I'm deriving the (well, "a") process of long division from principles so I can teach it to an adult that never learned so much as single-digit multiplication tables in grade school. I suck at math tutoring. Doing things like working backwards from algebra to arithmetic in from of the student is partly why. Protip: if your explanation of 4 ÷ 2 involves the letter ε, the parents are not going to invite you back next week.