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 227: 19

Answer

Estimated answer = 38 Exact answer = $38\frac{5}{28}$

Work Step by Step

$22\frac{3}{4}$ + $15\frac{3}{7}$ Estimation: $22\frac{3}{4}\approx 23$ $15\frac{3}{7} \approx 15$ Therefore $22\frac{3}{4}$ + $15\frac{3}{7}$ $\approx$ 23 + 15 = 38 Exact Calculation: $22\frac{3}{4}$ + $15\frac{3}{7}$ = $22\frac{3\times7}{4\times7}$ + $15\frac{3\times4}{7\times 4}$ (28 is the least common denominator) = $22\frac{21}{28}$ + $15\frac{12}{28}$ = $22$ + $15$ + $\frac{21}{28}$ + $\frac{12}{28}$ (Adding whole parts separately and fractional parts separately) = $37$ + $\frac{21 + 12}{28}$ = $37$ + $\frac{33}{28}$ = $37$ + $\frac{28 + 5}{28}$ = $37$ + $\frac{28}{28} + \frac{5}{28} $ = 37 + 1 + $\frac{5}{28}$ = $38\frac{5}{28}$ The estimate was 38, so the exact answer of $38\frac{5}{28}$ is reasonable.
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