Question 566235
Let p = a/b and q = c/d be two rational numbers, where a, b, c, d are integers.



Now add them:



p + q



a/b + c/d



(ad)/(bd)+(bc)/(bd)



(ad+bc)/(bd)



So p + q = (ad+bc)/(bd), which is a rational number (the numerator and denominator are both integers since integer addition and multiplication are both closed operations)



So this proves that the sum of any pair of rational numbers is a rational number.