$a)2\frac{1}{2}:3\frac{3}{4}+2\frac{1}{3}+{\left(\frac{1}{6}\right)}^2\cdot 6=$    $\frac{5}{2}:\frac{15}{4}+2\frac{1}{3}+\frac{1}{6}\cdot \frac{1}{6}\cdot 6=$   $\frac{5}{2}\cdot \frac{4}{15}+2\frac{1}{3}+\frac{1}{6}=$  

$=\frac{1}{2}\cdot \frac{4}{3}+2\frac{2}{6}+\frac{1}{6}=$   $\frac{2}{3}+2\frac{3}{6}=\frac{4}{6}+2\frac{3}{6}=$   $2\frac{7}{6}=3\frac{1}{6}$  

$b)2\frac{2}{5}\cdot 1\frac{7}{8}-{\left(1\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^3\cdot 2=$   $\frac{12}{5}\cdot \frac{15}{8}-\left(\frac{3}{2}\cdot \frac{3}{2}\right)+\frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}\cdot 2=$  

$=\frac{3}{5}\cdot \frac{15}{2}-\frac{9}{4}+\frac{1}{4}=$   $\frac{3}{1}\cdot \frac{3}{2}-\frac{9}{4}+\frac{1}{4}=$   $\frac{18}{4}-\frac{9}{4}+\frac{1}{4}=$   $\frac{9}{4}+\frac{1}{4}=\frac{10}{4}=\frac{5}{2}=2\frac{1}{2}$  

$c)2\frac{1}{7}+2\frac{1}{7}\cdot 2\frac{4}{5}-\left(1\frac{1}{2}:2\frac{1}{4}\right):\frac{1}{6}=$   $2\frac{1}{7}+\frac{15}{7}\cdot \frac{14}{5}-\left(\frac{3}{2}:\frac{9}{4}\right):\frac{1}{6}=$  

$=2\frac{1}{7}+\frac{3}{7}\cdot \frac{14}{1}-\left(\frac{3}{2}\cdot \frac{4}{9}\right)\cdot 6=$   $2\frac{1}{7}+6-\frac{2}{3}\cdot 6=$   $8\frac{1}{7}-2\cdot 8\frac{1}{7}-4=4\frac{1}{7}$

$d)3\frac{3}{7}-2\frac{1}{7}\cdot 2\frac{4}{5}:2=$   $3\frac{3}{7}-\frac{15}{7}\cdot \frac{14}{5}\cdot \frac{1}{2}=$   $3\frac{3}{7}-\frac{3}{7}\cdot \frac{14}{1}\cdot \frac{1}{2}=$  

$=3\frac{3}{7}-\frac{3}{1}\cdot \frac{2}{1}\cdot \frac{1}{2}=$   $3\frac{3}{7}-3=\frac{3}{7}$