## Basic College Mathematics (10th Edition)

Estimate : 19 + 9 + 12 = 40 Exact: $40\frac{29}{60}$
$18\frac{3}{4}+9\frac{2}{5}+12\frac{1}{3}$ Lets first Find Estimate of fraction: $18\frac{3}{4}$= 19, $9\frac{2}{5}$=9 $12\frac{1}{3}$=12 So $18\frac{3}{4}+9\frac{2}{5}+12\frac{1}{3}$ = 19 + 9 + 12 = 40 Now find Exact: $18\frac{3}{4}+9\frac{2}{5}+12\frac{1}{3}$ = $\frac{18\times4+3}{4}+\frac{9\times5+2}{5}+\frac{12\times3+1}{3}$ = $\frac{75}{4}+\frac{47}{5}+\frac{37}{3}$ = $\frac{75\times15}{4\times15}+\frac{47\times12}{5\times12}+\frac{37\times20}{3\times20}$ (Least common multiple of 4,5 & 3 is 60) = $\frac{1125}{60}+\frac{564}{60}+\frac{740}{60}$ = $\frac{1125+564+740}{60}$ (Addition of fraction with same denominator) = $\frac{2429}{60}$ = $40\frac{29}{60}$