$a)3\frac{1}{4}-2\frac{3}{4}=2\frac{5}{4}-2\frac{3}{4}=\frac{2}{4}=\frac{1}{2}$  

$b)13\frac{1}{7}+2\frac{2}{3}=13\frac{3}{21}+2\frac{14}{21}=$   $15\frac{17}{21}$  

$c)1\frac{3}{5}\cdot 2\frac{1}{4}=\frac{8}{5}\cdot \frac{9}{4}=$   $\frac{2}{5}\cdot \frac{9}{1}=\frac{18}{5}=3\frac{3}{5}$  

$d)4\frac{2}{3}-\frac{1}{3}:2=$   $4\frac{2}{3}-\frac{1}{3}\cdot \frac{1}{2}=4\frac{2}{3}-\frac{1}{6}=4\frac{4}{6}-\frac{1}{6}=4\frac{3}{6}=4\frac{1}{2}$  

$e)3\frac{3}{4}:\frac{5}{6}-\frac{1}{4}\cdot 1\frac{2}{3}=$   $\frac{15}{4}\cdot \frac{6}{5}-\frac{1}{4}\cdot \frac{5}{3}=$   $\frac{3}{4}\cdot \frac{6}{1}-\frac{5}{12}=$   $\frac{3}{2}-\frac{3}{1}-\frac{5}{12}=$  

$=\frac{9}{2}-\frac{5}{12}=4\frac{1}{2}-\frac{5}{12}=4\frac{6}{12}-\frac{5}{12}=4\frac{1}{12}$  

$f)1\frac{2}{5}\cdot 3\frac{4}{7}-2\frac{1}{8}\cdot 2\frac{6}{17}=$   $\frac{7}{5}\cdot \frac{25}{7}-\frac{17}{8}\cdot \frac{40}{17}=$   $\frac{1}{5}\cdot \frac{25}{1}-\frac{1}{8}\cdot \frac{40}{1}=$   $5-5=0$