58. Выполните действия:

Решение:

1. \( 6 \frac{7}{8} - 3 \frac{1}{3} + 5 \frac{5}{16} = \frac{47}{8} - \frac{10}{3} + \frac{85}{16} = \frac{47 \cdot 6}{48} - \frac{10 \cdot 16}{48} + \frac{85 \cdot 3}{48} = \frac{282 - 160 + 255}{48} = \frac{377}{48} = 7 \frac{41}{48} \)
2. \( 5 \frac{9}{14} - 2 \frac{3}{7} + 6,7 = \frac{79}{14} - \frac{17}{7} + 6,7 = \frac{79}{14} - \frac{34}{14} + \frac{67}{10} = \frac{45}{14} + \frac{67}{10} = \frac{45 \cdot 5}{70} + \frac{67 \cdot 7}{70} = \frac{225 + 469}{70} = \frac{694}{70} = \frac{347}{35} = 9 \frac{32}{35} \)
3. \( \left( 15 \frac{5}{6} - 9 \frac{25}{27} \right) - 2 \frac{17}{18} = \left( \frac{95}{6} - \frac{273}{27} \right) - \frac{53}{18} = \left( \frac{95 \cdot 9}{54} - \frac{273 \cdot 2}{54} \right) - \frac{53 \cdot 3}{54} = \left( \frac{855 - 546}{54} \right) - \frac{159}{54} = \frac{309}{54} - \frac{159}{54} = \frac{150}{54} = \frac{25}{9} = 2 \frac{7}{9} \)
4. \( \left( 18 - 10 \frac{5}{9} \right) - \left( 6 \frac{1}{8} - 3 \frac{2}{3} \right) = \left( 18 - \frac{95}{9} \right) - \left( \frac{49}{8} - \frac{11}{3} \right) = \left( \frac{162 - 95}{9} \right) - \left( \frac{49 \cdot 3}{24} - \frac{11 \cdot 8}{24} \right) = \frac{67}{9} - \left( \frac{147 - 88}{24} \right) = \frac{67}{9} - \frac{59}{24} = \frac{67 \cdot 8}{72} - \frac{59 \cdot 3}{72} = \frac{536 - 177}{72} = \frac{359}{72} = 4 \frac{71}{72} \)