multiplication and division have the same precedence, and division (like most operations) is left-associative. For example, exponentiation is right-associative, so 2^3^2 = 2^9 = 512, not 64.

While you're technically correct, of the standard four half (+, *) are both left- and right-associative. / and - are the ones that are only left-associative.

Best bet is to replace x÷y by x*(1/y) as division is not commutative while multiplication is commutative. Therefore 48÷2(9+3) => 48(1/(2(9+3)) => 2

You've still failed to correctly apply associativity, unfortunately. You're treating 2(9+3) as a single unit, but ÷ appears before the implicit multiplication between 2 and (9+3) and so should get evaluated first. The division should get simplified first with its immediate operands, 48 and 2. This yields (48÷2) * (9+3).

It's funny, the top Google result for [juxtaposition precedence] is exactly this question, posted on the PhysicsForum boards. 2 is actually leading 288 by a hair there.

http://www.physicsforums.com/showthread.php?p=3235154

Anyway, the answer depends completely on whether you believe that multiplication by juxtaposition has the same precedence as multiplication by explicit symbol. There're good reasons to believe it doesn't, eg. the first post on that linked thread, but whatever the answer, it's entirely based on typographical convention. I don't work in the community that cares, so I don't really have an opinion, other than to point out it's not as cut-and-dried as virtually ever poster here believes.

In the community that I do work, people who write parsers, things like this have to be explicitly specified. That's why I maintain that the correct answer is "syntax error".

the real answer is that thw juxtaposition rules are made up on the spit by people trying to rationilze their incorrect answer . there is not and never had been a n "implit mulitplication" rule in the irder if operations.

sent frim my drunk phone

They did, however, cite sources (possibly made up almost on the spot), which is more than anyone on this thread has done.

48÷2(9+3) => 48(1/2)(9+3) => 288