The fundamental issue here is, while math is math--it gets translated into language before it is executed. Language can be ambiguous; people can legitimately understand words differently.

1/2a can be understood as .5a, or it can be understood as 1/(2a). Because the convention differs in different fields. We have examples right in this thread of both--in published textbooks. Referring to a textbook is of course just an appeal to authority, and authorities can be wrong. Here we have different authorities each claiming their way is the only way. It doesn't *have to* be either way; the answer depends on the convention.

Order of operations is a convention on how we write/say math problems as much as on how we solve them. If you are the one doing real math based on real world problems, you bloody well know whether you are dividing 1 by 2a, or whether you want half of a--you'll do it whichever way it needs done. But if you need to write it down for someone else to do it--It is possible to write this in ways that only the truly ignorant (or deliberately obtuse) will get wrong.

From the poll itself, we have 55% in favor of the "left to right" convention, and 45% in favor of something else. This is not an issue of democracy or majority rule or even about being right when other people are wrong. It's about using language in a way that other people understand you. Whichever side you're on, 45% or 55% of people have a different understanding of the order of operations than you do. That's huge. So when calculations need to be done correctly, write it in a way everyone agrees on. If you mean (6/2)(1+2) just say that. If you mean 6/(2(1+2)) say that instead. We are only arguing because of ambiguity; if you can't see that it's ambiguous at least recognize that a LOT of other don't understand the rules the same way you do.

I quoted my textbook as an example of convention in the field of physics (not as an appeal to authority), and indicated that even subfields and journals have different conventions from that textbook -- i completely agree with you other than that.

this should probably be more of an example as to why math isn't traditionally written inline

Your style of debate is belligerent and lacks humility, which seems to suggest that you are not only unable to control your emotions but may even enjoy being despised. Not enough time to fix you, so we'll just continue with the ongoing debate.

Anyway, Distributive Properties... sure... but might it not also be viewed as:

6÷2(1+2) =

6÷2(1) + 6÷2(2) =

6÷2x1 + 6÷2x2 =

3x1 + 3x2 =

3 + 6 = 9

So, indeed parentheses and distributive properties are both dealt with first here THEN division and multiplication from left to right, then finally concluding with addition.

At the very least I admit that there is a bit of a grey area as far as the order of operation arguments go and I'm willing to stop there if you are...

Oh yeah, some supporting documentation in case you're convinced that I'm just making things up (and insist on keeping this hamster wheel debate going):

Thats not how the distributive property works unfortunately.

You can view it like that but again thats not how distribution works and again will provide the wrong answer simply put because distribution comes before division.

As far as sources go mine is pretty simple. Actual math books and actually doing the real math and learning it from scratch.

Actually taking College Level math and doing the work actually taking College level Calculus and I dont mean to be on a high horse about it but these are my actual resources and well respectfully I understand how hard it is to wrap ones head around the logic of the math here but the logic speaks for itself especially if your trying to get correct answers not just in a classroom but for problems in the real world.

Going back to the "invisible" parenthesis there really is no need for the additional parenthesis if you understand the logic one can just do it mentally. The main reason you need the parentheses is when your plugging them into a calc or comp program so it can make this distinction and apply the distribution property correctly but if you did it by hand there is no need unless its a really big equation to help compartmentalize it.

So basically if you did the real math correctly your never ever ever in an infinite amount of time are ever going to get 9.

Getting the correct answer involves doing the math correctly and actually understanding basic math otherwise you get the wrong answer and fall for this simple math trick.

In Fields and Waves, I got dinged on an answer because I put 1/(2*pi) which was the correct answer. My teacher said that I was supposed to write my answer with 3 significant figures. I argued that my answer was more accurate. He agreed to take off 1 point rather than 2.

Thats not how the distributive property works unfortunately.

You can view it like that but again thats not how distribution works and again will provide the wrong answer simply put because distribution comes before division.

As far as sources go mine is pretty simple. Actual math books and actually doing the real math and learning it from scratch.

