I get irrationally annoyed when the "order of operations" argument comes up. I maintain that division and subtraction don't exist. Only multiplication and addition.
But wait! Isn't multiplication just extended additions?
Why do you need multiplication at all?
Well, not all fields (a set of objects closed under two operations where associativity and disributivity hold) have that property. It is a property that only the smallest subfield of a field possesses.