58. Выполните действия: 1) $$6\frac{7}{8} - 3\frac{1}{3} + 5\frac{5}{16}$$; 2) $$5\frac{9}{14} - 2\frac{3}{7} + 6.7$$; 3) $$(15\frac{5}{6} - 9\frac{25}{27}) - 2\frac{17}{18}$$; 4) $$(18 - 10\frac{5}{9}) - (6\frac{1}{8} - 3\frac{3}{2})$$

**1) $$6\frac{7}{8} - 3\frac{1}{3} + 5\frac{5}{16}$$** $$6 - 3 + 5 = 8$$ $$\frac{7}{8} - \frac{1}{3} + \frac{5}{16} = \frac{7 \cdot 6}{8 \cdot 6} - \frac{1 \cdot 16}{3 \cdot 16} + \frac{5 \cdot 3}{16 \cdot 3} = \frac{42}{48} - \frac{16}{48} + \frac{15}{48} = \frac{42 - 16 + 15}{48} = \frac{41}{48}$$ $$8 + \frac{41}{48} = 8\frac{41}{48}$$ **2) $$5\frac{9}{14} - 2\frac{3}{7} + 6.7$$** Переведем десятичную дробь в обыкновенную: $$6.7 = 6\frac{7}{10}$$ $$5 - 2 + 6 = 9$$ $$\frac{9}{14} - \frac{3}{7} + \frac{7}{10} = \frac{9}{14} - \frac{6}{14} + \frac{7}{10} = \frac{3}{14} + \frac{7}{10} = \frac{3 \cdot 5}{14 \cdot 5} + \frac{7 \cdot 7}{10 \cdot 7} = \frac{15}{70} + \frac{49}{70} = \frac{64}{70} = \frac{32}{35}$$ $$9 + \frac{32}{35} = 9\frac{32}{35}$$ **3) $$(15\frac{5}{6} - 9\frac{25}{27}) - 2\frac{17}{18}$$** $$15 - 9 = 6$$ Приведем дроби к общему знаменателю, который равен 54. $$\frac{5}{6} = \frac{5 \cdot 9}{6 \cdot 9} = \frac{45}{54}$$ $$\frac{25}{27} = \frac{25 \cdot 2}{27 \cdot 2} = \frac{50}{54}$$ $$6\frac{45}{54} - \frac{50}{54} = 5 + 1\frac{45}{54} - \frac{50}{54} = 5 + \frac{99}{54} - \frac{50}{54} = 5\frac{49}{54}$$ $$5\frac{49}{54} - 2\frac{17}{18} = 5 - 2 + \frac{49}{54} - \frac{17}{18} = 3 + \frac{49}{54} - \frac{51}{54} = 3 - \frac{2}{54} = 2 + \frac{54}{54} - \frac{2}{54} = 2\frac{52}{54} = 2\frac{26}{27}$$ **4) $$(18 - 10\frac{5}{9}) - (6\frac{1}{8} - 3\frac{3}{2})$$** $$18 - 10\frac{5}{9} = 7 + \frac{9}{9} - \frac{5}{9} = 7\frac{4}{9}$$ $$6\frac{1}{8} - 3\frac{3}{2} = 6\frac{1}{8} - 3\frac{12}{8} = 5\frac{9}{8} - 3\frac{12}{8} = 2 - \frac{3}{8} = 1 + \frac{8}{8} - \frac{3}{8} = 1\frac{5}{8}$$ $$7\frac{4}{9} - 1\frac{5}{8} = 6 + \frac{4}{9} - \frac{5}{8} = 6 + \frac{32}{72} - \frac{45}{72} = 6 - \frac{13}{72} = 5 + \frac{72}{72} - \frac{13}{72} = 5\frac{59}{72}$$