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: 18

Answer

Estimated answer = 26 Exact answer = $25\frac{7}{24}$

Work Step by Step

$18\frac{5}{8}$ + $6\frac{2}{3}$ Estimation: $18\frac{5}{8}\approx 19$ $6\frac{2}{3} \approx 7$ Therefore $18\frac{5}{8}$ + $6\frac{2}{3}$ $\approx$ 19 + 7 = 26 Exact Calculation: $18\frac{5}{8}$ + $6\frac{2}{3}$ = $18\frac{5\times3}{8\times3}$ + $6\frac{2\times8}{3\times8}$ (24 is the least common denominator) = $18\frac{15}{24}$ + $6\frac{16}{24}$ = $18$ + $6$ + $\frac{15}{24}$ + $\frac{16}{24}$ (Adding whole part separately and fractional part separately) = $24$ + $\frac{15 + 16}{24}$ = $24$ + $\frac{31}{24}$ = $24$ + $\frac{24 + 7}{24}$ = $24$ + $\frac{24}{24} + \frac{7}{24} $ = 24 + 1 + $\frac{7}{24}$ = $25\frac{7}{24}$ The estimate was 26, so the exact answer of $25\frac{7}{24}$ is reasonable.
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