Originally Posted by Janszoon

When you google "order of operations" it doesn't seem like there's much disagreement at all. Every link I click on seems to say that multiplication and division are of equal rank, as are addition and subtraction.

Originally Posted by MoonlitSunshine

And generally, that's fine, as multiplication and addition are associative operations (it doesn't matter what order you do them in). It's where there's ambiguity over which elements the inverse is being applied to that there's a problem.

Consider a situation where you have a/b/c. Is that (a/b)/c, or a/(b/c)? take an example, 2/3/4. (2/3)/4 = 2/12 = 1/6, but 2/(3/4) = 8/3. The two answers are very, very different, but how do you define which one is the fraction? Which equal priority operation needs to be done first? The same problem holds when you have a/b*c. Is that (a/b)*c, or a/(b*c)? The fact that most people assume it is (a/b)*c does not make the syntax any more correct: If someone writes "I hae that" you could assume they left out a t or a v; depending on which it is they've left out, it makes a big difference to the meaning of the sentence, but you can usually figure out which they mean by the context of the sentence. It doesn't however, make the sentence, if isolated from the context, any less ambiguous. Does that make sense?