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: 14

Answer

Estimated answer = 14 Exact answer = $13\frac{1}{2}$

Work Step by Step

$12\frac{4}{5}$ + $\frac{7}{10}$ Estimation: $12\frac{4}{5} \approx 13$ $\frac{7}{10} \approx 1$ Therefore $12\frac{4}{5}$ + $\frac{7}{10}$ $\approx$ 13 + 1 = 14 Exact Calculation: $12\frac{4}{5}$ + $\frac{7}{10}$ = $12\frac{4\times2}{5\times2}$ + $\frac{7}{10}$ (10 is the least common denominator) = $12\frac{8}{10}$ + $\frac{7}{10}$ = $12$ + $\frac{8}{10}$ + $\frac{7}{10}$ (taking whole part separately and fractional part separately) = $12$ + $\frac{8 + 7}{10}$ = $12$ + $\frac{15}{10}$ = $12$ + $\frac{10 + 5}{10}$ = $12$ + $\frac{10}{10} + \frac{5}{10} $ = 12 + 1 + $\frac{1}{2}$ = $13\frac{1}{2}$ The estimate was 14, so the exact answer of $13\frac{1}{2}$ is reasonable.
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