Вычислите: а) 3/7 * 4/5; б) 5/9 * 2/5; в) 6/7 * 21/22; г) (3/4)^3

**№ 1. Вычислите:** а) $\frac{3}{7} \cdot \frac{4}{5} = \frac{12}{35}$ б) $\frac{5}{9} \cdot \frac{2}{5} = \frac{1}{9} \cdot \frac{2}{1} = \frac{2}{9}$ в) $\frac{6}{7} \cdot \frac{21}{22} = \frac{3}{1} \cdot \frac{3}{11} = \frac{9}{11}$ г) $(\frac{3}{4})^3 = \frac{3^3}{4^3} = \frac{27}{64}$ д) $\frac{3}{5} : \frac{4}{7} = \frac{3}{5} \cdot \frac{7}{4} = \frac{21}{20} = 1\frac{1}{20}$ е) $\frac{25}{24} : \frac{15}{16} = \frac{25}{24} \cdot \frac{16}{15} = \frac{5 \cdot 2}{3 \cdot 3} = \frac{10}{9} = 1\frac{1}{9}$ ж) $\frac{6}{7} : 3 = \frac{6}{7} \cdot \frac{1}{3} = \frac{2}{7}$ **№ 2. Вычислите:** а) $\frac{2}{5} \cdot 1\frac{1}{4} = \frac{2}{5} \cdot \frac{5}{4} = \frac{1}{2}$ б) $2\frac{1}{9} \cdot 4 = \frac{19}{9} \cdot 4 = \frac{76}{9} = 8\frac{4}{9}$ в) $2\frac{1}{7} \cdot 1\frac{2}{5} = \frac{15}{7} \cdot \frac{7}{5} = 3$ г) $1\frac{9}{11} : \frac{4}{5} = \frac{20}{11} \cdot \frac{5}{4} = \frac{5 \cdot 5}{11} = \frac{25}{11} = 2\frac{3}{11}$ д) $17 : 1\frac{8}{9} = 17 : \frac{17}{9} = 17 \cdot \frac{9}{17} = 9$ е) $1\frac{1}{14} : 1\frac{2}{7} = \frac{15}{14} : \frac{9}{7} = \frac{15}{14} \cdot \frac{7}{9} = \frac{5 \cdot 1}{2 \cdot 3} = \frac{5}{6}$ **№ 3. Вычислите:** а) $\frac{51}{25} : (\frac{8}{25} + \frac{9}{20}) - \frac{64}{35} \cdot \frac{5}{4}$ 1) $\frac{8}{25} + \frac{9}{20} = \frac{32 + 45}{100} = \frac{77}{100}$ 2) $\frac{51}{25} : \frac{77}{100} = \frac{51}{25} \cdot \frac{100}{77} = \frac{51 \cdot 4}{77} = \frac{204}{77} = 2\frac{50}{77}$ 3) $\frac{64}{35} \cdot \frac{5}{4} = \frac{16}{7} = 2\frac{2}{7}$ 4) $2\frac{50}{77} - 2\frac{2}{7} = \frac{204}{77} - \frac{16}{7} = \frac{204 - 176}{77} = \frac{28}{77} = \frac{4}{11}$ **Ответ:** $\frac{4}{11}$ **№ 4. Найдите x, для которого верно равенство:** а) $x \cdot \frac{3}{7} = \frac{2}{14}$ $x = \frac{2}{14} : \frac{3}{7} = \frac{1}{7} \cdot \frac{7}{3} = \frac{1}{3}$ **Ответ: $x = \frac{1}{3}$** б) $x : \frac{3}{5} = \frac{5}{9}$ $x = \frac{5}{9} \cdot \frac{3}{5} = \frac{1}{3}$ **Ответ: $x = \frac{1}{3}$** в) $\frac{4}{9} : x = \frac{8}{9}$ $x = \frac{4}{9} : \frac{8}{9} = \frac{4}{9} \cdot \frac{9}{8} = \frac{1}{2}$ **Ответ: $x = \frac{1}{2}$**