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 229: 32

Answer

Estimated answer = 11 Exact answer = $10\frac{23}{24}$

Work Step by Step

$14\frac{5}{8}$ - $3\frac{2}{3}$ Estimation: $14\frac{5}{8} \approx 15$ $3\frac{2}{3} \approx 4$ Therefore $14\frac{5}{8}$ - $3\frac{2}{3}$ $\approx$ 15 - 4 = 11 Exact Calculation: $14\frac{5}{8}$ - $3\frac{2}{3}$ = $14\frac{5\times3}{8\times3}$ - $3\frac{2\times8}{3\times8}$ (24 is the least common denominator) = $14\frac{15}{24}$ - $3\frac{16}{24}$ = $14$ + $\frac{15}{24}$ - ($3$ + $\frac{16}{24})$ = $14$ + $\frac{15}{24}$ - $3$ - $\frac{16}{24}$ = ($14$ - $3$) + ($\frac{15}{24}$ - $\frac{16}{24}$) (Solving whole parts separately and fractional parts separately) = $11$ + $\frac{15 - 16}{24}$ = $11$ + $\frac{-1}{24}$ = $10 + 1$ - $\frac{1}{24}$ = $10$ + $\frac{24}{24}$ - $\frac{1}{24}$ = $10$ + $\frac{24 - 1}{24}$ = $10$ + $\frac{23}{24}$ = $10\frac{23}{24}$ The estimate was 11, so the exact answer of $10\frac{23}{24}$ is reasonable.
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