I find rules such as GEMDAS or PEMDAS or BODMAS somewhat misleading. There is no reason to perform addition before subtraction or multiplication before division. I would use PEMA instead (operations in parentheses first, then Exponentiation and the associated inverse operation of extracting roots and taking logs, then somewhat easier operation of Multiplication and the associated inverse operation of division, then the simplest possible operation of Addition and the associated inverse operation of subtraction). No need for any mnemonics either!
Very interesting topic, thank you for posting.