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: 23

Answer

Exact answer = $2\frac{5}{8}$

Work Step by Step

$14\frac{7}{8}$ - $12\frac{1}{4}$ Estimation: $14\frac{7}{8} \approx 15$ $12\frac{1}{4} \approx 12$ Therefore $14\frac{7}{8}$ - $12\frac{1}{4}$ $\approx$ 15 - 12 = 3 Exact Calculation: $14\frac{7}{8}$ - $12\frac{1}{4}$ = $14\frac{7}{8}$ - $12\frac{1\times2}{4\times2}$ (8 is the least common denominator) = $14\frac{7}{8}$ - $12\frac{2}{8}$ = $14$ + $\frac{7}{8}$ - ($12$ + $\frac{2}{8})$ = $14$ + $\frac{7}{8}$ - $12$ - $\frac{2}{8}$ = ($14$ - $12$) + ($\frac{7}{8}$ - $\frac{2}{8}$) (Solving whole parts separately and fractional parts separately) = $2$ + $\frac{7 - 2}{8}$ = $2$ + $\frac{5}{8}$ = $2\frac{5}{8}$ The estimate was 3, so the exact answer of $2\frac{5}{8}$ is reasonable.
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