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1. $$1-\frac{1}{3} = \frac{3}{3}-\frac{1}{3} = \frac{3-1}{3} = \frac{2}{3}$$
2. $$1-\frac{7}{10} = \frac{10}{10}-\frac{7}{10} = \frac{10-7}{10} = \frac{3}{10}$$
3. $$8-\frac{2}{3} = \frac{8}{1}-\frac{2}{3} = \frac{8\cdot3}{1\cdot3}-\frac{2}{3} = \frac{24}{3}-\frac{2}{3} = \frac{24-2}{3} = \frac{22}{3} = 7\frac{1}{3}$$
4. $$10-\frac{5}{6} = \frac{10}{1}-\frac{5}{6} = \frac{10\cdot6}{1\cdot6}-\frac{5}{6} = \frac{60}{6}-\frac{5}{6} = \frac{60-5}{6} = \frac{55}{6} = 9\frac{1}{6}$$
5. $$7-5\frac{3}{4} = 7-\frac{5\cdot4+3}{4} = 7-\frac{23}{4} = \frac{7}{1}-\frac{23}{4} = \frac{7\cdot4}{1\cdot4}-\frac{23}{4} = \frac{28}{4}-\frac{23}{4} = \frac{28-23}{4} = \frac{5}{4} = 1\frac{1}{4}$$
6. $$6-3\frac{2}{5} = 6-\frac{3\cdot5+2}{5} = 6-\frac{17}{5} = \frac{6}{1}-\frac{17}{5} = \frac{6\cdot5}{1\cdot5}-\frac{17}{5} = \frac{30}{5}-\frac{17}{5} = \frac{30-17}{5} = \frac{13}{5} = 2\frac{3}{5}$$
7. $$5-2\frac{1}{2} = 5-\frac{2\cdot2+1}{2} = 5-\frac{5}{2} = \frac{5}{1}-\frac{5}{2} = \frac{5\cdot2}{1\cdot2}-\frac{5}{2} = \frac{10}{2}-\frac{5}{2} = \frac{10-5}{2} = \frac{5}{2} = 2\frac{1}{2}$$
8. $$9-5\frac{1}{6} = 9-\frac{5\cdot6+1}{6} = 9-\frac{31}{6} = \frac{9}{1}-\frac{31}{6} = \frac{9\cdot6}{1\cdot6}-\frac{31}{6} = \frac{54}{6}-\frac{31}{6} = \frac{54-31}{6} = \frac{23}{6} = 3\frac{5}{6}$$