Find the mistakes in the “proofs” that the sum of any two rational numbers is a rational n...

Find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.

Exercise

“Proof: Suppose r and s are rational numbers. Then r = a/b and s = c/d for some integers a, b, c, and d with b ≠ 0 and d ≠ 0 (by definition of rational). Then

But this is a sum of two fractions, which is a fraction. So r + s is a rational number since a rational number is a fraction.”