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: 21

Answer

Estimated answer = 47 Exact answer = = $45\frac{5}{6}$

Work Step by Step

$12\frac{8}{15}$ + $18\frac{3}{5} + 14\frac{7}{10}$ Estimation: $12\frac{8}{15}\approx 13$ $18\frac{3}{5} \approx 19$ $14\frac{7}{10} \approx 15$ Therefore $12\frac{8}{15}$ + $18\frac{3}{5} + 14\frac{7}{10}$ $\approx$ 13 + 19 + 15 = 47 Exact Calculation: $12\frac{8}{15}$ + $18\frac{3}{5} + 14\frac{7}{10}$ = $12\frac{8\times2}{15\times2}$ + $18\frac{3\times6}{5\times6}$ + $14\frac{7\times3}{10\times3}$ (30 is the least common denominator) = $12\frac{16}{30}$ + $18\frac{18}{30}$ + $14\frac{21}{30}$ = $12$ +$18$ + $14$ + $\frac{16}{30}$ + $\frac{18}{30}$ + $\frac{21}{30}$ (Adding whole parts separately and fractional parts separately) = $44$ + $\frac{16 + 18 + 21}{30}$ = $44$ + $\frac{55}{30}$ = $44$ + $\frac{30 + 25}{30}$ = $44$ + $\frac{30}{30} + \frac{25}{30} $ = 44 + 1 + $\frac{5}{6}$ = $45\frac{5}{6}$ The estimate was 47, so the exact answer of = $45\frac{5}{6}$ is reasonable.
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