Дз І Найдите значение выражения: 1) $$3\frac{3}{4}: \frac{3}{8} : 1\frac{1}{7}$$; 2) $$3\frac{3}{4}: (\frac{3}{8}: 1\frac{3}{7})$$; 3) $$1\frac{7}{9} \cdot \frac{15}{32} : 1\frac{19}{36}$$; 4) $$1\frac{7}{9} \cdot (\frac{15}{32} : 1\frac{19}{36})$$; 5) $$3\frac{4}{7} : 1\frac{1}{7} \cdot \frac{2}{3}$$; 6) $$3\frac{4}{7} : (1\frac{1}{4} \cdot \frac{2}{3})$$; 7) $$( \frac{5}{12} + \frac{1}{8}) : \frac{3}{8}$$; 8) $$\frac{5}{12} + \frac{1}{8} : \frac{3}{8}$$; 9) $$2\frac{6}{7} : (\frac{5}{6} - \frac{9}{14})$$; 10) $$2\frac{6}{7} : \frac{5}{6} - \frac{9}{14}$$

Решим данные примеры:

1. $$3\frac{3}{4}: \frac{3}{8} : 1\frac{1}{7} = \frac{15}{4} : \frac{3}{8} : \frac{8}{7} = \frac{15}{4} \cdot \frac{8}{3} \cdot \frac{7}{8} = \frac{5 \cdot 2 \cdot 7}{4} = \frac{35}{4} = 8\frac{3}{4}$$
   Ответ: $$8\frac{3}{4}$$
2. $$3\frac{3}{4}: (\frac{3}{8}: 1\frac{3}{7}) = \frac{15}{4} : (\frac{3}{8} : \frac{10}{7}) = \frac{15}{4} : (\frac{3}{8} \cdot \frac{7}{10}) = \frac{15}{4} : \frac{21}{80} = \frac{15}{4} \cdot \frac{80}{21} = \frac{5 \cdot 20}{7} = \frac{100}{7} = 14\frac{2}{7}$$
   Ответ: $$14\frac{2}{7}$$
3. $$1\frac{7}{9} \cdot \frac{15}{32} : 1\frac{19}{36} = \frac{16}{9} \cdot \frac{15}{32} : \frac{55}{36} = \frac{16}{9} \cdot \frac{15}{32} \cdot \frac{36}{55} = \frac{16 \cdot 3 \cdot 5 \cdot 4 \cdot 9}{9 \cdot 32 \cdot 5 \cdot 11} = \frac{6}{11}$$
   Ответ: $$\frac{6}{11}$$
4. $$1\frac{7}{9} \cdot (\frac{15}{32} : 1\frac{19}{36}) = \frac{16}{9} \cdot (\frac{15}{32} : \frac{55}{36}) = \frac{16}{9} \cdot (\frac{15}{32} \cdot \frac{36}{55}) = \frac{16}{9} \cdot (\frac{15 \cdot 36}{32 \cdot 55}) = \frac{16}{9} \cdot \frac{27}{44} = \frac{4}{1} \cdot \frac{3}{11} = \frac{12}{11} = 1\frac{1}{11}$$
   Ответ: $$1\frac{1}{11}$$
5. $$3\frac{4}{7} : 1\frac{1}{7} \cdot \frac{2}{3} = \frac{25}{7} : \frac{8}{7} \cdot \frac{2}{3} = \frac{25}{7} \cdot \frac{7}{8} \cdot \frac{2}{3} = \frac{25}{1} \cdot \frac{1}{4} \cdot \frac{1}{3} = \frac{25}{12} = 2\frac{1}{12}$$
   Ответ: $$2\frac{1}{12}$$
6. $$3\frac{4}{7} : (1\frac{1}{4} \cdot \frac{2}{3}) = \frac{25}{7} : (\frac{5}{4} \cdot \frac{2}{3}) = \frac{25}{7} : \frac{5 \cdot 2}{4 \cdot 3} = \frac{25}{7} : \frac{5}{6} = \frac{25}{7} \cdot \frac{6}{5} = \frac{5 \cdot 6}{7} = \frac{30}{7} = 4\frac{2}{7}$$
   Ответ: $$4\frac{2}{7}$$
7. $$( \frac{5}{12} + \frac{1}{8}) : \frac{3}{8} = (\frac{5 \cdot 2 + 1 \cdot 3}{24}) : \frac{3}{8} = (\frac{10 + 3}{24}) : \frac{3}{8} = \frac{13}{24} : \frac{3}{8} = \frac{13}{24} \cdot \frac{8}{3} = \frac{13}{3} \cdot \frac{1}{3} = \frac{13}{9} = 1\frac{4}{9}$$
   Ответ: $$1\frac{4}{9}$$
8. $$\frac{5}{12} + \frac{1}{8} : \frac{3}{8} = \frac{5}{12} + \frac{1}{8} \cdot \frac{8}{3} = \frac{5}{12} + \frac{1}{3} = \frac{5 + 1 \cdot 4}{12} = \frac{9}{12} = \frac{3}{4}$$
   Ответ: $$\frac{3}{4}$$
9. $$2\frac{6}{7} : (\frac{5}{6} - \frac{9}{14}) = \frac{20}{7} : (\frac{5 \cdot 7 - 9 \cdot 3}{42}) = \frac{20}{7} : (\frac{35 - 27}{42}) = \frac{20}{7} : \frac{8}{42} = \frac{20}{7} \cdot \frac{42}{8} = \frac{20 \cdot 6}{8} = \frac{5 \cdot 6}{2} = 5 \cdot 3 = 15$$
   Ответ: $$15$$
10. $$2\frac{6}{7} : \frac{5}{6} - \frac{9}{14} = \frac{20}{7} : \frac{5}{6} - \frac{9}{14} = \frac{20}{7} \cdot \frac{6}{5} - \frac{9}{14} = \frac{4 \cdot 6}{7} - \frac{9}{14} = \frac{24}{7} - \frac{9}{14} = \frac{24 \cdot 2 - 9}{14} = \frac{48 - 9}{14} = \frac{39}{14} = 2\frac{11}{14}$$
    Ответ: $$2\frac{11}{14}$$