The product of two rational numbers is always what?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

The product of two rational numbers is always what?

Explanation:
Rational numbers stay closed under multiplication. A rational number can be written as a/b with integers a and b (b ≠ 0). Multiplying two such numbers, a/b and c/d, gives (ac)/(bd). Since ac and bd are integers and bd ≠ 0, the product is again a fraction of integers, i.e., rational. The only time the product isn’t a nonzero number is if one factor is zero, and that just yields zero, which is also rational. So the product of two rational numbers is always rational.

Rational numbers stay closed under multiplication. A rational number can be written as a/b with integers a and b (b ≠ 0). Multiplying two such numbers, a/b and c/d, gives (ac)/(bd). Since ac and bd are integers and bd ≠ 0, the product is again a fraction of integers, i.e., rational. The only time the product isn’t a nonzero number is if one factor is zero, and that just yields zero, which is also rational. So the product of two rational numbers is always rational.

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