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: 16

Answer

Estimated answer = 31 Exact answer = $30\frac{5}{14}$

Work Step by Step

$14\frac{6}{7}$ + $15\frac{1}{2}$ Estimation: $14\frac{6}{7}\approx 15$ $15\frac{1}{2} \approx 16$ Therefore $14\frac{6}{7}$ + $15\frac{1}{2}$ $\approx$ 15 + 16 = 31 Exact Calculation: $14\frac{6}{7}$ + $15\frac{1}{2}$ = $14\frac{6\times2}{7\times2}$ + $15\frac{1\times7}{2\times7}$ (14 is the least common denominator) = $14\frac{12}{14}$ + $15\frac{7}{14}$ = $14$ + $15$ + $\frac{12}{14}$ + $\frac{7}{14}$ (Adding whole part separately and fractional part separately) = $29$ + $\frac{12 + 7}{14}$ = $29$ + $\frac{19}{14}$ = $29$ + $\frac{14 + 5}{14}$ = $29$ + $\frac{14}{14} + \frac{5}{14} $ = 29 + 1 + $\frac{5}{14}$ = $30\frac{5}{14}$ The estimate was 31, so the exact answer of $30\frac{5}{14}$ is reasonable.
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