## 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 229: 33

#### Answer

Estimated answer = 8 Exact answer = $7\frac{11}{12}$

#### Work Step by Step

$19\frac{2}{3}$ - $11\frac{3}{4}$ Estimation: $19\frac{2}{3} \approx 20$ $11\frac{3}{4} \approx 12$ Therefore $19\frac{2}{3}$ - $11\frac{3}{4}$ $\approx$ 20 - 12 = 8 Exact Calculation: $19\frac{2}{3}$ - $11\frac{3}{4}$ = $19\frac{2\times4}{3\times4}$ - $11\frac{3\times3}{4\times3}$ (12 is the least common denominator) = $19\frac{8}{12}$ - $11\frac{9}{12}$ = ($19$ - $11$) + ($\frac{8}{12}$ - $\frac{9}{12}$) (Solving whole parts separately and fractional parts separately) = $8$ + $\frac{8 - 9}{12}$ = $8$ + $\frac{-1}{12}$ = $7 + 1$ - $\frac{1}{12}$ = $7$ + $\frac{12}{12}$ - $\frac{1}{12}$ = $7$ + $\frac{12 - 1}{12}$ = $7$ + $\frac{11}{12}$ = $7\frac{11}{12}$ The estimate was 8, so the exact answer of $7\frac{11}{12}$ is reasonable.

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