Решение:

а) $$2 + 3\frac{1}{5} = 2 + \frac{3*5+1}{5} = 2 + \frac{16}{5} = \frac{2*5}{5} + \frac{16}{5} = \frac{10}{5} + \frac{16}{5} = \frac{10+16}{5} = \frac{26}{5} = 5\frac{1}{5}$$ б) $$4\frac{1}{4} + 15 = \frac{4*4+1}{4} + 15 = \frac{17}{4} + 15 = \frac{17}{4} + \frac{15*4}{4} = \frac{17}{4} + \frac{60}{4} = \frac{17+60}{4} = \frac{77}{4} = 19\frac{1}{4}$$ в) $$23\frac{12}{13} + 7\frac{2}{13} = (23+7) + (\frac{12}{13} + \frac{2}{13}) = 30 + \frac{12+2}{13} = 30 + \frac{14}{13} = 30 + 1\frac{1}{13} = 31\frac{1}{13}$$ г) $$2\frac{2}{3} + 5\frac{2}{3} = (2+5) + (\frac{2}{3} + \frac{2}{3}) = 7 + \frac{2+2}{3} = 7 + \frac{4}{3} = 7 + 1\frac{1}{3} = 8\frac{1}{3}$$

Ответ:

а) $$\textbf{5\frac{1}{5}}$$ б) $$\textbf{19\frac{1}{4}}$$ в) $$\textbf{31\frac{1}{13}}$$ г) $$\textbf{8\frac{1}{3}}$$