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 228: 22

Answer

Estimated answer = 37 Exact answer = $36\frac{3}{4}$

Work Step by Step

$14\frac{9}{10}$ + $8\frac{1}{4} + 13\frac{3}{5}$ Estimation: $14\frac{9}{10}\approx 15$ $8\frac{1}{4} \approx 8$ $13\frac{3}{5} \approx 14$ Therefore $14\frac{9}{10}$ + $8\frac{1}{4} + 13\frac{3}{5}$ $\approx$ 15 + 8 + 14 = 37 Exact Calculation: $14\frac{9}{10}$ + $8\frac{1}{4} + 13\frac{3}{5}$ = $14\frac{9\times2}{10\times2}$ + $8\frac{1\times5}{4\times5}$ + $13\frac{3\times4}{5\times4}$ (20 is the least common denominator) = $14\frac{18}{20}$ + $8\frac{5}{20}$ + $13\frac{12}{20}$ = $14$ +$8$ + $13$ + $\frac{18}{20}$ + $\frac{5}{20}$ + $\frac{12}{20}$ (Adding whole parts separately and fractional parts separately) = $35$ + $\frac{18 + 5 + 12}{20}$ = $35$ + $\frac{35}{20}$ = $35$ + $\frac{20 + 15}{20}$ = $35$ + $\frac{20}{20} + \frac{15}{20} $ = 35 + 1 + $\frac{3}{4}$ = $36\frac{3}{4}$ The estimate was 37, so the exact answer of = $36\frac{3}{4}$ is reasonable.
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