Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 2 - Section 2.4 - Signed Fractions - Exercises - Page 119: 44


$\displaystyle \frac{11}{16}$

Work Step by Step

First, write mixed numbers as improper fractions, Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ $ \displaystyle \left(-\frac{11}{4} \right)\div\left(+\frac{8}{5} \right)\left(-\frac{2}{5} \right)$ Dividing with a fraction $\displaystyle \frac{a}{b} $ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$ = $\displaystyle \left(-\frac{11}{4} \right)\cdot\left(+\frac{5}{8} \right)\left(-\frac{2}{5} \right)$ There are 2 minus signs in the product: the result is positive. = $+\displaystyle \left(\frac{11}{4} \cdot\frac{5}{8}\cdot\frac{2}{5} \right)$ Reduce by the common factors, 5 and 2 = $\displaystyle \frac{11}{2} \cdot\frac{1}{8}\cdot\frac{1}{1} $ Now, multiply the numerators and place the product over the product of the denominators. = $\displaystyle \frac{11}{16}$
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