Why is the product of two rational numbers always rational?

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Let a/b and c/d represent two rational numbers. This means a, b, c,and d are (integers, irrational numbers) , and b and d are not 0. The product of the numbers is ac/bd , where bd is not 0. Both ac and bd are (integers, irrational numbers) , and ​ bd ​ is not 0. Because ​ ac/bd ​ is the ratio of two (integers, irrational numbers) , the product is a rational number.