I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It's about a 30min read so thank you in advance if you really take the time to read it, but I think it's worth it if you joined such discussions in the past, but I'm probably biased because I wrote it :)
Without any additional parentheses, the division sign is assumed to separate numerators and denominators within a complete expression, in which case you would reduce each separately. It's very, very marginally ambiguous at best.
Assumed by whom? Clearly not everyone.
It's what is actually taught in high school, so there are those who remember and those who don't.
You are correct with your definition - Terms are separated by operators and joined by grouping symbols - and it's consequently not ambiguous at all (using so-called "weak juxtaposition" breaks that rule).