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Математика336. 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 \(\frac{2}{3}\).
Ответ:
1) \(\frac{7}{18} + \frac{5}{18} = \frac{7+5}{18} = \frac{12}{18} = \frac{2}{3}\)
Ответ: \(\frac{2}{3}\)
2) \(\frac{29}{64} - \frac{14}{64} - \frac{9}{64} = \frac{29-14-9}{64} = \frac{6}{64} = \frac{3}{32}\)
Ответ: \(\frac{3}{32}\)
3) \(\frac{3}{28} + \frac{5}{14} = \frac{3}{28} + \frac{5 \cdot 2}{14 \cdot 2} = \frac{3}{28} + \frac{10}{28} = \frac{3+10}{28} = \frac{13}{28}\)
Ответ: \(\frac{13}{28}\)
4) \(\frac{9}{11} - \frac{2}{5} = \frac{9 \cdot 5}{11 \cdot 5} - \frac{2 \cdot 11}{5 \cdot 11} = \frac{45}{55} - \frac{22}{55} = \frac{45-22}{55} = \frac{23}{55}\)
Ответ: \(\frac{23}{55}\)
5) \(\frac{9}{16} + \frac{7}{24} - \frac{3}{8} = \frac{9 \cdot 3}{16 \cdot 3} + \frac{7 \cdot 2}{24 \cdot 2} - \frac{3 \cdot 6}{8 \cdot 6} = \frac{27}{48} + \frac{14}{48} - \frac{18}{48} = \frac{27+14-18}{48} = \frac{23}{48}\)
Ответ: \(\frac{23}{48}\)
6) \(1 \frac{1}{7} + 2 \frac{1}{3} = \frac{1 \cdot 7 + 1}{7} + \frac{2 \cdot 3 + 1}{3} = \frac{8}{7} + \frac{7}{3} = \frac{8 \cdot 3}{7 \cdot 3} + \frac{7 \cdot 7}{3 \cdot 7} = \frac{24}{21} + \frac{49}{21} = \frac{24+49}{21} = \frac{73}{21} = 3 \frac{10}{21}\)
Ответ: 3 \(\frac{10}{21}\)
7) \(7 - 3 \frac{9}{16} = \frac{7 \cdot 16}{16} - \frac{3 \cdot 16 + 9}{16} = \frac{112}{16} - \frac{57}{16} = \frac{112-57}{16} = \frac{55}{16} = 3 \frac{7}{16}\)
Ответ: 3 \(\frac{7}{16}\)
8) \(4 \frac{7}{33} - 2 \frac{3}{22} = \frac{4 \cdot 33 + 7}{33} - \frac{2 \cdot 22 + 3}{22} = \frac{139}{33} - \frac{47}{22} = \frac{139 \cdot 2}{33 \cdot 2} - \frac{47 \cdot 3}{22 \cdot 3} = \frac{278}{66} - \frac{141}{66} = \frac{278 - 141}{66} = \frac{137}{66} = 2 \frac{5}{66}\)
Ответ: 2 \(\frac{5}{66}\)
9) \(6 \frac{1}{6} - 2 \frac{2}{3} = \frac{6 \cdot 6 + 1}{6} - \frac{2 \cdot 3 + 2}{3} = \frac{37}{6} - \frac{8}{3} = \frac{37}{6} - \frac{8 \cdot 2}{3 \cdot 2} = \frac{37}{6} - \frac{16}{6} = \frac{37-16}{6} = \frac{21}{6} = \frac{7}{2} = 3 \frac{1}{2}\)
Ответ: 3 \(\frac{1}{2}\)
Похожие
- 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 \(\frac{11}{12}\).
- 338. 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 = \(\frac{5}{18}\).
- 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 \(\frac{1}{18}\).
