\(4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}=\frac{22}{5}+\frac{17}{3}+\frac{11}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}=\left(\frac{22}{5}+\frac{3}{5}\right)+\left(\frac{17}{3}+\frac{1}{3}\right)+\left(\frac{11}{4}+\frac{1}{4}\right)\)\(=\frac{25}{5}+\frac{18}{3}+\frac{12}{4}=5+6+3=11+3=14\)