6. Вычислите:
а) $$1\frac{2}{7} \cdot 1\frac{1}{4} = \frac{9}{7} \cdot \frac{5}{4} = \frac{9 \cdot 5}{7 \cdot 4} = \frac{45}{28} = 1\frac{17}{28}$$
Ответ: $$1\frac{17}{28}$$
б) $$2\frac{3}{4} \cdot \frac{4}{11} = \frac{11}{4} \cdot \frac{4}{11} = \frac{11 \cdot 4}{4 \cdot 11} = 1$$
Ответ: 1
в) $$3\frac{5}{6} \cdot 1\frac{1}{23} = \frac{23}{6} \cdot \frac{24}{23} = \frac{23 \cdot 24}{6 \cdot 23} = \frac{24}{6} = 4$$
Ответ: 4
г) $$4\frac{2}{3} \cdot \frac{2}{5} = \frac{14}{3} \cdot \frac{2}{5} = \frac{14 \cdot 2}{3 \cdot 5} = \frac{28}{15} = 1\frac{13}{15}$$
Ответ: $$1\frac{13}{15}$$
д) $$1\frac{1}{2} \cdot 2\frac{2}{5} = \frac{3}{2} \cdot \frac{12}{5} = \frac{3 \cdot 12}{2 \cdot 5} = \frac{36}{10} = 3.6$$
Ответ: $$3.6$$
e) $$11\frac{2}{5} : 3\frac{4}{5} = \frac{57}{5} : \frac{19}{5} = \frac{57}{5} \cdot \frac{5}{19} = \frac{57 \cdot 5}{5 \cdot 19} = \frac{57}{19} = 3$$
Ответ: $$3$$
ж) $$8\frac{1}{3} : 2\frac{2}{3} = \frac{25}{3} : \frac{8}{3} = \frac{25}{3} \cdot \frac{3}{8} = \frac{25 \cdot 3}{3 \cdot 8} = \frac{25}{8} = 3\frac{1}{8}$$
Ответ: $$3\frac{1}{8}$$
з) $$9\frac{5}{7} : 1\frac{23}{28} = \frac{68}{7} : \frac{51}{28} = \frac{68}{7} \cdot \frac{28}{51} = \frac{68 \cdot 28}{7 \cdot 51} = \frac{68 \cdot 4}{51} = \frac{272}{51} = 5\frac{17}{51} = 5\frac{1}{3}$$
Ответ: $$5\frac{1}{3}$$
и) $$6\frac{2}{3} : 1\frac{1}{8} = \frac{20}{3} : \frac{9}{8} = \frac{20}{3} \cdot \frac{8}{9} = \frac{20 \cdot 8}{3 \cdot 9} = \frac{160}{27} = 5\frac{25}{27}$$
Ответ: $$5\frac{25}{27}$$
к) Здесь пропущено условие. Решить невозможно.
л) $$\frac{6}{11} : 3 = \frac{6}{11} \cdot \frac{1}{3} = \frac{6 \cdot 1}{11 \cdot 3} = \frac{6}{33} = \frac{2}{11}$$
Ответ: $$\frac{2}{11}$$