College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.2 - Real Numbers - P.2 Exercises: 6

Answer

(a) Yes, rational. (b) No, the sum can be rational.

Work Step by Step

(a) $\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}=\frac{ad+cb}{db}$ Since a, b, c, and d are whole numbers, multiplying them keeps them whole. So the final fraction is also rational. Therefore, yes, two rational numbers add up to another rational number. (b) No, two irrational numbers can add up to a rational number. For example, $-\sqrt2+\sqrt2=0$, and $0$ is a rational number.
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