Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10:
ISBN 13:

Chapter 3 - Adding and Subtracting Fractions - 3.4 Adding and Subtracting Mixed Numbers - 3.4 Exercises - Page 234: 89

Answer

(a) $\frac{23}{24}$ (b) $\frac{8}{15}$ (c) $\frac{43}{48}$ (d) $\frac{4}{21}$

Work Step by Step

We add or subtract the given fractions: (a) $\displaystyle \frac{5}{8}+\frac{1}{3}$ We see that the Lowest Common Denominator is 24: $\displaystyle =\frac{15}{24}+\frac{8}{24}$ $\displaystyle =\frac{15+8}{24}$ $\displaystyle =\frac{23}{24}$ (b) $\displaystyle \frac{19}{20}-\frac{5}{12}$ We see that the Lowest Common Denominator is 60: $\displaystyle =\frac{57}{60}-\frac{25}{60}$ $\displaystyle =\frac{57-25}{60}$ $\displaystyle =\frac{32}{60}$ $\displaystyle =\frac{8}{15}$ (c) $\displaystyle \frac{7}{12}+\frac{3}{16}+\frac{3}{24}$ We see that the Lowest Common Denominator is 48: $\displaystyle =\frac{28}{48}+\frac{9}{48}+\frac{6}{48}$ $\displaystyle =\frac{43}{48}$ (d) $\displaystyle \frac{6}{7}-\frac{2}{3}$ We see that the Lowest Common Denominator is 21: $\displaystyle =\frac{18}{21}-\frac{14}{21}$ $\displaystyle =\frac{18-14}{21}$ $\displaystyle =\frac{4}{21}$
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