Найди значение выражения: ($5\frac{8}{9} : 1\frac{17}{36} + 1\frac{1}{4}$) : $4\frac{1}{5}$

1. Найди значение выражения: ($$5\frac{8}{9} : 1\frac{17}{36} + 1\frac{1}{4}$) : $4\frac{1}{5}$ 1) $$5\frac{8}{9} : 1\frac{17}{36} = \frac{53}{9} : \frac{53}{36} = \frac{53}{9} \cdot \frac{36}{53} = \frac{36}{9} = 4$$ 2) $$4 + 1\frac{1}{4} = 5\frac{1}{4}$$ 3) $$5\frac{1}{4} : 4\frac{1}{5} = \frac{21}{4} : \frac{21}{5} = \frac{21}{4} \cdot \frac{5}{21} = \frac{5}{4} = 1\frac{1}{4}$$ **Ответ:** $1\frac{1}{4}$ ($$2\frac{1}{4} + 4\frac{5}{6}$) : $3\frac{2}{5} - \frac{3}{4} : \frac{3}{5}$ 1) $$2\frac{1}{4} + 4\frac{5}{6} = 2\frac{3}{12} + 4\frac{10}{12} = 6\frac{13}{12} = 7\frac{1}{12}$$ 2) $$7\frac{1}{12} : 3\frac{2}{5} = \frac{85}{12} : \frac{17}{5} = \frac{85}{12} \cdot \frac{5}{17} = \frac{5 \cdot 5}{12} = \frac{25}{12} = 2\frac{1}{12}$$ 3) $$\frac{3}{4} : \frac{3}{5} = \frac{3}{4} \cdot \frac{5}{3} = \frac{5}{4} = 1\frac{1}{4}$$ 4) $$2\frac{1}{12} - 1\frac{1}{4} = 2\frac{1}{12} - 1\frac{3}{12} = \frac{25}{12} - \frac{15}{12} = \frac{10}{12} = \frac{5}{6}$$ **Ответ:** $$\frac{5}{6}$$ 2. Реши уравнение: $$3\frac{3}{4}x - 1\frac{2}{3} = 2\frac{11}{12}$$ $$3\frac{3}{4}x = 2\frac{11}{12} + 1\frac{2}{3}$$ $$3\frac{3}{4}x = 2\frac{11}{12} + 1\frac{8}{12}$$ $$3\frac{3}{4}x = 3\frac{19}{12}$$ $$3\frac{3}{4}x = 4\frac{7}{12}$$ $$\frac{15}{4}x = \frac{55}{12}$$ $$x = \frac{55}{12} : \frac{15}{4}$$ $$x = \frac{55}{12} \cdot \frac{4}{15}$$ $$x = \frac{55 \cdot 4}{12 \cdot 15}$$ $$x = \frac{11 \cdot 1}{3 \cdot 3}$$ $$x = \frac{11}{9}$$ $$x = 1\frac{2}{9}$$ **Ответ:** $x = 1\frac{2}{9}$ $$4\frac{2}{15} - 3\frac{1}{9}x = 1\frac{4}{5}$$ $$-3\frac{1}{9}x = 1\frac{4}{5} - 4\frac{2}{15}$$ $$-3\frac{1}{9}x = 1\frac{12}{15} - 4\frac{2}{15}$$ $$-3\frac{1}{9}x = \frac{27}{15} - \frac{62}{15}$$ $$-3\frac{1}{9}x = -\frac{35}{15}$$ $$-3\frac{1}{9}x = -\frac{7}{3}$$ $$\frac{28}{9}x = \frac{7}{3}$$ $$x = \frac{7}{3} : \frac{28}{9}$$ $$x = \frac{7}{3} \cdot \frac{9}{28}$$ $$x = \frac{1 \cdot 3}{1 \cdot 4}$$ $$x = \frac{3}{4}$$ **Ответ:** $x = \frac{3}{4}$ $$\frac{4}{15}x + 2\frac{1}{3} = 7\frac{8}{15}$$ $$\frac{4}{15}x = 7\frac{8}{15} - 2\frac{1}{3}$$ $$\frac{4}{15}x = 7\frac{8}{15} - 2\frac{5}{15}$$ $$\frac{4}{15}x = 5\frac{3}{15}$$ $$\frac{4}{15}x = 5\frac{1}{5}$$ $$\frac{4}{15}x = \frac{26}{5}$$ $$x = \frac{26}{5} : \frac{4}{15}$$ $$x = \frac{26}{5} \cdot \frac{15}{4}$$ $$x = \frac{26 \cdot 3}{1 \cdot 4}$$ $$x = \frac{13 \cdot 3}{1 \cdot 2}$$ $$x = \frac{39}{2}$$ $$x = 19\frac{1}{2}$$ **Ответ:** $x = 19\frac{1}{2}$