Решение:
а) $\frac{1}{2} * (-\frac{2}{3}) + (-\frac{1}{2})^2 = -\frac{1 * \overset{1}{\cancel{2}}}{\underset{1}{\cancel{2}} * 3} + \frac{1}{4} = -\frac{1 * 1}{1 * 3} + \frac{1}{4} = -\frac{1}{3} + \frac{1}{4} = -\frac{4}{12} + \frac{3}{12} = -(\frac{4}{12} - \frac{3}{12}) = -\frac{1}{12}$;
б) $-\frac{3}{4} * \frac{12}{7} - (-\frac{1}{7})^2 = -\frac{3 * \overset{3}{\cancel{12}}}{\underset{1}{\cancel{4}} * 7} - \frac{1}{49} = -\frac{3 * 3}{1 * 7} - \frac{1}{49} = -\frac{9}{7} - \frac{1}{49} = -(\frac{63}{49} - \frac{1}{49}) = -\frac{63 + 1}{49} = -\frac{64}{49} = -1\frac{15}{49}$;
в) $-\frac{1}{3} * \frac{6}{5} - \frac{5}{6} * \frac{3}{25} = -\frac{1 * \overset{2}{\cancel{6}}}{\underset{1}{\cancel{3}} * 5} - \frac{\overset{1}{\cancel{5}} * \overset{1}{\cancel{3}}}{\underset{2}{\cancel{6}} * \underset{5}{\cancel{25}}} = -\frac{1 * 2}{1 * 5} - \frac{1 * 1}{2 * 5} = -\frac{2}{5} - \frac{1}{10} = -(\frac{4}{10} + \frac{1}{10}) = -\frac{4 + 1}{10} = -\frac{5}{10} = -\frac{1}{2}$;
г) $\frac{3}{10} * (-\frac{5}{6}) + \frac{2}{3} * (-\frac{3}{8}) = -\frac{\overset{1}{\cancel{3}} * \overset{1}{\cancel{5}}}{\underset{2}{\cancel{10}} * \underset{2}{\cancel{6}}} - \frac{\overset{1}{\cancel{2}} * \overset{1}{\cancel{3}}}{\underset{1}{\cancel{3}} * \underset{4}{\cancel{8}}} = -\frac{1 * 1}{2 * 2} - \frac{1 * 1}{1 * 4} = -\frac{1}{4} - \frac{1}{4} = -(\frac{1}{4} + \frac{1}{4}) = -\frac{1 + 1}{4} = -\frac{2}{4} = -\frac{1}{2}$.
Ответ:
а) $-\frac{1}{12}$;
б) $-1\frac{15}{49}$;
в) $-\frac{1}{2}$;
г) $-\frac{1}{2}$.