Why is the product of two rational numbers always rational? select from the bold words to correctly complete the proof. let ab and cd represent two rational numbers. this means a, b, c, and d are (integers or irrational numbers), and (b is not 0, d is not 0 or b and d are 0). the product of the numbers is acbd, where bd is not 0. because integers are closed under (addition or multiplication), acbd is the ratio of two integers, making it a rational number.