5.470 Найдите значение выражения: а) 6/7 · 7/12 - 5/3; б) 3/4 · 10/13 + 39/40; в) 11 · 5/33 - 3/10; г) 3/4 · 4/5 : 12.

a) $$\frac{6}{7} \cdot \frac{7}{12} - \frac{5}{3} = \frac{6 \cdot 7}{7 \cdot 12} - \frac{5}{3} = \frac{42}{84} - \frac{5}{3} = \frac{1}{2} - \frac{5}{3} = \frac{3}{6} - \frac{10}{6} = \frac{3 - 10}{6} = \frac{-7}{6} = -1 \frac{1}{6}$$.

б) $$\frac{3}{4} \cdot \frac{10}{13} + \frac{39}{40} = \frac{3 \cdot 10}{4 \cdot 13} + \frac{39}{40} = \frac{30}{52} + \frac{39}{40} = \frac{15}{26} + \frac{39}{40} = \frac{15 \cdot 20 + 39 \cdot 13}{520} = \frac{300 + 507}{520} = \frac{807}{520} = 1 \frac{287}{520}$$.

в) $$11 \cdot \frac{5}{33} - \frac{3}{10} = \frac{11 \cdot 5}{33} - \frac{3}{10} = \frac{55}{33} - \frac{3}{10} = \frac{5}{3} - \frac{3}{10} = \frac{50 - 9}{30} = \frac{41}{30} = 1 \frac{11}{30}$$.

г) $$\frac{3}{4} \cdot \frac{4}{5} : 12 = \frac{3 \cdot 4}{4 \cdot 5} : 12 = \frac{12}{20} : 12 = \frac{3}{5} : 12 = \frac{3}{5} \cdot \frac{1}{12} = \frac{3}{60} = \frac{1}{20}$$.

Ответ: а) $$-1 \frac{1}{6}$$; б) $$1 \frac{287}{520}$$; в) $$1 \frac{11}{30}$$; г) $$\frac{1}{20}$$