If this is your goal you better teach the student about how to define addition and multiplication using the the formalization from the Peano axioms, i. e. +(

If this is your goal you better teach the student about how to define addition and multiplication using the the formalization from the Peano axioms, i. e. +(0, y) = y for all y in N +(S(x), y) = S(+(x, y)) for all x, y in N *(0, y) = 0 for all y in N *(S(x), y) = +(y, *(x, y)) for all x, y in N I know no way that states more clearly how addition and multiplication are related. Division is than simply stated as: for given a, b in N find x such that *(b, x) = a. This states clearly how multiplication (obvious) and addition (by definition of multiplication) is related to division.