$\frac{3}{10}\times \frac{4}{9}= \frac{3 \times 4}{10\times 9}=\frac{12}{90}$
$\frac{6}{5}:\frac{3}{7}=\frac{6}{5}\times \frac{7}{3}=\frac{6\times 7}{5\times 3}=\frac{42}{15}$
$\frac{3}{4}\times \frac{2}{5}=\frac{3\times 2}{4\times 5}=\frac{6}{20}$
$\frac{5}{8}:\frac{1}{2}=\frac{5}{8}\times \frac{2}{1}=\frac{5\times 2}{8\times 1}=\frac{10}{8}$