PEMDAS is a convention that is linked to how we write equations. The order is arbitrary and we could rearrange it, but we would need to write our equations differently to match.
If you don’t follow the PEMDAS order of operations for equations written with that expectation then you will end up with the wrong answer. The equation 5+4×7 should result in the answer of 33 because first you multiply 4 by 7, then add 5. If you just solved it left to right you would add 5 and 4 to get 9, then multiply by 7 to get 63 which is wrong.
You could flip the order of operations to something like PEASMD so you first add then multiply, but you would need to change the equation to something like (4×7)+5 to get the same answer.
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