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: 27

Answer

Estimated answer = 22 Exact answer = $22\frac{7}{30}$

Work Step by Step

$28\frac{3}{10}$ - $6\frac{1}{15}$ Estimation: $28\frac{3}{10} \approx 28$ $6\frac{1}{15} \approx 6$ Therefore $28\frac{3}{10}$ - $6\frac{1}{15}$ $\approx$ 28 - 6 = 22 Exact Calculation: $28\frac{3}{10}$ - $6\frac{1}{15}$ = $28\frac{3\times3}{10\times3}$ - $6\frac{1\times2}{15\times2}$ (30 is the least common denominator) = $28\frac{9}{30}$ - $6\frac{2}{30}$ = $28$ + $\frac{9}{30}$ - ($6$ + $\frac{2}{30})$ = $28$ + $\frac{9}{30}$ - $6$ - $\frac{2}{30}$ = ($28$ - $6$) + ($\frac{9}{30}$ - $\frac{2}{30}$) (Solving whole parts separately and fractional parts separately) = $22$ + $\frac{9 - 2}{30}$ = $22$ + $\frac{7}{30}$ = $22\frac{7}{30}$ The estimate was 22, so the exact answer of $22\frac{7}{30}$ is reasonable.
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