TITLE: What is $48\div2(9+3)$?
QUESTION [44 upvotes]: There is a huge debate on the internet on the value of $48\div2(9+3)$.
I believe the answer $2$ as I believe it is part of the bracket operation in BEDMAS. Mathway yields the same answer. I also believe that if $48\div2\times(9+3)$ was asked it would be $288$ which Mathway agrees with as well.
However, WolframAlpha says it is $288$ either way.
A friend of mine (who is better at math) told me that there is no such thing as 'implicit multiplication', only shorthand so that is in fact done after the division (going left to right, not necessarily because division occurs before multiplication. But he didn't explicitly give a reason)
What is the answer and why?

REPLY [176 votes]: There is no Supreme Court for mathematical notation; there were no commandments handed down on Sinai concerning operational precedence; all there is, is convention, and different people are free to adhere to different conventions. Wise people will stick in enough parentheses to make it impossible for anyone to mistake the meaning. If they mean, $(48\div2)(9+3)$, they'll write it that way; if they mean $48\div\bigl(2(9+3)\bigr)$, they'll write it that way.