View Poll Results: 6÷2(1+2) equals what?
1 44 46.81%
7 1 1.06%
9 47 50.00%
No idea 2 2.13%

"I think this is far preferable to making detailed rules that are
likely to trick people. Sometimes one rule seems natural, and
sometimes another, so people will forget any rule we choose to teach
in this area. I've heard from too many students whose texts do "give
an example that really puts this rule to the test," but do so by
having them evaluate an expression like:

6/2(3)

that is too ambiguous for any reasonable mathematician ever to write.
And no matter what the rule, we would still constantly see students
write things like "1/2x" meaning half of x, so we'd still have to make
reasonable guesses rather than stick to the rule"

...

I've been continuing to research the history of Order of Operations,
and one of the references in our FAQ now includes a mention of
something I had also discovered, that the multiplication-division rule
has never really been fully accepted:

...

P.S. Some people argue about arithmetic-operation precedence by
referring to what this or that calculator or programming language
does. However, I believe all such references are irrelevant; for what
may be syntactically convenient for some computing device need not be
convenient (or traditional) for human mathematical writing.

Now go and argue there, and come back with the results.
The Maths experts have agreed, there is ambiguity, confusion and contradiction teaching of the rules. No rule has actually reached precedent or is universally accepted.

This is what you all cannot accept. That what you have been taught is wrong.

This is where you have to give way.

You have been fooled , mislead for so long, it's no wonder you are all open mouthed and confused. Now, deep breath, out with the old, in with the new.

I myself started off as a "1" person, as I was taught, and then researched the experts views, agreed and reported it all back here. So blind were you all, so convinced were you that you were right, you refused to accept anything to the contrary.

“None so blind as those that will not see.” Matthew Henry (1662-1714)

The Maths experts have agreed, there is ambiguity, confusion and a contradictory teaching of the rules. No rule has actually reached precedent or is universally accepted.

No they haven't. Some guy on a website has stated his opinion which as it happens is pretty much at odds with the entire arithmetical establishment.

How do you know 6/2(1+2) means any number? Symbols mean nothing until we agree on rules for interpreting them.

Somehow you've decided to accept the standard definitions of individual symbols but rejected the standard rules of syntax as optional. Why? Both are equally arbitrary, both equally a matter of consensus and standardization. You're like a pedant who nitpicks people's spelling mistakes but rejects any sort of prescriptive grammar.

A solid consensus is not invalidated by one contrarian, or a dozen.

Lest you misunderstand, the consensus I'm talking about is not the consensus on the answer to this problem, but on the rules for parsing these expressions in general. I've already explained why this convention makes eminent mathematical sense and the other way wouldn't, but even that's beside the point. We do it this way because this is the way we all do it. No other argument can or need be made.

No they haven't. Some guy on a website has stated his opinion which as it happens is pretty much at odds with the entire arithmetical establishment.

How do you know 6/2(1+2) means any number? Symbols mean nothing until we agree on rules for interpreting them.

Somehow you've decided to accept the standard definitions of individual symbols but rejected the standard rules of syntax as optional. Why? Both are equally arbitrary, both equally a matter of consensus and standardization. You're like a pedant who nitpicks people's spelling mistakes but rejects any sort of prescriptive grammar.

A solid consensus is not invalidated by one contrarian, or a dozen.

Lest you misunderstand, the consensus I'm talking about is not the consensus on the answer to this problem, but on the rules for parsing these expressions in general. I've already explained why this convention makes eminent mathematical sense and the other way wouldn't, but even that's beside the point. We do it this way because this is the way we all do it. No other argument can or need be made.

I believe those in the "There is only one method/answer camp" have to prove that their interpretation/method and ordering have gained universal acceptance and precedence. You, nor anyone in your camp can do that, and so should have the grace to accept that both methods are acceptable. There is no solid consensus as you claim.

It's night here, in Europe, it's daylight in Japan. Look where you want, in this dilemma, there will always be two answers, both correct.

I believe those in the "There is only one method/answer camp" have to prove that their interpretation/method and ordering have gained universal acceptance and precedence. You, nor anyone in your camp can do that, and so should have the grace to accept that both methods are acceptable. There is no solid consensus as you claim.

It's night here, in Europe, it's daylight in Japan. Look where you want, in this dilemma, there will always be two answers, both correct.

Tell me, old chap:

What does the string of characters that looks like this- apple- mean to you?

What does the string of characters that looks like this- apple- mean to you?

All possible answers are equally correct. I don't expect a response to this post: all possible ways of reading it are equally correct, so how would you know I'm even making sense or writing on topic? Fgrrgtburmxosiehfkvos!!!

Syntactic error. "looks" was paired with "string" not "characters" ... But from your point of view, everything's correct so you don't need to bother correcting others.

Syntactic error. "looks" was paired with "string" not "characters" ... But from your point of view, everything's correct so you don't need to bother correcting others.

Correction. Looks was paired with string (plural). What do they look like, not what do they looks like.

I believe those in the "There is only one method/answer camp" have to prove that their interpretation/method and ordering have gained universal acceptance and precedence. You, nor anyone in your camp can do that, and so should have the grace to accept that both methods are acceptable.

