5. Домании радами. ④ Вычислить: 1) 2 5/6 * 4/15 + 2 1/6 * 4/15 = 2) 3 2/3 * 1 1/2 + 1 1/3 * 1 1/2 = 3) (5/6 - 1/8) * 24 = 4) (5/6 + 5/9) * 18/25 = 5) 10 5/9 - 1 7/32 * (4 14/15 + 3 1/15) = 6) 1/13 * (2 3/8 - 1 5/6) * 2 2/5 + 9/10 =

1) \( 2\frac{5}{6} \cdot \frac{4}{15} + 2\frac{1}{6} \cdot \frac{4}{15} = \frac{17}{6} \cdot \frac{4}{15} + \frac{13}{6} \cdot \frac{4}{15} = \frac{4}{15} \cdot (\frac{17}{6} + \frac{13}{6}) = \frac{4}{15} \cdot \frac{30}{6} = \frac{4}{15} \cdot 5 = \frac{4 \cdot 5}{15} = \frac{4}{3} = 1\frac{1}{3} \)

2) \( 3\frac{2}{3} \cdot 1\frac{1}{2} + 1\frac{1}{3} \cdot 1\frac{1}{2} = \frac{11}{3} \cdot \frac{3}{2} + \frac{4}{3} \cdot \frac{3}{2} = \frac{3}{2} \cdot (\frac{11}{3} + \frac{4}{3}) = \frac{3}{2} \cdot \frac{15}{3} = \frac{3}{2} \cdot 5 = \frac{15}{2} = 7\frac{1}{2} \)

3) \( (\frac{5}{6} - \frac{1}{8}) \cdot 24 = (\frac{5 \cdot 4}{6 \cdot 4} - \frac{1 \cdot 3}{8 \cdot 3}) \cdot 24 = (\frac{20}{24} - \frac{3}{24}) \cdot 24 = \frac{17}{24} \cdot 24 = 17 \)

4) \( (\frac{5}{6} + \frac{5}{9}) \cdot \frac{18}{25} = (\frac{5 \cdot 3}{6 \cdot 3} + \frac{5 \cdot 2}{9 \cdot 2}) \cdot \frac{18}{25} = (\frac{15}{18} + \frac{10}{18}) \cdot \frac{18}{25} = \frac{25}{18} \cdot \frac{18}{25} = 1 \)

5) \( 10\frac{5}{9} - 1\frac{7}{32} \cdot (4\frac{14}{15} + 3\frac{1}{15}) = \frac{95}{9} - \frac{39}{32} \cdot (\frac{74}{15} + \frac{46}{15}) = \frac{95}{9} - \frac{39}{32} \cdot \frac{120}{15} = \frac{95}{9} - \frac{39}{32} \cdot 8 = \frac{95}{9} - \frac{39}{4} = \frac{95 \cdot 4}{9 \cdot 4} - \frac{39 \cdot 9}{4 \cdot 9} = \frac{380}{36} - \frac{351}{36} = \frac{29}{36} \)

6) \( \frac{1}{13} \cdot (2\frac{3}{8} - 1\frac{5}{6}) \cdot 2\frac{2}{5} + \frac{9}{10} = \frac{1}{13} \cdot (\frac{19}{8} - \frac{11}{6}) \cdot \frac{12}{5} + \frac{9}{10} = \frac{1}{13} \cdot (\frac{19 \cdot 3}{8 \cdot 3} - \frac{11 \cdot 4}{6 \cdot 4}) \cdot \frac{12}{5} + \frac{9}{10} = \frac{1}{13} \cdot (\frac{57}{24} - \frac{44}{24}) \cdot \frac{12}{5} + \frac{9}{10} = \frac{1}{13} \cdot \frac{13}{24} \cdot \frac{12}{5} + \frac{9}{10} = \frac{1}{24} \cdot \frac{12}{5} + \frac{9}{10} = \frac{1}{2} \cdot \frac{1}{5} + \frac{9}{10} = \frac{1}{10} + \frac{9}{10} = \frac{10}{10} = 1 \)