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

The first. It’s just the order that everyone standardized on, so that we can all write equations and interpret them the same way. The actual order of the operations is not as important as making sure that we’re all doing them the same way.