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:
When you add two numbers that can be written as fractions (rationals), the result is also a fraction. If you have p/q and r/s with p, q, r, s integers and q and s not zero, their sum is (ps + rq) / (qs). Both ps + rq and qs are integers, and qs is nonzero, so the result is a ratio of integers. That means the sum is a rational number. The sum could be zero in some cases (like 1/2 + -1/2), but zero is still a rational number. It cannot be irrational or undefined when both addends are rational. Therefore, the sum is rational.

When you add two numbers that can be written as fractions (rationals), the result is also a fraction. If you have p/q and r/s with p, q, r, s integers and q and s not zero, their sum is (ps + rq) / (qs). Both ps + rq and qs are integers, and qs is nonzero, so the result is a ratio of integers. That means the sum is a rational number. The sum could be zero in some cases (like 1/2 + -1/2), but zero is still a rational number. It cannot be irrational or undefined when both addends are rational. Therefore, the sum is rational.

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