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When not using parenthesis, humans speak in an unqualified (as in no special clarifications) left to right order.

Think of someone vocally (because that's often how people type --- as though they're speaking) telling you a series of arithmetic:

One plus two times three minus four plus three times two.

To vocally say that, in the above order, with proper math, it would probably be something like: One, plus the result of two times six, minus four plus the result of four times two.

For reference, we have no idea what you meant by "One plus two times...". There is no meaning to us until you add commas or add some intonation or canter so that we can determine pauses to do sort of local evaluation. I can pretty easily read that to mean:

One + (2 * 3) - (4+(3 * 2)) ("One; plus two times three; minus four plus 3 * 2")

Or (One + (2 * 3) - (4+3) * 2) ("One; plus two times three, minus four plus three; [1] times two).

But in reality, even the times two is still quite vague, even being generous with taking pauses as groupings. That's why people say things like "... all times two." or more importantly why we rarely do math purely vocally and why we have "The quantity [...] plus the quantity [...]" etc.

edit: HN, it's 2012. Frigging implement Markdown and get it over with.

I was recalling how my mother would, in the past, relay me numbers for accounting, for example. Usually it was a large sequence of plusses; and, people don't always put pauses when they're rattling off numbers. That was my point. Glad to hear it confused you :)

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