Chessic_Sense:
BEDMAS is not universal. In fact, I, for one, didn’t even know it existed until a few years ago and I still think it’s as strange as saying “Why do you think this?” or “I’m off to phone me mum.”
It’s as close to universal in math as anything is. The BEDMAS/PEDMAS/BODMAS/etc mnemonic is relatively new (about a century - the history is somewhat unclear whether it was the end of the 1800s or the beginning of the 1900s).
Some notion of an operator precedence is, of course, centuries old implicitly and explicitly around 200 years old.
That said, it’s simple pedantry to see a rule and blindly apply it without explanation.
I’ll quote myself from a couple of the threads linked above:
Well, the Ancient Society of the No Homers has decreed it is actually 4 and a squiggle.
But seriously, it’s both.
Sorry about the ambiguous answer, but that’s the best we can do. The confusion comes from some textbooks and teachers teaching that if you see an implied multiplication, like 2(1+2), you should do that first. If that’s the case, the answer is 1.
Other textbooks and teachers teach that you should do the division before the implied multiplication, as you would under a normal order of operations order. Then, the answer is 9.
Of course, if there’s no agreement even among different teachers, that means there’s no hard and fast rule.
The problem is the the order of operations is itself a convention. It’s a way of codifying how most people approach arithmetic. In real life (even for mathematicians), we’d probably ask for clarification or curse the problem poser for giving us an ambiguous expression.
Most of us would use an extra set of parentheses to clarify the expression or use a rational expression with a numerator and denominator, instead.
We’ve been seeing this question submitted a lot on the “Ask Dr Math” site, and it’s the 2nd round of it. A similar question was posed a couple weeks ago and also spread like wildfire. These things come in waves.
The way we’ve been explaining it is to use the phrase “American history teacher”. When heard, is that a teacher of American history? Or a history teacher from America? It’s an ambiguous expression with no established rule to resolve the ambiguity.
Actually, thinking on it some more, the “real” answer is whatever your teacher says it is. Doesn’t change the ambiguity in the real world, but it does mean the difference between good and bad marks in class.
(bolding newly mine)
As noted above, there are teachers and even some numeric solvers that perform the implicit multiplication before explicit multiplication/division.
A rule is only absolute if everybody agrees on it. There’s sufficient argument over the application of implicit multiplication that there is a de facto ambiguity.
You can militantly insist one particularly way is correct, but that’s not going to change anybody’s mind or force the “mathematical community” (whatever that is) to accept it.
(bolding newly mine)