Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10: 0134467795
ISBN 13: 978-0-13446-779-5

Chapter 2 - Multiplying and Dividing Fractions - 2.7 Dividing Fractions - 2.7 Exercises - Page 164: 6



Work Step by Step

Remember, that the product of a number $a$ and its reciprocal is 1. Therefore, the reciprocal of $a$ must be $\frac{1}{a}$ (which is just $a$ flipped), so that $a\times\frac{1}{a}=1$. Therefore, the reciprocal of $\frac{2}{5}$ is $\frac{1}{\frac{2}{5}}=1\times\frac{5}{2}=\frac{5}{2}$. $\frac{2}{5}\times\frac{5}{2}=1$
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