Actually taking College Level math and doing the work actually taking College level Calculus and I dont mean to be on a high horse about it but these are my actual resources and well respectfully I understand how hard it is to wrap ones head around the logic of the math here but the logic speaks for itself especially if your trying to get correct answers not just in a classroom but for problems in the real world.

Going back to the "invisible" parenthesis there really is no need for the additional parenthesis if you understand the logic one can just do it mentally. The main reason you need the parentheses is when your plugging them into a calc or comp program so it can make this distinction and apply the distribution property correctly but if you did it by hand there is no need unless its a really big equation to help compartmentalize it.

So basically if you did the real math correctly your never ever ever in an infinite amount of time are ever going to get 9.

Getting the correct answer involves doing the math correctly and actually understanding basic math otherwise you get the wrong answer and fall for this simple math trick.

‘
Once again you provide nothing that supports your view, only claims that you’re so smart along with the juvenile tactic of belittling anyone who doesn’t agree with you.

I (as well as others) have at least found references that support an opposing view. What have you done? Nothing but upload some reference about “infinity” that is totally irrelevant here, that's what.

So either dig out those old math books and provide some tangible proof or shut the hell up...

This equation recently was found on Facebook, and I was surprised that there seemed to be two possible answers: 1, or 9. FWIW, I am in the x=1 camp as I see the problem like this:
6/2(1+2)= 6/2(3) = 6/6 = 1

Dear Mr Collen,
So surprised that the majority came up with x=9. There is not 2 possible solutions. Anyone who is acquainted with about 3rd grade fundamental Algebra, would know that you calculate the parentheses expression first (i.e. 2(1+2) before the division.
So you're dead right and the majority of members who voted for 9, evidently knew little or nothing about garden variety algebra.

I just don't care anymore. Life has just dealt me a wallop just now that this stupid math thing cannot compete with at all. I don't want to talk about it. I will be taking
A
Break
For
A
While
Hope
I
Get back
2 U
All

In all sincerity, definitely take care of yourself and the issues that you are going thru. Godspeed on that, a math formula doesn't matter in the grand scheme of it all.

‘
Once again you provide nothing that supports your view, only claims that you’re so smart along with the juvenile tactic of belittling anyone who doesn’t agree with you.

I (as well as others) have at least found references that support an opposing view. What have you done? Nothing but upload some reference about “infinity” that is totally irrelevant here, that's what.

So either dig out those old math books and provide some tangible proof or shut the hell up...

You have found zero references from reputable sources. Absolutely zero.

The basic maths speaks for itself. Again its not my job to prove to you how math works and neither is it my fault that you cant understand it. I cant force you to understand basic maths, thats really your deal to know, figure out and understand for yourself.

The basic maths speak for themselves. I recommend that you personally open a book and actually learn the proper way of doing math and how it works the right way from the best source and that is a math book vs using Mickey Mouse Math from random sources.

Dear Mr Collen,
So surprised that the majority came up with x=9. There is not 2 possible solutions. Anyone who is acquainted with about 3rd grade fundamental Algebra, would know that you calculate the parentheses expression first (i.e. 2(1+2) before the division.
So you're dead right and the majority of members who voted for 9, evidently knew little or nothing about garden variety algebra.

You have found zero references from reputable sources. Absolutely zero.

The basic maths speaks for itself. Again its not my job to prove to you how math works and neither is it my fault that you cant understand it. I cant force you to understand basic maths, thats really your deal to know, figure out and understand for yourself.

The basic maths speak for themselves. I recommend that you personally open a book and actually learn the proper way of doing math and how it works the right way from the best source and that is a math book vs using Mickey Mouse Math from random sources.

Open a math book yourself and learn real math the right way

Its healthy for your mind and its fun. The basic maths is all the proof you need and its not my fault you fail to understand them.

I already said its simple. Order of operations and distribution go hand and hand its really as simple and elementary as that. If you cant understand that from me actually open up a math book yourself and dont take my word for it.