5.470 Найдите значение выражения:

Решение:

1. \(\frac{6}{7} \cdot \frac{7}{12} \cdot \frac{5}{3} = \frac{6 \cdot 7 \cdot 5}{7 \cdot 12 \cdot 3} = \frac{6 \cdot 5}{12 \cdot 3} = \frac{30}{36} = \frac{5}{6}\)
2. \(11 \cdot \frac{5}{33} \cdot \frac{3}{10} = \frac{11 \cdot 5 \cdot 3}{33 \cdot 10} = \frac{165}{330} = \frac{1}{2}\)
3. \(\frac{3}{4} \cdot \frac{10}{13} \cdot \frac{39}{40} = \frac{3 \cdot 10 \cdot 39}{4 \cdot 13 \cdot 40} = \frac{3 \cdot 10 \cdot 3 \cdot 13}{4 \cdot 13 \cdot 4 \cdot 10} = \frac{9}{16}\)
4. \(\frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \cdot 12 = \frac{3 \cdot 4 \cdot 5 \cdot 12}{4 \cdot 5 \cdot 6} = \frac{3 \cdot 12}{6} = \frac{36}{6} = 6\)
5. \(\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1}{2 \cdot 3} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{8+3-5}{18} = \frac{6}{18} = \frac{1}{3}\)
6. \(\left(\frac{3}{7} - \frac{1}{7}\right)^2 \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \left(\frac{2}{7}\right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8}\)

Ответ: а) 5/6; б) 1/2; в) 9/16; г) 6; д) 1/3; е) 3/8.