why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?

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Answer 1

While the standard is just an agreed convention, it’s not really arbitrary. It can be summed up by saying “do the higher-order (more difficult/complicated) operations first”. Addition and subtraction, essentially the opposite of each other, are treated as equal and, within those two, the order of operation doesn’t matter. The same goes for multiplication and division. It’s only when you get to exponents that you need to know to go from right to left, i.e., 2^3^4 is 2^81 and not 8^4.