$a)\frac{1}{2}+\underline{\frac{1}{2}\cdot \frac{1}{2}}=\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}$

$b)\underline{\frac{1}{3}-\frac{1}{3}}+\frac{1}{3}=0+\frac{1}{3}=\frac{1}{3}$ $b)\underline{\frac{1}{3}-\frac{1}{3}}+\frac{1}{3}=0+\frac{1}{3}=\frac{1}{3}$

$c)\underline{\left(\frac{1}{4}+\frac{1}{4}\right)}:\frac{1}{4}=\frac{2}{4}:\frac{1}{4}=\frac{2}{4}\cdot \frac{4}{1}=2$

$d)\underline{\frac{1}{5}:\frac{1}{5}}-\frac{1}{5}=1-\frac{1}{5}=\frac{5}{5}-\frac{1}{5}=\frac{4}{5}$

$e)\frac{1}{6}-\underline{\frac{1}{6}\cdot \frac{1}{6}}=\frac{1}{6}-\frac{1}{36}=\frac{6}{36}-\frac{1}{36}=\frac{5}{36}$

$f)\frac{1}{7}\cdot \underline{\left(\frac{1}{7}+\frac{1}{7}\right)}=\frac{1}{7}\cdot \frac{2}{7}=\frac{2}{49}$