355. Вычислите значение выражения наиболее удобным способом: 1) $$3 \frac{5}{14} \cdot \frac{7}{9} - 2 \frac{3}{14} \cdot \frac{7}{9}$$; 2) $$7 \frac{1}{5} \cdot 2 \frac{1}{8} + 7 \frac{1}{5} \cdot 1 \frac{5}{8}$$; 3) $$3 \frac{3}{4} \cdot 1 \frac{3}{5} + 1 \frac{3}{5} \cdot 1 \frac{1}{2} - 1 \frac{3}{5} \cdot 1 \frac{1}{3}$$; 4) $$3 \frac{9}{14} \cdot 0.3 - 0.3 \cdot \frac{10}{21} + 0.3 \cdot 1 \frac{1}{6}$$

Решение:

1. $$3 \frac{5}{14} \cdot \frac{7}{9} - 2 \frac{3}{14} \cdot \frac{7}{9} = \frac{7}{9} \cdot (3 \frac{5}{14} - 2 \frac{3}{14}) = \frac{7}{9} \cdot (\frac{47}{14} - \frac{31}{14}) = \frac{7}{9} \cdot \frac{16}{14} = \frac{7}{9} \cdot \frac{8}{7} = \frac{8}{9}$$
2. $$7 \frac{1}{5} \cdot 2 \frac{1}{8} + 7 \frac{1}{5} \cdot 1 \frac{5}{8} = 7 \frac{1}{5} \cdot (2 \frac{1}{8} + 1 \frac{5}{8}) = 7 \frac{1}{5} \cdot (3 + \frac{6}{8}) = 7 \frac{1}{5} \cdot 3 \frac{3}{4} = \frac{36}{5} \cdot \frac{15}{4} = \frac{36 \cdot 3}{4} = 9 \cdot 3 = 27$$
3. $$3 \frac{3}{4} \cdot 1 \frac{3}{5} + 1 \frac{3}{5} \cdot 1 \frac{1}{2} - 1 \frac{3}{5} \cdot 1 \frac{1}{3} = 1 \frac{3}{5} \cdot (3 \frac{3}{4} + 1 \frac{1}{2} - 1 \frac{1}{3}) = \frac{8}{5} \cdot (3 + \frac{3}{4} + 1 + \frac{1}{2} - 1 - \frac{1}{3}) = \frac{8}{5} \cdot (3 + \frac{3}{4} + \frac{1}{2} - \frac{1}{3}) = \frac{8}{5} \cdot (3 + \frac{9 + 6 - 4}{12}) = \frac{8}{5} \cdot (3 + \frac{11}{12}) = \frac{8}{5} \cdot \frac{36 + 11}{12} = \frac{8}{5} \cdot \frac{47}{12} = \frac{2}{5} \cdot \frac{47}{3} = \frac{94}{15} = 6 \frac{4}{15}$$
4. $$3 \frac{9}{14} \cdot 0.3 - 0.3 \cdot \frac{10}{21} + 0.3 \cdot 1 \frac{1}{6} = 0.3 \cdot (3 \frac{9}{14} - \frac{10}{21} + 1 \frac{1}{6}) = 0.3 \cdot (3 + \frac{9}{14} - \frac{10}{21} + 1 + \frac{1}{6}) = 0.3 \cdot (4 + \frac{9}{14} - \frac{10}{21} + \frac{1}{6}) = 0.3 \cdot (4 + \frac{27 - 20 + 7}{42}) = 0.3 \cdot (4 + \frac{14}{42}) = 0.3 \cdot (4 + \frac{1}{3}) = 0.3 \cdot \frac{13}{3} = \frac{3}{10} \cdot \frac{13}{3} = \frac{13}{10} = 1.3$$