Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 2 - Real Numbers - 2.1 - Rational Numbers: Multiplication and Division - Problem Set 2.1 - Page 48: 69



Work Step by Step

(-$\frac{6}{7}$) $\div$ ($\frac{5}{7}$) $\times$ (-$\frac{5}{6}$) = RECALL: $\frac{a}{b}$ $\div$ $\frac{c}{d}$ = $\frac{a}{b}$ $\times$ $\frac{d}{c}$ Use the rule above to obtain: (-$\frac{6}{7}$) $\times$ ($\frac{7}{5}$) $\times$ (-$\frac{5}{6}$) = Multiply the numerators by each other, and multiply the denominators by each other: $\frac{(-6)\ \times\ (7)\ \times\ (-5)}{7\ \times\ 5\ \times\ 6}$ = Factor the numerator and the denominator $\frac{(-1)\ \times\ 2\ \times\ 3\ \times\ (7)\ \times\ (-5)}{7\ \times\ 5\ \times\ 2\ \times\ 3}$ = Cancel the common factors in the numerator and the denominator to obtain: $\frac{-1\times-1}{1}=1$
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