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: 24

Answer

Exact answer = $3\frac{3}{8}$

Work Step by Step

$14\frac{3}{4}$ - $11\frac{3}{8}$ Estimation: $14\frac{3}{4} \approx 15$ $11\frac{3}{8} \approx 11$ Therefore $14\frac{3}{4}$ - $11\frac{3}{8}$ $\approx$ 15 - 11 = 4 Exact Calculation: $14\frac{3}{4}$ - $11\frac{3}{8}$ = $14\frac{3\times2}{4\times2}$ - $11\frac{3}{8}$ (8 is the least common denominator) = $14\frac{6}{8}$ - $11\frac{3}{8}$ = $14$ + $\frac{6}{8}$ - ($11$ + $\frac{3}{8})$ = $14$ + $\frac{6}{8}$ - $11$ - $\frac{3}{8}$ = ($14$ - $11$) + ($\frac{6}{8}$ - $\frac{3}{8}$) (Solving whole parts separately and fractional parts separately) = $3$ + $\frac{6 - 3}{8}$ = $3$ + $\frac{3}{8}$ = $3\frac{3}{8}$ The estimate was 4, so the exact answer of $3\frac{3}{8}$ is reasonable.
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