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3

In the order of operations, one multiplication does not take precedence over another; all multiplications and divisions are performed from left to right. A so-called "concatenation" with parentheses a(b) has the exact same meaning as "a times b". The parenthesis operation only takes precedence over other operations to evaluate what is inside. After that, ...


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I think (other than the fact that it's pretty much a deliberately ambiguous question) the thing that is missing is the concept of things being single terms, which ought to be evaluated first. I would interpret the expression as 1, because I'd consider 2(2 + 2) to be a single term that should be evaluated first before the answer is substituted back into the ...


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This would be better as a comment but I don't have sufficient reputation. Daniel R. Collins asked for an example of a mathematical text writing something like $a/bc$ to mean $a/(bc)$, and it might be useful as a counterexample to the strong claims that a mathematician would never write such a thing. On page 2 of Geometry Revisited by Coxeter and Greitzer, ...


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At first I thought comments would suffice, instead of an answer, because there have been a couple good answers already. However, it appears that there are a number of issues at hand, some of them regarding math education rather than mathematical notation. Nevertheless, let me first make a couple notes about notation though, as part of the subject. I ...


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Part of the difficulty is that order of operations is taught wrong. The basic rule of order of operations is this: "Operations are performed from left to right unless..." The first unless is the existence of parentheses. Now here's where another factor (pun unintentional) comes into play: we write in lines. Because of that, something has to come first ...


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