337. Вычислите: 1) \(\frac{31}{58} - \frac{16}{58}\); 2) \(\frac{19}{25} + \frac{4}{25} + \frac{22}{25}\); 3) \(\frac{1}{6} + \frac{7}{15}\); 4) \(\frac{5}{14} - \frac{1}{4}\); 5) \(\frac{3}{4} - \frac{5}{12} + \frac{5}{9}\); 6) 2 \(\frac{3}{8}\) + 4 \(\frac{5}{12}\); 7) 3 \(\frac{5}{6}\) - 1 \(\frac{7}{12}\); 8) 9 \(\frac{2}{15}\) - 6 \(\frac{3}{5}\); 9) 5 \(\frac{7}{18}\) - 4 \(\frac{11}{12}\).

1) \(\frac{31}{58} - \frac{16}{58} = \frac{31-16}{58} = \frac{15}{58}\)

Ответ: \(\frac{15}{58}\)

2) \(\frac{19}{25} + \frac{4}{25} + \frac{22}{25} = \frac{19+4+22}{25} = \frac{45}{25} = \frac{9}{5} = 1 \frac{4}{5}\)

Ответ: 1 \(\frac{4}{5}\)

3) \(\frac{1}{6} + \frac{7}{15} = \frac{1 \cdot 5}{6 \cdot 5} + \frac{7 \cdot 2}{15 \cdot 2} = \frac{5}{30} + \frac{14}{30} = \frac{5+14}{30} = \frac{19}{30}\)

Ответ: \(\frac{19}{30}\)

4) \(\frac{5}{14} - \frac{1}{4} = \frac{5 \cdot 2}{14 \cdot 2} - \frac{1 \cdot 7}{4 \cdot 7} = \frac{10}{28} - \frac{7}{28} = \frac{10-7}{28} = \frac{3}{28}\)

Ответ: \(\frac{3}{28}\)

5) \(\frac{3}{4} - \frac{5}{12} + \frac{5}{9} = \frac{3 \cdot 9}{4 \cdot 9} - \frac{5 \cdot 3}{12 \cdot 3} + \frac{5 \cdot 4}{9 \cdot 4} = \frac{27}{36} - \frac{15}{36} + \frac{20}{36} = \frac{27-15+20}{36} = \frac{32}{36} = \frac{8}{9}\)

Ответ: \(\frac{8}{9}\)

6) \(2 \frac{3}{8} + 4 \frac{5}{12} = \frac{2 \cdot 8 + 3}{8} + \frac{4 \cdot 12 + 5}{12} = \frac{19}{8} + \frac{53}{12} = \frac{19 \cdot 3}{8 \cdot 3} + \frac{53 \cdot 2}{12 \cdot 2} = \frac{57}{24} + \frac{106}{24} = \frac{57+106}{24} = \frac{163}{24} = 6 \frac{19}{24}\)

Ответ: 6 \(\frac{19}{24}\)

7) \(3 \frac{5}{6} - 1 \frac{7}{12} = \frac{3 \cdot 6 + 5}{6} - \frac{1 \cdot 12 + 7}{12} = \frac{23}{6} - \frac{19}{12} = \frac{23 \cdot 2}{6 \cdot 2} - \frac{19}{12} = \frac{46}{12} - \frac{19}{12} = \frac{46-19}{12} = \frac{27}{12} = \frac{9}{4} = 2 \frac{1}{4}\)

Ответ: 2 \(\frac{1}{4}\)

8) \(9 \frac{2}{15} - 6 \frac{3}{5} = \frac{9 \cdot 15 + 2}{15} - \frac{6 \cdot 5 + 3}{5} = \frac{137}{15} - \frac{33}{5} = \frac{137}{15} - \frac{33 \cdot 3}{5 \cdot 3} = \frac{137}{15} - \frac{99}{15} = \frac{137-99}{15} = \frac{38}{15} = 2 \frac{8}{15}\)

Ответ: 2 \(\frac{8}{15}\)

9) \(5 \frac{7}{18} - 4 \frac{11}{12} = \frac{5 \cdot 18 + 7}{18} - \frac{4 \cdot 12 + 11}{12} = \frac{97}{18} - \frac{59}{12} = \frac{97 \cdot 2}{18 \cdot 2} - \frac{59 \cdot 3}{12 \cdot 3} = \frac{194}{36} - \frac{177}{36} = \frac{194-177}{36} = \frac{17}{36}\)

Ответ: \(\frac{17}{36}\)