Решение:

a)

$$\frac{1}{12} + \frac{3}{4} = \frac{1}{12} + \frac{3 \cdot 3}{4 \cdot 3} = \frac{1}{12} + \frac{9}{12} = \frac{1 + 9}{12} = \frac{10}{12} = \frac{5}{6}$$

б)

$$2\frac{1}{4} : \frac{1}{6} = \frac{2 \cdot 4 + 1}{4} : \frac{1}{6} = \frac{9}{4} : \frac{1}{6} = \frac{9}{4} \cdot \frac{6}{1} = \frac{9 \cdot 6}{4 \cdot 1} = \frac{54}{4} = \frac{27}{2} = 13\frac{1}{2}$$

в)

$$2 - 1\frac{3}{7} = 2 - \frac{1 \cdot 7 + 3}{7} = 2 - \frac{10}{7} = \frac{2 \cdot 7}{7} - \frac{10}{7} = \frac{14}{7} - \frac{10}{7} = \frac{14 - 10}{7} = \frac{4}{7}$$

г)

$$12 \cdot \frac{3}{4} = \frac{12}{1} \cdot \frac{3}{4} = \frac{12 \cdot 3}{1 \cdot 4} = \frac{36}{4} = 9$$