Is $a/bc$ unambiguous?

Question

In several contributions here on M.SE I saw notations like $$a/bc$$ where from the context one could conclude that it actually meant $a/(bc)$, not $(a/b)c$.

Both terms are obviously different in general, and the programming languages I know of have semantics

a/b*c = (a/b)*c

i.e. evaluate left-to-right.

The examples I saw all had "$b$" and "$c$" short like in $1/2x$ and did obviously not mean $\frac12x$ but $\frac1{2x}$as the context revealed.

How should one handle this? I am always avoiding such ambiguities and am writing the clunky $1/(2x)$, but then $1/2x$ could still be misread as $\frac1{2x}$. If typesetting is available, then I'd use $\frac12x$ vs. $\frac1{2x}$ or $(2x)^{-1}$ or $0.5x$ or $0.5/x$, where the decimal expansions are ugly, IMO, even uglier for ⅙ etc.

Are there different conventions, e.g. in the U.S., Europe, Russia, Far East?

Using / vs. ÷ wouldn't help either. Never used the latter though, only know it from calculator's key for division.

The question about different conventions depending on the corner of the planet you live in or school vs. university is because there are already related questions, and their answers are far from conclusive. For example this one claims $abc/xyz$ is to be read as $(abc)/(xyz)$ because "dropping the multiplication glyph (·, ×, * or whatever) binds stronger than with explicit mention, i.e. $$abc/xzy\neq a·b·c/x·y·z=abc/x·yz$$

So my question is less on which exact notation to use but rather on cultural differences and how established that juxtaposition rule is.

Answer 1

I would advise you never to use this notation. You can make your meaning unambiguous by writing $\frac{a}{bc}$ or $a/(bc)$.

However, no reasonable person would write $a/bc$ to mean $(a/b)c$, since that is more succinctly (and unambiguously) expressed as $ac/b$. So if someone does write $a/bc$, it is very likely that they are being lazy and mean $a/(bc)$. (Quite possibly it came from a bad transcription of $\frac{a}{bc}$.)

There is no universal convention for how to interpret the expression; I suspect most mathematicians would say "it's ambiguous". However, as wikipedia points out,

For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.

(i.e. these journals interpret it as meaning $a/(bc)$.)