It was a trick question......much like the equation in OP.

5 builders and a Manager at Home-Depot could figure it out but we just need 1 @Bob the builder to get the correct answer.

Sorry for the horse play but just had to.

Whether higher or simple maths no maths are possible without following simple arithmetic and the fundamentals here such as the basic properties of math and proper order of operations.

Either way you get a pack of smarties and a golden star sticker!!!

Yeah trust me and tell me about it hell I forgot how to find the Maximum Area here for this word problem and I just learned the math for it about 2-3 years ago.

Honestly forgot much of it but again remember the basic properties of math and the proper way of doing order of operations following the properties of math which is essential to all maths.

Like I dont mean to be a complete asshat about the math here and well it really isnt like this forum is going to dictate how math works by popular opinion but as Ive said over and over again......

The basic principles of maths and the fundamental properties of maths is all one needs to do real math correctly along with some plain old common sense and well out of all the things folks disagree on out of bad faith or lack of good faith, IMO math is the one place we can and should all agree on just faith alone to be a certain way and show us a little bit of whats still good in the world.

Math is just undeniably beautiful IMO and its just a real force of nature, a force of the universe and a force of life.

Here your actually following the correct order of operations and the properties of math.

There are no parenthesis so you can clean start from left to right regardless of whether division or multiplication comes first and your not disrupting any properties here or order of operations.

When there is a number next to parenthesis then you have to evaluate the number and whatever is inside the parenthesis as a term and solve for it before it is divided or multiplied.

Order of operations follows properties of math, order of operations are as such because they follow the properties of math and again here starting from left to right is the correct way because there are no parenthesis to begin with, the numbers themselves are plain terms with no further break downs needed so you straight out just start going from left to right.

You get a golden star sticker and 100% for the result of this equation lol !!!! *_*

Listen, I’m sincerely not trying to start a new pissing match with you, but am just hoping we can at least agree on one thing (please hear me out before jumping to any conclusions)...

Parentheses aside, if one sees 6÷2(1+2) as being the same as 6÷2x3, then we are talking about the same basic expression as the one used in the example I showed earlier:

I’m NOT asking anyone to agree with that, but, to hopefully understand how that conclusion can be made. And whatever ratio of “right” vs “wrong” that exists appears to have been notably obscured because of it.

My point here is NOT to prove one or the other is correct, but that “AMBIGUITY” does in fact exist (as it pertains to this seemingly simple, seemingly innocent expression).

To remove all doubt, the equation should have been absolutely written as:

6÷(2(1+2))=x

or

(6÷2)x(1+2)=x

Then it would have been 100% crystal clear! Either way, I am now whole-heartedly in agreement with those who believe that an immeasurable degree of ambiguity is undoubtedly the crux of this paradoxical debate.

So, whether it’s “1” or “9” is no longer my argument, but whether a “sufficient cause for disagreement on both sides” plays a significant role.

Once again, I’m NOT trying to state this as some sort of fact that “proves” or “disproves” anything, but rather, I’m just conveying what I have found (or more accurately, what I haven’t found), as it relates to the “Distributive Properties” argument.

So I scoured that Algebra book I mentioned previously and actually found nothing that resembled a “division sign” (÷) followed by “distributive properties” type equation a(b+c).

In other words, I found nothing that even remotely suggests that our 6÷2(1+2) expression is a thing... which actually struck me as being quite odd.

I’m not saying it doesn’t exist, but (assuming the people who wrote that textbook were aware) I can only conclude at this time that they purposely avoided it altogether to remove any chance for misunderstanding or maybe never considered it in the first place because it wasn’t concise enough.

If that is the case then I give them a lot of credit for their foresight.

Anyway, I’m not saying a÷b(c+d) doesn’t exist, just that I haven’t discovered the “missing link” to support its existence...

Once again, I’m NOT trying to state this as some sort of fact that “proves” or “disproves” anything, but rather, I’m just conveying what I have found (or more accurately, what I haven’t found), as it relates to the “Distributive Properties” argument.

So I scoured that Algebra book I mentioned previously and actually found nothing that resembled a “division sign” (÷) followed by “distributive properties” type equation a(b+c).

In other words, I found nothing that even remotely suggests that our 6÷2(1+2) expression is a thing... which actually struck me as being quite odd.

I’m not saying it doesn’t exist, but (assuming the people who wrote that textbook were aware) I can only conclude at this time that they purposely avoided it altogether to remove any chance for misunderstanding or maybe never considered it in the first place because it wasn’t concise enough.

If that is the case then I give them a lot of credit for their foresight.

Anyway, I’m not saying a÷b(c+d) doesn’t exist, just that I haven’t discovered the “missing link” to support its existence...

Yeah I hear you and most likely you will probably not find an equation like that in Algebra. In any event the distribution property, commutative property and associative properties and their different types apply here IME.

In Calc and Pre Calc you find a couple equations like the one in OP frequently and usually they are a part of an even bigger and longer equation with other parts similar to it.

You also sometimes had to convert fractions into a single line usually and it would look like this equation when changed from a fraction to a straight line equation.

I recognize it and the type of equations because it was one of those type of equations that when typed in a calculator without additional brackets would not yield the correct answer in the back of the book and when doing on real paper with a pencil would screw everything up if you didnt compartmentalize terms like this properly.

Even the best students had a hard time understanding it and even though they didnt understand it fully, and hell I didnt either in PreCalc at the time, pretty much we simply followed the properties of math and did it this way even though we didnt fully understand it as our tutors and Professors told us to just do it this way.

By the time we got to real Calc it just made sense and like a lightbulb the reasoning/logic behind it went off in my head half way in because we were dealing with infinity and even crazier numbers and symbols and conversions of math. Math was just not possible without the basics and it became evidently clear how much they mattered and why they mattered.

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In light of no new evidence this discussion appears to be at a stalemate, since (after 751 posts) there appears to be nothing that specifically proves or disproves either of these conclusion to be absolutely right or wrong:

Furthermore, this contradiction and lack of any credible evidence to clarify things indicates that the real answer (to the question of "Which one is the correct one?") can even potentially lead to an equally contradictory: "Neither" and "Both"...

The reason "Both" may apply can be likened to asking people whether the color of the sky is "Blue" or "Azure". Either would be considered perfectly acceptable as far as I can tell.

The reason I include "Neither" is because I haven't found any evidence that the expression a÷b(c+d)=x even exists, and, if something doesn't exist, then how can it ever be quantified? It can't.

And just because I can actually "see" the expression 6÷2(1+2)=x right in front of my stupid face, that only means it's been "illustrated" but not necessarily "Proven to exist in the real world in some meaningful way". For instance, just because the word "Zombie" exists doesn't prove that actual zombies really do exist (except for the musical group "The Zombies" and the ones in "The Walking Dead" TV series of course).

Anyway, in such a divided, contemptuous debate there has to be irrefutable proof or it's "NotaThing"...