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 :)
I concur with everything you’ve written here.
I concur that a left-to-right interpretation of consecutive explicit multiplication and division is wide spread and how most calculators and computers would interpret:
a / b * c.
But the sources you quote in your blog post and the style guides I’ve read, state that a fraction bar or parenthesis should be used to clarify if it should be interpreted as:
(a / b) * c
or
a / (b * c)
You make the argument in your post that:
a / bc
is ambiguous (which I agree with)
but
a / b * c
is not ambiguous. Which is the part I disagree with, and I think the sources you quoted disagree with you as well. But I’m open to being wrong about that and am interested if you have sources that prove otherwise.
If I’m understanding your response correctly, you believe that
a / b * c
is unambiguous, and always treated like
(a / b) * c
because of a wide spread convention of left-to-right interpretation (a convention that we both agree exists), not because you found a source that states that.
Anyhow… I’m not out to convince you of anything and I appreciate you taking the time to explain your thinking to me.
Exactly a/b*c equals (a/b)*c but I’d instantly reconsider my position if you can show me a single calculator that would handle that diffently (credible calculator, not the once that some students program for homework assignments).
Even though one shouldn’t treat calculators as some kind of authority but if all calculators handle it that way (all calculators of the five major manufacturers, Google, MathCad, Mathematics, various open source CAS) it’s probably a very good indictator that it’s not ambiguous.
What I also mentioned in the article is that standards and guidelines are typically stricter than most conventions in the name of clarity. So some of them even forbid things like “a / b * c” even if practically everybody agrees how this should be interpreted, just to be “extra-safe”