It's weird because usually the people writing the expressions want to communicate clearly, and stuff like 1/2x is not immediately clear to everyone, so they write the 1/2 as a fraction.

The same expression on both sides of the division sign only reduce to one if they actually bind to the division sign, which is rarely an issue, but that is exactly the thing that is in question here. I think it's clear that 1 + 1/1 + 1 is 3, not 1, even though 1+1 = 1+1.

But as you said, of course, the evaluation order is just convention, you can just as well write everything in https://en.m.wikipedia.org/wiki/Reverse_Polish_notation