Does an inline algebra expression with multiplication in the dividend imply a quantity?

Question

Here's a trivial one. Given the inline algebra expression (2a + b) / 3c imply that the 3c is a quantity, and that the order of operations should be equivalent to (2a + b) / (3c) ? Or should it be understood as ((2a + b) / 3) c ?

Answer 1

While I'm not aware of any source that specifically says this, I would say that pretty much everyone would (just by "eye") read it the first way, with $3c$ treated as a unit. If you intend the second interpretation and you write it this way, then there is a very high probability you will be misunderstood, so it is not recommended.

Some sources consider expressions like $z/xy$ to be ambiguous. That same link says that "some of the Texas Instruments calculators follow two conventions, according to whether multiplication is indicated by juxtaposition or a symbol", which is actually the convention I would prefer (in case of juxtaposition, the multiplication is treated as a unit).

A computer program will be more strict and quite possibly interpret it in the second way, especially if it does not distinguish between implicit multiplication versus multiplication indicated by a symbol, but if you are writing for human readers the first interpretation should prevail.