78. Выполните деление: 1) \(\frac{5}{7} \cdot \frac{4}{5}\); 2) \(\frac{6}{35} : \frac{18}{49}\); 3) \(\frac{27}{28} : \frac{9}{56}\); 4) \(\frac{28}{45} : \frac{63}{40}\) 79. Найдите частное: 1) 6 : \(\frac{2}{7}\); 3) \(\frac{7}{25} : 28\); 5) \(2\frac{2}{3} : 2\frac{2}{7}\); 2) 1 : \(\frac{8}{19}\); 4) \(16\frac{1}{3} : 5\frac{5}{6}\); 6) \(4\frac{4}{9} : \frac{5}{27}\) Ле 81. Решите уравнение: 1) \(\frac{5}{13}x = \frac{2}{13}\); 3) \(\frac{6}{7}x = 24\); 5) \(\frac{3}{11}x = \frac{22}{27}\); 2) \(\frac{8}{9}x = 1\); 4) \(7x = \frac{3}{4}\); 6) \(3\frac{3}{5} : x = \frac{9}{35}\)

Задание 78. Выполните деление:

1. \[\frac{5}{7} \cdot \frac{4}{5} = \frac{5 \cdot 4}{7 \cdot 5} = \frac{20}{35} = \frac{4}{7}\]
2. \[\frac{6}{35} : \frac{18}{49} = \frac{6}{35} \cdot \frac{49}{18} = \frac{6 \cdot 49}{35 \cdot 18} = \frac{6 \cdot 7 \cdot 7}{5 \cdot 7 \cdot 6 \cdot 3} = \frac{7}{5 \cdot 3} = \frac{7}{15}\]
3. \[\frac{27}{28} : \frac{9}{56} = \frac{27}{28} \cdot \frac{56}{9} = \frac{27 \cdot 56}{28 \cdot 9} = \frac{3 \cdot 9 \cdot 2 \cdot 28}{28 \cdot 9} = 3 \cdot 2 = 6\]
4. \[\frac{28}{45} : \frac{63}{40} = \frac{28}{45} \cdot \frac{40}{63} = \frac{28 \cdot 40}{45 \cdot 63} = \frac{4 \cdot 7 \cdot 8 \cdot 5}{9 \cdot 5 \cdot 9 \cdot 7} = \frac{4 \cdot 8}{9 \cdot 9} = \frac{32}{81}\]

Задание 79. Найдите частное:

1. \[6 : \frac{2}{7} = 6 \cdot \frac{7}{2} = \frac{6 \cdot 7}{2} = \frac{3 \cdot 2 \cdot 7}{2} = 3 \cdot 7 = 21\]
2. \[1 : \frac{8}{19} = 1 \cdot \frac{19}{8} = \frac{19}{8} = 2\frac{3}{8}\]
3. \[\frac{7}{25} : 28 = \frac{7}{25} : \frac{28}{1} = \frac{7}{25} \cdot \frac{1}{28} = \frac{7 \cdot 1}{25 \cdot 28} = \frac{7 \cdot 1}{25 \cdot 4 \cdot 7} = \frac{1}{25 \cdot 4} = \frac{1}{100} = 0.01\]
4. \[16\frac{1}{3} : 5\frac{5}{6} = \frac{16 \cdot 3 + 1}{3} : \frac{5 \cdot 6 + 5}{6} = \frac{49}{3} : \frac{35}{6} = \frac{49}{3} \cdot \frac{6}{35} = \frac{49 \cdot 6}{3 \cdot 35} = \frac{7 \cdot 7 \cdot 2 \cdot 3}{3 \cdot 5 \cdot 7} = \frac{7 \cdot 2}{5} = \frac{14}{5} = 2\frac{4}{5}\]
5. \[2\frac{2}{3} : 2\frac{2}{7} = \frac{2 \cdot 3 + 2}{3} : \frac{2 \cdot 7 + 2}{7} = \frac{8}{3} : \frac{16}{7} = \frac{8}{3} \cdot \frac{7}{16} = \frac{8 \cdot 7}{3 \cdot 16} = \frac{8 \cdot 7}{3 \cdot 2 \cdot 8} = \frac{7}{3 \cdot 2} = \frac{7}{6} = 1\frac{1}{6}\]
6. \[4\frac{4}{9} : \frac{5}{27} = \frac{4 \cdot 9 + 4}{9} : \frac{5}{27} = \frac{40}{9} : \frac{5}{27} = \frac{40}{9} \cdot \frac{27}{5} = \frac{40 \cdot 27}{9 \cdot 5} = \frac{8 \cdot 5 \cdot 3 \cdot 9}{9 \cdot 5} = 8 \cdot 3 = 24\]

Ле 81. Решите уравнение:

1. \[\frac{5}{13}x = \frac{2}{13}\] \[x = \frac{2}{13} : \frac{5}{13}\] \[x = \frac{2}{13} \cdot \frac{13}{5}\] \[x = \frac{2 \cdot 13}{13 \cdot 5}\] \[x = \frac{2}{5}\]
2. \[\frac{8}{9}x = 1\] \[x = 1 : \frac{8}{9}\] \[x = 1 \cdot \frac{9}{8}\] \[x = \frac{9}{8}\] \[x = 1\frac{1}{8}\]
3. \[\frac{6}{7}x = 24\] \[x = 24 : \frac{6}{7}\] \[x = 24 \cdot \frac{7}{6}\] \[x = \frac{24 \cdot 7}{6}\] \[x = \frac{4 \cdot 6 \cdot 7}{6}\] \[x = 4 \cdot 7\] \[x = 28\]
4. \[7x = \frac{3}{4}\] \[x = \frac{3}{4} : 7\] \[x = \frac{3}{4} : \frac{7}{1}\] \[x = \frac{3}{4} \cdot \frac{1}{7}\] \[x = \frac{3 \cdot 1}{4 \cdot 7}\] \[x = \frac{3}{28}\]
5. \[\frac{3}{11}x = \frac{22}{27}\] \[x = \frac{22}{27} : \frac{3}{11}\] \[x = \frac{22}{27} \cdot \frac{11}{3}\] \[x = \frac{22 \cdot 11}{27 \cdot 3}\] \[x = \frac{242}{81}\] \[x = 2\frac{80}{81}\]
6. \[3\frac{3}{5} : x = \frac{9}{35}\] \[\frac{3 \cdot 5 + 3}{5} : x = \frac{9}{35}\] \[\frac{18}{5} : x = \frac{9}{35}\] \[x = \frac{18}{5} : \frac{9}{35}\] \[x = \frac{18}{5} \cdot \frac{35}{9}\] \[x = \frac{18 \cdot 35}{5 \cdot 9}\] \[x = \frac{2 \cdot 9 \cdot 7 \cdot 5}{5 \cdot 9}\] \[x = 2 \cdot 7\] \[x = 14\]

Ответ: Задание решено!

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