453. Решите уравнение:

Решение:

1. \(\frac{25}{27} x = \frac{5}{18}\)
   \(x = \frac{5}{18} : \frac{25}{27}\)
   \(x = \frac{5}{18} \cdot \frac{27}{25}\)
   \(x = \frac{5 \cdot 27}{18 \cdot 25}\)
   \(x = \frac{1 \cdot 3}{2 \cdot 5} = \frac{3}{10}\)
2. \(\frac{13}{17} x = 39\)
   \(x = 39 : \frac{13}{17}\)
   \(x = 39 \cdot \frac{17}{13}\)
   \(x = 3 \cdot 17 = 51\)
3. \(4x = \frac{5}{7}\)
   \(x = \frac{5}{7} : 4\)
   \(x = \frac{5}{7} \cdot \frac{1}{4}\)
   \(x = \frac{5}{28}\)
4. \(x : 2 \frac{2}{15} = 1 \frac{9}{16}\)
   \(x : \frac{32}{15} = \frac{25}{16}\)
   \(x = \frac{25}{16} \cdot \frac{32}{15}\)
   \(x = \frac{25 \cdot 32}{16 \cdot 15}\)
   \(x = \frac{5 \cdot 2}{3} = \frac{10}{3}\)
5. \(4 \frac{4}{9} : x = \frac{5}{27}\)
   \(\frac{40}{9} : x = \frac{5}{27}\)
   \(x = \frac{40}{9} : \frac{5}{27}\)
   \(x = \frac{40}{9} \cdot \frac{27}{5}\)
   \(x = \frac{40 \cdot 27}{9 \cdot 5}\)
   \(x = 8 \cdot 3 = 24\)
6. \(1 \frac{4}{9} x = 5,2\)
   \(\frac{13}{9} x = \frac{52}{10}\)
   \(x = \frac{52}{10} : \frac{13}{9}\)
   \(x = \frac{52}{10} \cdot \frac{9}{13}\)
   \(x = \frac{4 \cdot 9}{10}\)
   \(x = \frac{36}{10} = 3,6\)

Ответ: 1) \(x = \frac{3}{10}\) 2) \(x = 51\) 3) \(x = \frac{5}{28}\) 4) \(x = \frac{10}{3}\) 5) \(x = 24\) 6) \(x = 3,6\)