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: 38


$ \displaystyle \frac{2}{9}$

Work Step by Step

$\displaystyle \left(\frac{-4}{9} \right)\div\left(-2 \right)=$ Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ $\displaystyle \left(-\frac{4}{9} \right)\div\left(-2 \right)=$ Dividing two numbers with like signs: Divide their absolute values; the sign of the result is $"+"$. Also, write $2$ as $\displaystyle \frac{2}{1}.$ $=+\displaystyle \left(\frac{4}{9} \div \frac{2}{1} \right)$ Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$. $=\displaystyle \frac{4}{9} \cdot \frac{1}{2} $ Multiply fractions: Reduce by the common factor, 2. $=\displaystyle \frac{2}{9} \cdot \frac{1}{1} $ Now, multiply the numerators and place the product over the product of the denominators. $=\displaystyle \frac{2}{9}$
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