re: This math problem is clearly only for geniuses...

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I don't remember anyone thinking multiplication should go before division or addition before subtraction. It was the left to right rule that was in question. I've never been taught that and have a pretty extensive math background. On that other problem I see it both ways and think that problem is ambiguous. I don't think equations should be looked at as sentences reading left to right. If they were, it would be fricking retarded to write this current problem as is. Why would you not move the 3x0 to the front and not even have to worry about PEMDAS. Just answer the whole thing left to right. The other problem lacked punctuation to differentiate between doing multiplication and division first (in my opinion since I don't use left to right often). This one doesn't even bring up that issue.

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Using order of operations precludes the need to worry about left/right. If you follow the order of operations, you don't have to go left/right.

And I agree, I have an extensive math background and in my opinion, going left-right is completely unimportant. I routinely broke complex problems down in a non-left/right manner, in whatever way allowed me to simplify the problem.

Order of operations is absolutely key, though.

It's completely okay to put the 3x0 in the middle of the problem.

And no, this problem is not ambiguous at all. There is only one correct way to solve the problem, period. If you disagree, it's because you don't understand the language of mathematics (which does have some arbitrary rules, like the order of operations). It's just like grammar in English. Why is it correct to say "I like the brown dog" instead of "I like the dog brown"? Just because--that's how our language works.

Why do we do multiplication/division before addition/subtraction? Just because

We have order of operations to cut down on parentheses, to be honest. There's no other reason for it.

edit: had to fix a grammar problem in my explanation of grammar and how our language works