Show that the Distributive Law is true for balance numbers. In other words, suppose that x = a|b,y =c|d, z = e|f (where a, b, c, d, e, f are

non-negative rational numbers). Show that x(y+ z) = xy + xz. You may assume that the Distributive Law is true for non-negative rational numbers. Recall the rule for multiplying balance numbers: xy = (a|b)(c]d) = (ac +bd) I (ad + bc). (Construct a chain of equalities.)