1. Вычислите: a) \frac{2}{5} \cdot 1\frac{1}{4}; б) 2\frac{1}{9} \cdot 4; в) 2\frac{1}{7} \cdot 1\frac{2}{5}; г) 1\frac{9}{11}:\frac{4}{5}; д) 17:1\frac{8}{9}; e) 1\frac{1}{14}:1\frac{2}{7}.

Решение:

a) $$ \frac{2}{5} \cdot 1\frac{1}{4} = \frac{2}{5} \cdot \frac{5}{4} = \frac{2 \cdot 5}{5 \cdot 4} = \frac{10}{20} = \frac{1}{2} $$

б) $$ 2\frac{1}{9} \cdot 4 = \frac{19}{9} \cdot 4 = \frac{19 \cdot 4}{9} = \frac{76}{9} = 8\frac{4}{9} $$

в) $$ 2\frac{1}{7} \cdot 1\frac{2}{5} = \frac{15}{7} \cdot \frac{7}{5} = \frac{15 \cdot 7}{7 \cdot 5} = \frac{105}{35} = 3 $$

г) $$ 1\frac{9}{11}:\frac{4}{5} = \frac{20}{11}:\frac{4}{5} = \frac{20}{11} \cdot \frac{5}{4} = \frac{20 \cdot 5}{11 \cdot 4} = \frac{100}{44} = \frac{25}{11} = 2\frac{3}{11} $$

д) $$ 17:1\frac{8}{9} = 17:\frac{17}{9} = 17 \cdot \frac{9}{17} = \frac{17 \cdot 9}{17} = 9 $$

e) $$ 1\frac{1}{14}:1\frac{2}{7} = \frac{15}{14}:\frac{9}{7} = \frac{15}{14} \cdot \frac{7}{9} = \frac{15 \cdot 7}{14 \cdot 9} = \frac{105}{126} = \frac{5}{6} $$

Ответ: a) $$\frac{1}{2}$$, б) $$8\frac{4}{9}$$, в) $$3$$, г) $$2\frac{3}{11}$$, д) $$9$$, e) $$\frac{5}{6}$$