You can do it like this: First define a*b for integers by addition. Define the the rational numbers as ordered pairs of integers where the last number may not

You can do it like this: First define a*b for integers by addition. Define the the rational numbers as ordered pairs of integers where the last number may not be 0. Consider the rational number (a,b) to be equivalent to (c, d) if a*d = b*c (Exercise for the reader: Prove that this is an equivalence relation) Now define (a, b) + (c, d) = (ad + bc, bd), (a, b) * (c, d) = (ac, bd) (Exercise for the reader: Prove that the subset of rationals (n, 1) behaves just like the integers)