## Basic College Mathematics (10th Edition)

Published by Pearson

# Chapter 3 - Adding and Subtracting Fractions - 3.4 Adding and Subtracting Mixed Numbers - 3.4 Exercises - Page 228: 31

#### Answer

Estimated answer = 13 Exact answer = $12\frac{19}{20}$

#### Work Step by Step

$18\frac{3}{4}$ - $5\frac{4}{5}$ Estimation: $18\frac{3}{4} \approx 19$ $5\frac{4}{5} \approx 6$ Therefore $18\frac{3}{4}$ - $5\frac{4}{5}$ $\approx$ 19 - 6 = 13 Exact Calculation: $18\frac{3}{4}$ - $5\frac{4}{5}$ = $18\frac{3\times5}{4\times5}$ - $5\frac{4\times4}{5\times4}$ (20 is the least common denominator) = $18\frac{15}{20}$ - $5\frac{16}{20}$ = $18$ + $\frac{15}{20}$ - ($5$ + $\frac{16}{20})$ = $18$ + $\frac{15}{20}$ - $5$ - $\frac{16}{20}$ = ($18$ - $5$) + ($\frac{15}{20}$ - $\frac{16}{20}$) (Solving whole parts separately and fractional parts separately) = $13$ + $\frac{15 - 16}{20}$ = $13$ + $\frac{-1}{20}$ = $12 + 1$ - $\frac{1}{20}$ = $12$ + $\frac{20}{20}$ - $\frac{1}{20}$ = $12$ + $\frac{20 - 1}{20}$ = $12$ + $\frac{19}{20}$ = $12\frac{19}{20}$ The estimate was 13, so the exact answer of $12\frac{19}{20}$ is reasonable.

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