Do values attached to integers have implicit parentheses? 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.

The conventions that $a/bc$ means $a/(bc)$, that $\ln 2x$ means $\ln(2x)$, and so on were universally established and very useful. Unfortunately, the combined influence of computer-style notation and excessive safe-playing by mathematics examiners has led to the present clutter of parentheses. Just pick up any maths book printed before 1970 (and many more recent ones), and you will see that absolutely no ambiguity arises. We need conventions like these; otherwise we will find ourselves having to write $\sin(4x) = (2\sin(2x))\cos(2x)$ for $\sin 4x = 2 \sin 2x \cos 2x$, to prove that we don't mean $(\sin 4)x = 2 \sin((2x \cos2)x)$, etc.  
