Mathematics III: PEMDAS

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6 ÷ 2 (1 + 2) =

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9 by the rules I was always taught.  Incidentally, in the US : is not generally used to indicate division.  Either / or ÷ is used.

You mean the obelus.
At elementary school we always used the slash, later at high school we only wrote in fractions, but in this case both would be misleading.

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1 by the rules I was taught (multiplication and division in order from left to right).

Which gives 9 here, not 1.

6 ÷ 2 (1 + 2) =
6 ÷ 2 (3) =
3 (3) =
9

Now if you do multiplications before you do divisions, you get 1, but that's not the usual PEMDAS order of operations.

Shouldn't you distribute the 2, since it's in from of a parenthese? The inverse of a factorisation, sort of?

6 ÷ 2 (1 + 2) =
6 ÷ (2 + 4) =
6 ÷ (6) =
1

That's the question.

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Well, is there is a definite way to have a final answer (the right one)?

Yes. Ask Muon2.

Is Muon2 a mathematician?

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6 ÷ 2 (1 + 2) =

Interestingly, on my Casio fx260solar I actually get a 2 as the answer.

Two? Really? Made in China?

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One issue that confuses people looking at the expression in the OP is that it isn't very well formed. In particular it mixes expressions from different contexts. Most importantly an expression that uses the division sign would almost always use the matching times sign, not use the implied multiplication by contact. That a consistent use of is the OP should look like

6 ÷ 2 x (1 + 2)

Leaving out the times sign becomes a syntax error if the expression is entered in a spreadsheet cell. For example 6/2(1+2) gives an error while 6/2*(1+2) does not. When typed correctly the answer is unambiguously 9.

Now some writers might be lazy and write 6/2(1+2) instead of 6/[2(1+2)] which would then give 1 as an answer. That's why mixing the types of usage without full use of parentheses and brackets is strongly discouraged.

Another way the OP expression might arise is when someone starts with an expression using a fraction form and tries to convert it to a linear expression. For example

     6
______  might be written as 6/2(1+2), but that misses the implied extra set of brackets
2(1+2)

that would result in the correct transcription as 6/[2(1+2)].

Thus, you consider 9 the correct answer?