Домашняя работа. 1. Вычислите: 11 7 8 a) 15 - 6 · 35 4 16 3 4 8 б) 1 - 9 : 27; в) 16 · (9 - 27).

a) $$\frac{11}{15} - \frac{7}{6} \cdot \frac{8}{35} = \frac{11}{15} - \frac{7 \cdot 8}{6 \cdot 35} = \frac{11}{15} - \frac{7 \cdot 4 \cdot 2}{3 \cdot 2 \cdot 7 \cdot 5} = \frac{11}{15} - \frac{4}{15} = \frac{11-4}{15} = \frac{7}{15}$$

б) $$1 - \frac{4}{9} : \frac{16}{27} = 1 - \frac{4}{9} \cdot \frac{27}{16} = 1 - \frac{4 \cdot 27}{9 \cdot 16} = 1 - \frac{4 \cdot 3 \cdot 9}{9 \cdot 4 \cdot 4} = 1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{4-3}{4} = \frac{1}{4}$$

в) $$\frac{3}{16} \cdot (\frac{4}{9} - \frac{8}{27}) = \frac{3}{16} \cdot (\frac{4 \cdot 3}{9 \cdot 3} - \frac{8}{27}) = \frac{3}{16} \cdot (\frac{12}{27} - \frac{8}{27}) = \frac{3}{16} \cdot \frac{12-8}{27} = \frac{3}{16} \cdot \frac{4}{27} = \frac{3 \cdot 4}{16 \cdot 27} = \frac{3 \cdot 4}{4 \cdot 4 \cdot 3 \cdot 9} = \frac{1}{36}$$

Ответ: а) $$\frac{7}{15}$$, б) $$\frac{1}{4}$$, в) $$\frac{1}{36}$$