$a)1\frac{1}{3}\cdot \frac{2}{5}=\frac{4}{3}\cdot \frac{2}{5}=\frac{8}{15}$  

$b)3\frac{1}{2}\cdot \frac{3}{4}=\frac{7}{2}\cdot \frac{3}{4}=\frac{21}{8}=2\frac{5}{8}$  

$c)\frac{3}{7}\cdot 4\frac{3}{4}=\frac{3}{7}\cdot \frac{19}{4}=\frac{57}{28}=2\frac{1}{28}$  

$d)2\frac{4}{5}\cdot 3\frac{2}{3}=\frac{14}{5}\cdot \frac{11}{3}=\frac{154}{15}=10\frac{4}{15}$  

$e)1\frac{2}{3}\cdot 3\frac{1}{2}=\frac{5}{3}\cdot \frac{7}{2}=\frac{35}{6}=5\frac{5}{6}$  

$f)2\frac{1}{4}\cdot 3\frac{4}{5}=\frac{9}{4}\cdot \frac{19}{5}=\frac{171}{20}=8\frac{11}{20}$