4. a) 3\frac{3}{4} + 1\frac{1}{2}; в) 4 - 1\frac{2}{3}; д) 1\frac{1}{3} \cdot 4; ж) 2\frac{1}{4} : 3; б) 2\frac{5}{6} - 1\frac{5}{12}; г) 3\frac{2}{7} - \frac{6}{7}; е) 3\frac{1}{4} \cdot \frac{2}{5}; з) 20 : 2\frac{1}{2}.

a) $$3\frac{3}{4} + 1\frac{1}{2} = 3\frac{3}{4} + 1\frac{2}{4} = (3+1) + (\frac{3}{4} + \frac{2}{4}) = 4 + \frac{5}{4} = 4 + 1\frac{1}{4} = 5\frac{1}{4}$$.

б) $$2\frac{5}{6} - 1\frac{5}{12} = 2\frac{10}{12} - 1\frac{5}{12} = (2-1) + (\frac{10}{12} - \frac{5}{12}) = 1 + \frac{5}{12} = 1\frac{5}{12}$$.

в) $$4 - 1\frac{2}{3} = 3\frac{3}{3} - 1\frac{2}{3} = (3-1) + (\frac{3}{3} - \frac{2}{3}) = 2 + \frac{1}{3} = 2\frac{1}{3}$$.

г) $$3\frac{2}{7} - \frac{6}{7} = 3\frac{2}{7} - \frac{6}{7} = 2\frac{9}{7} - \frac{6}{7} = 2 + \frac{3}{7} = 2\frac{3}{7}$$.

д) $$1\frac{1}{3} \cdot 4 = \frac{4}{3} \cdot 4 = \frac{16}{3} = 5\frac{1}{3}$$.

e) $$3\frac{1}{4} \cdot \frac{2}{5} = \frac{13}{4} \cdot \frac{2}{5} = \frac{26}{20} = \frac{13}{10} = 1\frac{3}{10}$$.

ж) $$2\frac{1}{4} : 3 = \frac{9}{4} : 3 = \frac{9}{4} \cdot \frac{1}{3} = \frac{9}{12} = \frac{3}{4}$$.

з) $$20 : 2\frac{1}{2} = 20 : \frac{5}{2} = 20 \cdot \frac{2}{5} = \frac{40}{5} = 8$$.

Ответ: а) $$5\frac{1}{4}$$, б) $$1\frac{5}{12}$$, в) $$2\frac{1}{3}$$, г) $$2\frac{3}{7}$$, д) $$5\frac{1}{3}$$, е) $$1\frac{3}{10}$$, ж) $$\frac{3}{4}$$, з) 8