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: 71

Answer

$\frac{2}{3}$

Work Step by Step

($\frac{4}{9}$) $\times$ (-$\frac{9}{8}$) $\div$ (-$\frac{3}{4}$) = RECALL: $\frac{a}{b}$ $\div$ $\frac{c}{d}$ = $\frac{a}{b}$ $\times$ $\frac{d}{c}$ Use the rule above to obtain: ($\frac{4}{9}$) $\times$ (-$\frac{9}{8}$) $\times$ (-$\frac{4}{3}$) = Multiply the numerators by each other, and multiply the denominators by each other: $\frac{(4)\ \times\ (-9)\ \times\ (-4)}{9\ \times\ 8\ \times\ 3}$ = Factor the numerator and the denominator $\frac{2\ \times\ 2\ \times\ (-1)\ \times\ 3\ \times\ 3\ \times\ (-1)\ \times\ 2\ \times\ 2}{3\ \times\ 3\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 3}$ = Cancel the common factors in the numerator and the denominator to obtain: $\frac{2}{3}$
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