"Universal"? It doesn't have to be universal. Spelling rules aren't invalidated wholesale by some crank with a green crayon - or even the same crank with a youtube video or a self-published spelling book.

It doesn't even have to be, say, correctly applied consistently by 90% of the population (common misspellings are still misspellings after all.)

But you want quantification, I'll give you quantification. I believe that this syntactical convention (PEMDAS/BODMAS/whatever you want to call it, with complementary operations taking equal precedence) is, at the very least:
(a) the one taught in every primary school math textbook in the English-, Irish- or German-speaking world;
(b) the one implemented in every computer programming language equipped to parse such strings; and
(c) the one practiced by all mathematicians in the combined math departments of ETH and EPFL.

Give me a counterexample and I'll cheerfully admit you're right. Unless it's a counterexample to (a) in which case I shall haul out my own green crayon and take the publisher sternly to task.

I believe those in the "There is only one method/answer camp" have to prove that their interpretation/method and ordering have gained universal acceptance and precedence. You, nor anyone in your camp can do that, and so should have the grace to accept that both methods are acceptable.

This is mathematics you are talking about. It is not homeopathy or some other quasi-philosophical pseudo-science where you can make stuff up or change things to suit your personal beliefs.

In math you either get the answer right or you don't.
This is why buildings stand or planes fall. This is why science works. Mathematics are empirical.

Just because there are two significant answers being given does not make those got the answer wrong correct. There should only be one correct answer for a problem like this, and there is only one correct answer. Unfortunately there are obviously many people who don't know how to read basic arithmetic expressions. This is not a perception issue, it is a parsing issue.

__________________ Many men, of course, became extremely rich, but this was perfectly natural, and nothing to be ashamed of, because no one was really poor -- at least no one worth speaking of. - Douglas Adams

"Universal"? It doesn't have to be universal. Spelling rules aren't invalidated wholesale by some crank with a green crayon - or even the same crank with a youtube video or a self-published spelling book.

It doesn't even have to be, say, correctly applied consistently by 90% of the population (common misspellings are still misspellings after all.)

But you want quantification, I'll give you quantification. I believe that this syntactical convention (PEMDAS/BODMAS/whatever you want to call it, with complementary operations taking equal precedence) is, at the very least:
(a) the one taught in every primary school math textbook in the English-, Irish- or German-speaking world;
(b) the one implemented in every computer programming language equipped to parse such strings; and
(c) the one practiced by all mathematicians in the combined math departments of ETH and EPFL.

Give me a counterexample and I'll cheerfully admit you're right. Unless it's a counterexample to (a) in which case I shall haul out my own green crayon and take the publisher sternly to task.

I've highlighted you inaccuracies.

Referring you a little closer to home, try the American Mathematical Society and their views.

All you needed was MS Excel and Google and Texas Instrumens branded calculators. Not much maths has been done outside of these over the past decade. They get 9. Either there's one answer or all the bridges and planes are about to fall.

"Universal"? It doesn't have to be universal. Spelling rules aren't invalidated wholesale by some crank with a green crayon - or even the same crank with a youtube video or a self-published spelling book.

It doesn't even have to be, say, correctly applied consistently by 90% of the population (common misspellings are still misspellings after all.)

But you want quantification, I'll give you quantification. I believe that this syntactical convention (PEMDAS/BODMAS/whatever you want to call it, with complementary operations taking equal precedence) is, at the very least:
(a) the one taught in every primary school math textbook in the English-, Irish- or German-speaking world;
(b) the one implemented in every computer programming language equipped to parse such strings; and
(c) the one practiced by all mathematicians in the combined math departments of ETH and EPFL.

Give me a counterexample and I'll cheerfully admit you're right. Unless it's a counterexample to (a) in which case I shall haul out my own green crayon and take the publisher sternly to task.

"Universal"? It doesn't have to be universal. Spelling rules aren't invalidated wholesale by some crank with a green crayon - or even the same crank with a youtube video or a self-published spelling book.

It doesn't even have to be, say, correctly applied consistently by 90% of the population (common misspellings are still misspellings after all.)

But you want quantification, I'll give you quantification. I believe that this syntactical convention (PEMDAS/BODMAS/whatever you want to call it, with complementary operations taking equal precedence) is, at the very least:
(a) the one taught in every primary school math textbook in the English-, Irish- or German-speaking world;
(b) the one implemented in every computer programming language equipped to parse such strings; and
(c) the one practiced by all mathematicians in the combined math departments of ETH and EPFL.

Give me a counterexample and I'll cheerfully admit you're right. Unless it's a counterexample to (a) in which case I shall haul out my own green crayon and take the publisher sternly to task.

I've highlighted you inaccuracies.

(a) It was not taught to me like that.

(b) Some people argue about arithmetic-operation precedence by
referring to what this or that calculator or programming language
does. However, I believe all such references are irrelevant; for what
may be syntactically convenient for some computing device need not be
convenient (or traditional) for human mathematical writing.

(c) They have to teach one of the methods don't they ? They can choose either one, as either is correct/acceptable.

Referring you a little closer to home, try the American Mathematical Society and their views.