Решение

a) $$\begin{aligned}5\frac{1}{2}+1\frac{1}{6}&=5+\frac{1}{2}+1+\frac{1}{6}=\\\&=(5+1)+\left(\frac{1}{2}+\frac{1}{6}\right)=6+\left(\frac{3}{6}+\frac{1}{6}\right)=6+\frac{4}{6}=6+\frac{2}{3}=6\frac{2}{3}\end{aligned}$$

б) $$\begin{aligned}2\frac{4}{9}+3\frac{1}{2}&=2+\frac{4}{9}+3+\frac{1}{2}=\\\&=(2+3)+\left(\frac{4}{9}+\frac{1}{2}\right)=5+\left(\frac{8}{18}+\frac{9}{18}\right)=5+\frac{17}{18}=5\frac{17}{18}\end{aligned}$$

в) $$\begin{aligned}5\frac{7}{12}+1\frac{1}{8}&=5+\frac{7}{12}+1+\frac{1}{8}=\\\&=(5+1)+\left(\frac{7}{12}+\frac{1}{8}\right)=6+\left(\frac{14}{24}+\frac{3}{24}\right)=6+\frac{17}{24}=6\frac{17}{24}\end{aligned}$$

г) $$\begin{aligned}6\frac{2}{5}-1\frac{1}{10}&=6+\frac{2}{5}-1-\frac{1}{10}=\\\&=(6-1)+\left(\frac{2}{5}-\frac{1}{10}\right)=5+\left(\frac{4}{10}-\frac{1}{10}\right)=5+\frac{3}{10}=5\frac{3}{10}\end{aligned}$$

д) $$\begin{aligned}4\frac{5}{7}-1\frac{1}{3}&=4+\frac{5}{7}-1-\frac{1}{3}=\\\&=(4-1)+\left(\frac{5}{7}-\frac{1}{3}\right)=3+\left(\frac{15}{21}-\frac{7}{21}\right)=3+\frac{8}{21}=3\frac{8}{21}\end{aligned}$$

е) $$\begin{aligned}3\frac{1}{2}-1\frac{1}{3}&=3+\frac{1}{2}-1-\frac{1}{3}=\\\&=(3-1)+\left(\frac{1}{2}-\frac{1}{3}\right)=2+\left(\frac{3}{6}-\frac{2}{6}\right)=2+\frac{1}{6}=2\frac{1}{6}\end{aligned}$$