#post1045402

No that's not the case. Left to Right as BD brought up still applies. What I'm trying to say the way it is written on the computer in a single line is limited than how it would be written on paper.

If you looking at it as 6/2*(1+2) equals


then you are going to run into some problem.

If you understand that when the "/" line is used, only divided the number underneath divides the number on top, in this case 6/2 means 6 divided by 2, (only 2 not the rest of the equation),
6/2 = 6÷2

The aliens got to your head. I learned that multiplication and division are equal. I Googled "order of operations", clicked every link on the first page.

To name a few. But here's the problem and how I solved it Mr. oojay. First, parentheses. You get: 3!

6/2*(3)=?

Now it's division and multiplication, so left to right.

6/2*3=?

3*3=9

I'm sorry, but I've literally never heard anyone ever say one was more important than the other. I even Googled the problem, and Google calculator was the only thing that came up. It told me the answer was 9.

:confused: “By Jove, Holmes, however did you solve that?”

I got a 94 in Algebra II bro. I can do anything.

You got mad math skills bro. :thumb:

Put me squarely in the "9" camp please.

You got 3 factorial? Well this just adds a whole new twist. ;)

But yes, it's 9.

You know it!

No, 3 excited.

I did it the way I was taught my entire life, and got 9. I also asked a friend of mine who is working on a Master's degree in mathematics what the solution is and guess what she said? Nine.

lol how did that conversation go? I'd imagine your friend thought you were mocking them, correct?

I don't think so! I just said "hey what's the answer to this problem", and she said 9. She said that when you follow the formula, the equation moves from left to right and no math function takes precedence over another. Basically everything that's been said here already.

Yup! I say it could probably be locked now.

Did you feel like a bit of an idiot as she was explaining it to you, despite her saying everything you already knew?

Again, this adds nothing to the argument, it simply states it differently. Here is where we see to be coming to a disagreement at:

You say that multiplication and division both bear equal precedence between one another, therefore, in a complex equation involving both multiplication and division, one should simply operate from left to right.

My disagreement, which I supported with numerous and equally credible links, says that multiplication ALWAYS takes precedence over division, just as addition ALWAYS takes precedence over subtraction, per the PEMDAS method of operation that was cited in my links, and has been taught to me my entire life, with which Big3 also agreed with.

We both cited sources that are completely conflicting with one another as far as the precedence involved within the order of operations goes. One source says A, the other says B. Both are not correct, but both are not wrong either. As MoonlitSunshine has said, the equation is too ambiguous at this point to be correctly solved using either method of operation.

And I have literally NEVER heard anyone say that they bear the same precedence to one another. I was never taught that in my middle school Pre-Algebra class, Statistics, Algebra, Pre-Calculus, Trigonometry, Calculus I, Calculus II, Calculus III, or the Differential Equations courses that I have completed. I feel that my professors who hold Masters and Doctorates degrees would be a better authority than Google. Again, there seems to be a fundamental difference between the sources that really makes no sense to me.

But if asked to explain why one method of operation would be superior to the other, I would posit this:

Addition is positive, meaning that you are adding something to the number. Subtraction is negative, meaning that you are taking something away from the number. Rather than a left to right interpretation for a method of operation between the two, one should use a Positive>Negative order of operation, as a positive number > a negative number. Do the positive (Addition) first, and the negative (Subtraction) second.

Thusly, Multiplication should be considered the "positive" operation, as the exponents are positive, and Division should be considered the "negative" operation, as it is the inverse of multiplacation, meaning that the exponent is negative.

As all sources have stated, exponents takes precedence over ALL other operations. Per the transitive property, Multiplication (utilizing a positive exponent) therefore takes precedence over Division (utilizing in essence a negative exponent).

With that being said, and Multiplication being the positive operation, and Division being the negative operation, it is easy to come to the result that:

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

I remember clearly being taught in my California high school what Burning Down said about P.E.(M./D.)(A./S.) with the left to right. And I made it to AP Calculus and I remember that being taught in a few classes.

I think, oojay, that there are a handful of teachers simply forgetting to tell some generations of students about that important piece of info, that they share precedence and go left to right.

9

seven pages of this... what has the forum come to especially when i'm pretty sure we've had threads related to order of operations before

Considering that the site you quoted forgets to mention subtraction altogether, I don't see it as the most reliable source of information.

By multiplying the 2 by 3, wouldn't that mean you're pairing it with the divisor? Even if you did multiplication first, shouldn't you be multiplying 6 by 3? And then getting 18, then dividing by 2? Thereby getting 9.

http://i392.photobucket.com/albums/p...g?t=1304136614

The 1 is unnecessary, but I wanted to add it so that everything would line up nicely in Photoshop.

Haha this is great, oojay just got schooled completely by canwllcorfe who makes an excellent point. Fifty bucks says he still refuses to admit he's doing it completely wrong

He appears to think the the equation reads as 6/(2*(1+2)), but its obviously how canwll's doing it. And that's only if you ignore the PEMDAS rule, which clearly puts multiplication and division on the same level.

I'm lol'ing because I have, and the PEMDAS rule says you're wrong.

http://edu.glogster.com/media/5/25/75/42/25754207.jpg

Where would you multiply 6 by 3? I got 1, and I'm not seeing your logic.

You posted in "The Worst Music You Will Ever Hear" before this. I'll stick to math.

I still say that it's ambiguous due to the lack of a standard convention, and that it requires an extra set of parentheses to be exact in the order of evaluation, but hey, there's not much point in beating my head against a brick wall, people can easily read my previous posts in the thread :P

Well, I don't know how else to say it. :o: 6/2 * 3. You would multiply the 6 by 3, because if you didn't, you'd be pairing it with the divisor. Which would pretty much mean you're doing 6/2 * 1/3, getting 6/6. 3, as a fraction, is 3/1. 6/2 * 3/1 = 18/2 = 9.

EDIT: Here's a picture:

http://i392.photobucket.com/albums/p...fe/mathtos.jpg

You multiply the 6 by 3, getting 18. Then divide by 2.

I think I get it, looking at your previous post. You're using multiplication as the main operation here, and then turning it into a simple fraction by using 6x3 as the numerator and 2x1 as the denominator. So, logically, the next step is 18/2, which of course equals 9. Right?