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 227: 13

Answer

Estimated answer = 5 Exact answer = $4\frac{5}{24}$

Work Step by Step

$\frac{5}{8}$ + $3\frac{7}{12}$ Estimate Calculation: $\frac{5}{8} \approx 1$ $3\frac{7}{12} \approx 4$ Therefore $\frac{5}{8}$ + $3\frac{7}{12}$ $\approx$ 1 + 4 = 5 Exact Calculation: $\frac{5}{8}$ + $3\frac{7}{12}$ = $\frac{5\times3}{8\times3}$ + $3\frac{7\times2}{12\times2}$ (24 is the least common denominator) = $\frac{15}{24}$ + $3\frac{14}{24}$ = $3$ + $\frac{15}{24}$ + $\frac{14}{24}$ (taking whole part separately and fractional part separately) = $3$ + $\frac{15 + 14}{24}$ = $3$ + $\frac{29}{24}$ = $3$ + $\frac{24 + 5}{24}$ = $3$ + $\frac{24}{24} + \frac{5}{24} $ = 3 + 1 + $\frac{5}{24}$ = $4\frac{5}{24}$ The estimate was 5, so the exact answer of $4\frac{5}{24}$ is reasonable.
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