1) \frac{5}{12} + \frac{5}{18} = \frac{5 * 3}{12 * 3} + \frac{5 * 2}{18 * 2} = \frac{15}{36} + \frac{10}{36} = \frac{15 + 10}{36} = \frac{25}{36}.
2) 9 \frac{3}{5} + 2 \frac{7}{10} = (9 + 2) + (\frac{3}{5} + \frac{7}{10}) = 11 + (\frac{3 * 2}{5 * 2} + \frac{7}{10}) = 11 + (\frac{6}{10} + \frac{7}{10}) = 11 + \frac{13}{10} = 11 + 1 \frac{3}{10} = 12 \frac{3}{10}.
3) 1 - \frac{18}{27} = \frac{27}{27} - \frac{18}{27} = \frac{27 - 18}{27} = \frac{9}{27} = \frac{1}{3}.
4) 7 \frac{3}{7} - 2 \frac{6}{7} = (7 - 2) + (\frac{3}{7} - \frac{6}{7}) = 5 - \frac{3}{7} = 4 \frac{7}{7} - \frac{3}{7} = 4 \frac{4}{7}.