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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>was it the result of higher math only making sense when equations are done in that order

If you think about it, you would realize that isn’t the case. We could just have parentheses around everything a hundred times to communicate whatever we want. Time if we were doing 5 * 2 + 3, we could do the 5 * 2 first by writing (5 * 2) + 3 or we could do the 2 + 3 first by writing 5 * (2 + 3). We just agree on doing PEMDAS in that order because it means that we can use less parentheses in most situations