Выполни действия: 1) 2 1/6 - 1 2/9 : 3 2/3;

Привет! Давай решим задания. Начнем с №381 (примеры с дробями) и №386 (уравнения). ### №381. Выполни действия: 1) $2 \frac{1}{6} - 1 \frac{2}{9} : 3 \frac{2}{3} = 2 \frac{1}{6} - \frac{11}{9} : \frac{11}{3} = 2 \frac{1}{6} - \frac{11}{9} \cdot \frac{3}{11} = 2 \frac{1}{6} - \frac{1}{3} = 2 \frac{1}{6} - \frac{2}{6} = 1 \frac{6+1-2}{6} = 1 \frac{5}{6}$ 2) $4 \frac{2}{5} : (\frac{7}{10} + 2 \frac{3}{5}) = \frac{22}{5} : (\frac{7}{10} + \frac{13}{5}) = \frac{22}{5} : (\frac{7}{10} + \frac{26}{10}) = \frac{22}{5} : \frac{33}{10} = \frac{22}{5} \cdot \frac{10}{33} = \frac{2}{1} \cdot \frac{2}{3} = \frac{4}{3} = 1 \frac{1}{3}$ 3) $5 \cdot (\frac{2}{3})^3 : (\frac{4}{9})^2 = 5 \cdot \frac{8}{27} : \frac{16}{81} = \frac{40}{27} \cdot \frac{81}{16} = \frac{5}{1} \cdot \frac{3}{2} = \frac{15}{2} = 7 \frac{1}{2}$ 4) $(\frac{5}{6} + 2 \frac{3}{4}) : 4 \frac{7}{9} \cdot 2 \frac{2}{3} = (\frac{10}{12} + \frac{33}{12}) : \frac{43}{9} \cdot \frac{8}{3} = \frac{43}{12} \cdot \frac{9}{43} \cdot \frac{8}{3} = \frac{3}{4} \cdot \frac{8}{3} = 2$ 5) $(1 \frac{1}{8} + 1 \frac{1}{2}) : 3 : (5 \frac{1}{2} - 9 \frac{1}{4}) = (\frac{9}{8} + \frac{12}{8}) : 3 : (\frac{22}{4} - \frac{37}{4}) = \frac{21}{8} : 3 : (-\frac{15}{4}) = \frac{7}{8} \cdot (-\frac{4}{15}) = -\frac{7}{30}$ 6) $\frac{9}{10} \cdot 1 \frac{1}{14} : 2 \frac{4}{7} \cdot 24 - 2 \frac{4}{15} : (1 \frac{1}{5} - \frac{2}{3}) = \frac{9}{10} \cdot \frac{15}{14} : \frac{18}{7} \cdot 24 - \frac{34}{15} : (\frac{18}{15} - \frac{10}{15}) = \frac{27}{28} \cdot \frac{7}{18} \cdot 24 - \frac{34}{15} : \frac{8}{15} = \frac{3}{8} \cdot 24 - \frac{34}{15} \cdot \frac{15}{8} = 9 - \frac{17}{4} = 9 - 4 \frac{1}{4} = 4 \frac{3}{4}$ ### №386. Реши уравнение: 1) $3x + 5x = 7 \Rightarrow 8x = 7 \Rightarrow x = \frac{7}{8}$ 2) $1 = 6x - 2x + x \Rightarrow 1 = 5x \Rightarrow x = \frac{1}{5}$ 3) $7 \frac{1}{4}x - x = 9 \frac{3}{8} \Rightarrow 6 \frac{1}{4}x = 9 \frac{3}{8} \Rightarrow \frac{25}{4}x = \frac{75}{8} \Rightarrow x = \frac{75}{8} \cdot \frac{4}{25} = \frac{3}{2} = 1 \frac{1}{2}$ 4) $1 : 2 \frac{7}{9} = x + 4 \frac{2}{5}x \Rightarrow 1 : \frac{25}{9} = 5 \frac{2}{5}x \Rightarrow \frac{9}{25} = \frac{27}{5}x \Rightarrow x = \frac{9}{25} \cdot \frac{5}{27} = \frac{1}{5} \cdot \frac{1}{3} = \frac{1}{15}$ 5) $3 \frac{1}{8} : (x - 4 \frac{7}{24}) = \frac{17}{18} + 1 \frac{5}{6} \Rightarrow \frac{25}{8} : (x - \frac{103}{24}) = \frac{17}{18} + \frac{11}{6} = \frac{17+33}{18} = \frac{50}{18} = \frac{25}{9} \Rightarrow x - \frac{103}{24} = \frac{25}{8} : \frac{25}{9} = \frac{25}{8} \cdot \frac{9}{25} = \frac{9}{8} \Rightarrow x = \frac{9}{8} + \frac{103}{24} = \frac{27+103}{24} = \frac{130}{24} = 5 \frac{10}{24} = 5 \frac{5}{12}$ 6) $24 \frac{1}{14} + 8 \frac{3}{7} = (x : 1 \frac{1}{9}) \cdot 5 \frac{5}{12} \Rightarrow \frac{337}{14} + \frac{59}{7} = \frac{337+118}{14} = \frac{455}{14} = 32 \frac{1}{2} = (x : \frac{10}{9}) \cdot \frac{65}{12} \Rightarrow \frac{65}{2} = (x \cdot \frac{9}{10}) \cdot \frac{65}{12} \Rightarrow x \cdot \frac{3}{4} = \frac{65}{2} : \frac{65}{12} = \frac{65}{2} \cdot \frac{12}{65} = 6 \Rightarrow x = 6 : \frac{3}{4} = 8$ 7) $(4 \frac{1}{5} : x + 1 \frac{1}{3}) : 2 \frac{4}{35} - \frac{4}{5} = 1 \frac{8}{15} \Rightarrow (\frac{21}{5} : x + \frac{4}{3}) : \frac{74}{35} = \frac{23}{15} + \frac{4}{5} = \frac{23+12}{15} = \frac{35}{15} = \frac{7}{3} \Rightarrow \frac{21}{5} : x + \frac{4}{3} = \frac{7}{3} \cdot \frac{74}{35} = \frac{1}{3} \cdot \frac{74}{5} = \frac{74}{15} \Rightarrow \frac{21}{5} : x = \frac{74}{15} - \frac{4}{3} = \frac{74-20}{15} = \frac{54}{15} = \frac{18}{5} \Rightarrow x = \frac{21}{5} : \frac{18}{5} = \frac{21}{18} = 1 \frac{3}{18} = 1 \frac{1}{6}$ 8) $4 \frac{1}{5} : 1 \frac{1}{5} = 2 \frac{3}{4} \cdot 4 - 1 \frac{7}{18} x \Rightarrow \frac{21}{5} : \frac{6}{5} = \frac{21}{6} = 3 \frac{3}{6} = 3 \frac{1}{2} = 11 - 1 \frac{7}{18} x \Rightarrow 1 \frac{7}{18} x = 11 - 3 \frac{1}{2} = 11 - 3 \frac{9}{18} = 7 \frac{9}{18} = 7 \frac{1}{2} \Rightarrow \frac{25}{18} x = \frac{15}{2} \Rightarrow x = \frac{15}{2} \cdot \frac{18}{25} = \frac{3}{1} \cdot \frac{9}{5} = \frac{27}{5} = 5 \frac{2}{5}$