TITLE: Do values attached to integers have implicit parentheses?
QUESTION [24 upvotes]: Given $5x/30x^2$ I was wondering which is the correct equivalent form.
According to BEDMAS this expression is equivalent to
$5*\cfrac{x}{30}*x^2$
but, intuitively, I believe that it could also look like:
$\cfrac{5x}{30x^2}$
I asked this question on MathOverflow (which was "Off-topic" and closed) and was told it was ambiguous. I was wondering what the convention was or if such a convention exists. According to Wikipedia the order of operations can be different based on the mnemonic used.

REPLY [3 votes]: In-line math expression can be ambiguous when working with implicit multiplication.
The "ambiguous" answer that MathOverflow gave you is the best one.
In you asked that to Wolfram Alpha, the result would have been $$5\times x/30\times x^{2} = x^{3}/6$$
But in that note http://mathworld.wolfram.com/Solidus.html , Wolfram Alpha indicate that with a/bc, textbooks often means a/(bc) but that they will interpret it (a/b)*c
[That note seems not to be known but lots of Wolfram Alpha user...]
[The same can be said for each calculator, you have to check how they wil interpret it by typing 6/2(3) and checking if the answer is 1 or 9]
Historicaly, you can read that document from 1917:
http://www.jstor.org/stable/2972726 
For the author, the usage is that 1/u*v = (1/u)v but 1/uv = 1/(uv)
And he indicate that the way the rule is writen (or rewriten by some author), lead to confusion.
The original author 'Crystal' that wrote the 'base' of the actual order of operation never wrote something like a/bc or a/b*c but always a/(bc) or (a/b)c [with parentheses!!]
So from both an historical document and a 'modern' calculating tool, you have the information that the confusion/ambiguity is known:
With implicit multiplication, some see a grouping intention, and some do not:
'ab = (a × b)' [then check if parentheses can be removed] or only 'ab = a × b'
So the best way to prevent confusion is to follow the 'rule' indicated by Wolfram Alpha :
"Parentheses should always be used when delineating compound denominators"
So when you have an expression like a/bc, it up to you to consider how you will work with the implicit multiplication, and rewrite it in accordance : (a/b)c or a/(bc), to have the answer/result you want.
Or from your expression : 
5x/30x² = (5x/30)*x = ... = x^3/6 
or 
5x/30x² = 5x/(30x²) = ... = 1/(6x)