The sum of two rational numbers is

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

The sum of two rational numbers is

Explanation:
The sum of two rational numbers is rational because rational numbers are closed under addition. If you have two fractions p/q and r/s with integers p, q, r, s and q and s nonzero, their sum is (ps + rq) / (qs). The numerator and the denominator are integers, and the product qs is nonzero, so the result is again a fraction of integers, which is, by definition, rational. This sum can be zero in a special case if the numbers cancel each other out, but it will always be a rational number. It cannot be irrational or undefined, since the operation stays within the set of rational numbers as long as you start with rationals.

The sum of two rational numbers is rational because rational numbers are closed under addition. If you have two fractions p/q and r/s with integers p, q, r, s and q and s nonzero, their sum is (ps + rq) / (qs). The numerator and the denominator are integers, and the product qs is nonzero, so the result is again a fraction of integers, which is, by definition, rational. This sum can be zero in a special case if the numbers cancel each other out, but it will always be a rational number. It cannot be irrational or undefined, since the operation stays within the set of rational numbers as long as you start with rationals.

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