$a)5\frac{1}{7}:0,9+0,1=\frac{36}{7}:\frac{9}{10}+0,1=$   $\frac{36}{7}\cdot \frac{10}{9}+0,1=$   $\frac{4}{7}\cdot \frac{10}{1}+\frac{1}{10}=$   $\frac{40}{7}+\frac{1}{10}=$   $\frac{400}{70}+\frac{7}{70}=\frac{407}{70}=5\frac{57}{70}$  

$b)\frac{1}{5}-0,01:0,2=\frac{2}{10}-0,1:2=0,2-0,05=0,15$