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Математика338. Решите уравнение: 1) x - 4 \(\frac{5}{8}\) = 7 \(\frac{17}{32}\); 2) x + \(\frac{8}{9}\) = 1 \(\frac{7}{12}\); 3) 3 \(\frac{1}{6}\) - x = \(\frac{5}{18}\).
Ответ:
1) \(x - 4 \frac{5}{8} = 7 \frac{17}{32}\)
\(x = 7 \frac{17}{32} + 4 \frac{5}{8}\)
\(x = \frac{7 \cdot 32 + 17}{32} + \frac{4 \cdot 8 + 5}{8}\)
\(x = \frac{231}{32} + \frac{37}{8}\)
\(x = \frac{231}{32} + \frac{37 \cdot 4}{8 \cdot 4}\)
\(x = \frac{231}{32} + \frac{148}{32}\)
\(x = \frac{231 + 148}{32}\)
\(x = \frac{379}{32}\)
\(x = 11 \frac{27}{32}\)
Ответ: \(11 \frac{27}{32}\)
2) \(x + \frac{8}{9} = 1 \frac{7}{12}\)
\(x = 1 \frac{7}{12} - \frac{8}{9}\)
\(x = \frac{1 \cdot 12 + 7}{12} - \frac{8}{9}\)
\(x = \frac{19}{12} - \frac{8}{9}\)
\(x = \frac{19 \cdot 3}{12 \cdot 3} - \frac{8 \cdot 4}{9 \cdot 4}\)
\(x = \frac{57}{36} - \frac{32}{36}\)
\(x = \frac{57 - 32}{36}\)
\(x = \frac{25}{36}\)
Ответ: \(\frac{25}{36}\)
3) \(3 \frac{1}{6} - x = \frac{5}{18}\)
\(x = 3 \frac{1}{6} - \frac{5}{18}\)
\(x = \frac{3 \cdot 6 + 1}{6} - \frac{5}{18}\)
\(x = \frac{19}{6} - \frac{5}{18}\)
\(x = \frac{19 \cdot 3}{6 \cdot 3} - \frac{5}{18}\)
\(x = \frac{57}{18} - \frac{5}{18}\)
\(x = \frac{57 - 5}{18}\)
\(x = \frac{52}{18}\)
\(x = \frac{26}{9}\)
\(x = 2 \frac{8}{9}\)
Ответ: \(2 \frac{8}{9}\)
Похожие
- 336. Выполните действия: 1) \(\frac{7}{18} + \frac{5}{18}\); 2) \(\frac{29}{64} - \frac{14}{64} - \frac{9}{64}\); 3) \(\frac{3}{28} + \frac{5}{14}\); 4) \(\frac{9}{11} - \frac{2}{5}\); 5) \(\frac{9}{16} + \frac{7}{24} - \frac{3}{8}\); 6) 1 \(\frac{1}{7}\) + 2 \(\frac{1}{3}\); 7) 7 - 3 \(\frac{9}{16}\); 8) 4 \(\frac{7}{33}\) - 2 \(\frac{3}{22}\); 9) 6 \(\frac{1}{6}\) - 2 \(\frac{2}{3}\).
- 337. Вычислите: 1) \(\frac{31}{58} - \frac{16}{58}\); 2) \(\frac{19}{25} + \frac{4}{25} + \frac{22}{25}\); 3) \(\frac{1}{6} + \frac{7}{15}\); 4) \(\frac{5}{14} - \frac{1}{4}\); 5) \(\frac{3}{4} - \frac{5}{12} + \frac{5}{9}\); 6) 2 \(\frac{3}{8}\) + 4 \(\frac{5}{12}\); 7) 3 \(\frac{5}{6}\) - 1 \(\frac{7}{12}\); 8) 9 \(\frac{2}{15}\) - 6 \(\frac{3}{5}\); 9) 5 \(\frac{7}{18}\) - 4 \(\frac{11}{12}\).
- 339. Решите уравнение: 1) x + \(\frac{7}{8}\) = 5; 2) x - 5 \(\frac{8}{21}\) = 1 \(\frac{17}{42}\); 3) 9 \(\frac{1}{45}\) - x = 3 \(\frac{1}{30}\).
- 340. Вычислите значение выражения наиболее удобным способом: 1) \(\frac{4}{11} + \frac{5}{33} + \frac{6}{33} + \frac{7}{11}\); 2) \(\frac{1}{25} + \frac{3}{20} + \frac{4}{25} + \frac{1}{20}\); 3) \(\frac{13}{72} + \frac{5}{56} + \frac{5}{72} + \frac{9}{56}\); 4) 1 \(\frac{5}{28}\) + 2 \(\frac{17}{64}\) + 3 \(\frac{2}{28}\) + 4 \(\frac{7}{64}\).
- 341. Вычислите значение выражения наиболее удобным способом: 1) \(\frac{4}{15} + \frac{13}{36} + \frac{1}{15} + \frac{5}{36}\); 2) 2 \(\frac{5}{18}\) + 4 \(\frac{1}{48}\) + 6 \(\frac{7}{48}\) + 3 \(\frac{1}{18}\).
