Rethinking the Order of Operations (or What Is the Matter with Dear Aunt Sally?)
Shortcomings in the traditional PEMDAS approach to teaching
the order of operations suggest a classroom-tested alternative, suitable for advanced
students, that conforms more closely to the intuitions of experienced
practitioners of mathematics.
View the issue here.
I have stopped teaching PEMDAS a decade ago. I currently use GEMA--Grouping, Exponents, Multiplication, Addition--as discussed in the site http://nixthetricks.com/. I have had students who would use PEMDAS incorrectly for years resulting in incorrect answers on simple problems.
Division is just multiplication using a fraction, and subtraction is just addition with signed numbers. Probably an oversimplication in terms.
For advanced mathematics, U can replace the E to give GUMA. U is for uniary operations.
The book Nix the Tricks shows readers how and why some favored mathematic tricks are harmful to our students.