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<Precedence vs Associativity vs Order ⁄ >

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I suspect that this confusion arises from the difference between how most people are trained to evaluate arithmetical expressions versus how compilers generate code to evaluate arithmetical expressions. As a child it was drilled into me that the way to evaluate an arithmetical expression was to recursively apply the PEDMAS rule. That is, evaluate anything in parentheses first. Then evaluate any exponentiations. Then divisions, multiplications, additions and subtractions, in that order. So if you had 4 x 5 x (20 - 12 / 3) you start by evaluating what's in parentheses: 20 - 12 / 3. In there, there are no parens or exponents, so start with the division. Replace 12 / 3 with 4 to get 20 - 4. Then evaluate the subtraction to get 16. Now we have the value for the parens, and we are down to 4 x 5 x 16. Evaluate one of the multiplications -- but wait, we do not know what order to evaluate the multiplications in. But we can do it in any old order, so lets say 5 x 16 is 80, so we have 4 x 80, which is 320, done.

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