6. Выполните умножение. a) 3.11. 74 б) 3.316. 583 в) 9.419. 61 г) 3.17.1 218 д) 16.2.1 36 )53- 3)331-

a) $$3\frac{3}{7} \cdot 1\frac{1}{4} = \frac{3\cdot7 + 3}{7} \cdot \frac{1\cdot4 + 1}{4} = \frac{21+3}{7} \cdot \frac{4+1}{4} = \frac{24}{7} \cdot \frac{5}{4} = \frac{6 \cdot 4 \cdot 5}{7 \cdot 4} = \frac{6 \cdot 5}{7} = \frac{30}{7} = 4\frac{2}{7}$$

Ответ: $$4\frac{2}{7}$$

б) $$3\frac{3}{5} \cdot \frac{16}{8} \cdot 3 = \frac{3\cdot5 + 3}{5} \cdot \frac{16}{8} \cdot 3 = \frac{15+3}{5} \cdot 2 \cdot 3 = \frac{18}{5} \cdot 6 = \frac{18 \cdot 6}{5} = \frac{108}{5} = 21 \frac{3}{5}$$

Ответ: $$21 \frac{3}{5}$$

в) $$9\frac{1}{6} \cdot 4\frac{1}{1} = \frac{9\cdot6 + 1}{6} \cdot \frac{4+1}{1} = \frac{54+1}{6} \cdot 5 = \frac{55 \cdot 5}{6} = \frac{275}{6} = 45 \frac{5}{6}$$

Ответ: $$45 \frac{5}{6}$$

г) $$3\frac{17}{21} \cdot 1\frac{1}{8} = \frac{3\cdot21 + 17}{21} \cdot \frac{1\cdot8 + 1}{8} = \frac{63+17}{21} \cdot \frac{8+1}{8} = \frac{80}{21} \cdot \frac{9}{8} = \frac{10 \cdot 8 \cdot 9}{21 \cdot 8} = \frac{10 \cdot 9}{21} = \frac{10 \cdot 3 \cdot 3}{3 \cdot 7} = \frac{10 \cdot 3}{7} = \frac{30}{7} = 4\frac{2}{7}$$

Ответ: $$4\frac{2}{7}$$

д) $$16\frac{2}{3} \cdot 1\frac{1}{6} = \frac{16\cdot3 + 2}{3} \cdot \frac{1\cdot6 + 1}{6} = \frac{48+2}{3} \cdot \frac{6+1}{6} = \frac{50}{3} \cdot \frac{7}{6} = \frac{50 \cdot 7}{3 \cdot 6} = \frac{350}{18} = \frac{175}{9} = 19\frac{4}{9}$$

Ответ: $$19\frac{4}{9}$$

е) $$5\frac{2}{3} \cdot \frac{1}{3} = \frac{5\cdot3 + 2}{3} \cdot \frac{1}{3} = \frac{15+2}{3} \cdot \frac{1}{3} = \frac{17}{3} \cdot \frac{1}{3} = \frac{17 \cdot 1}{3 \cdot 3} = \frac{17}{9} = 1\frac{8}{9}$$

Ответ: $$1\frac{8}{9}$$

ж) $$1\frac{1}{2} \cdot 1\frac{1}{4} = \frac{1\cdot2 + 1}{2} \cdot \frac{1\cdot4 + 1}{4} = \frac{2+1}{2} \cdot \frac{4+1}{4} = \frac{3}{2} \cdot \frac{5}{4} = \frac{3 \cdot 5}{2 \cdot 4} = \frac{15}{8} = 1\frac{7}{8}$$

Ответ: $$1\frac{7}{8}$$

з) $$33\frac{1}{3} \cdot 1\frac{1}{5} = \frac{33\cdot3 + 1}{3} \cdot \frac{1\cdot5 + 1}{5} = \frac{99+1}{3} \cdot \frac{5+1}{5} = \frac{100}{3} \cdot \frac{6}{5} = \frac{100 \cdot 6}{3 \cdot 5} = \frac{20 \cdot 5 \cdot 2 \cdot 3}{3 \cdot 5} = 20 \cdot 2 = 40$$

Ответ: 40