Here, for example, is the expression (as typed) input into the foremost mathematical engine in the world:
https://www.wolframalpha.com/input/?i=6%2F2(1%2B2)
I appreciate that you might
read it that way but you have to appreciate that you are mentally inserting something that is not there in order to give you the answer. In fact 6/2(1+2) is equivalent exactly to 6 ÷ 2 * (1+2). I trust that you will see this as (also) 9.
The key thing to remember with every symbol in maths, be it + - x ÷, is that they are binary relations -- they act on the numbers *immediately* on their left and right. Hence the / in the above expression acts only on the 6 and the 2, and doesn't "see" the (1+2).
The picture buenchico links to works out instead the expression 6/(2(1+2)), with the extra brackets. It's clunky to fit into one line, but the key is to try and derive this expression backwards, as follows:
1 = 6/6 = 6/(6) = 6/(2*3) = 6/ (2*(1+2)) = 6/(2(1+2)).
When written in that order, it is clear that the extra pair of brackets was always necessary and cannot therefore be omitted if you want to preserve the same expression. Compare to
9 = 3*3 = 3*(3) = 3*(1+2) = (3)*(1+2) = (6/2)*(1+2) = 6/2*(1+2) = 6/2(1+2)
where in the sixth equality I used that (a) = a and in the final step I simply omitted the multiplication symbol.
I hope this clarifies things. BODMAS is taught badly, and leads to a lot of confusion. I don't think it's anyone's fault, exactly, but the dogma over people who think they are right when demonstrably they are not is troubling, sad, and leads to further innumeracy.
Chris in his latest post is continuing the problem. It's perfectly possible to use / in a single line correctly, and there is no need to mark it wrong (although I agree about the point of clarifying notation -- all I am saying, Chris, is that you apparently don't understand the notation either).