How do you translate "the quotient of a number N and 4" into an algebraic expression?

This can be written as an algebraic expression as ##N/4## or as ##N-:4##

Either is acceptable.

The word "quotient" comes from the Latin "quotiens" meaning "how many times?", as in "How many times does ##4## go into ##N##?"

So it is talking about division of one number by another.