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: 20

Answer

Estimated answer = 33 Exact answer = $33\frac{1}{8}$

Work Step by Step

$7\frac{1}{4}$ + $25\frac{7}{8}$ Estimation: $7\frac{1}{4}\approx 7$ $25\frac{7}{8} \approx 26$ Therefore $7\frac{1}{4}$ + $25\frac{7}{8}$ $\approx$ 7 + 26 = 33 Exact Calculation: $7\frac{1}{4}$ + $25\frac{7}{8}$ = $7\frac{1\times2}{4\times2}$ + $25\frac{7}{8}$ (8 is the least common denominator) = $7\frac{2}{8}$ + $25\frac{7}{8}$ = $7$ + $25$ + $\frac{2}{8}$ + $\frac{7}{8}$ (Adding whole parts separately and fractional parts separately) = $32$ + $\frac{2 + 7}{8}$ = $32$ + $\frac{9}{8}$ = $32$ + $\frac{8 + 1}{8}$ = $32$ + $\frac{8}{8} + \frac{1}{8} $ = 32 + 1 + $\frac{1}{8}$ = $33\frac{1}{8}$ The estimate was 33, so the exact answer of $33\frac{1}{8}$ is reasonable.
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