Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter R - Section R.2 - Operations on Real Numbers - R.2 Exercises: 56

Answer

Because the "1" on top of the reciprocal is always positive and thus doesn't change the sign of the overall fraction.

Work Step by Step

If we take the reciprocal of a nonzero number, the sign stays the same: If $x\gt 0$: $\frac{1}{x}\gt 0$ If $x\lt 0$: $\frac{1}{x}\lt 0$ This is because the "1" on top of the reciprocal is always positive and thus doesn't change the sign of the overall fraction (i.e. positive/negative=negative; positive/positive=positive).
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