Elementary Algebra

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

Chapter 2 - Real Numbers - Chapters 1-2 Cumulative Review Problem Set: 8

Answer

$\frac{-7}{6}$

Work Step by Step

According to the rules of simplification, we first need to simplify the expressions in the parenthesis and then move on to addition/subtraction. Therefore, we first multiply the fractions in parenthesis together and reduce these fractions by cancelling out the common factors in the numerators and denominators. Step 1: $(\frac{2}{3})(-\frac{3}{4})-(\frac{5}{6})(\frac{4}{5})$ Step 2: $(\frac{2\times-3}{3\times4})-(\frac{5\times4}{6\times5})$ Step 3: $(\frac{2\times-1}{1\times4})-(\frac{1\times4}{6\times1})$ Step 4: $(\frac{1\times-1}{1\times2})-(\frac{1\times2}{3\times1})$ Then, we simplify the two fractions by finding the LCM of their denominators: Step 5: $(\frac{-1}{2})-(\frac{2}{3})$ Step 6: $\frac{-1(3)-2(2)}{6}$ Step 7: $\frac{-3-4}{6}$ Step 8: $\frac{-7}{6}$
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