№1. Сократите дроби 22. Найдите значение х:

№1. Сократите дроби

• \[\frac{75}{120} = \frac{75:15}{120:15} = \frac{5}{8}\]
• \[\frac{180}{150} = \frac{180:30}{150:30} = \frac{6}{5}\]
• \[\frac{3\cdot8}{16\cdot15} = \frac{3\cdot8}{2\cdot8\cdot3\cdot5} = \frac{1}{2\cdot5} = \frac{1}{10}\]
• \[\frac{24\cdot5}{25\cdot12} = \frac{24\cdot5}{5\cdot5\cdot12} = \frac{24}{5\cdot12} = \frac{2\cdot12}{5\cdot12} = \frac{2}{5}\]
• \[\frac{5\cdot6\cdot2}{3\cdot25\cdot4} = \frac{5\cdot6\cdot2}{3\cdot5\cdot5\cdot4} = \frac{6\cdot2}{3\cdot5\cdot4} = \frac{3\cdot2\cdot2}{3\cdot5\cdot4} = \frac{4}{5\cdot4} = \frac{1}{5}\]
• \[\frac{2835}{7425} = \frac{2835:45}{7425:45} = \frac{63}{165} = \frac{63:3}{165:3} = \frac{21}{55}\]
• \[\frac{21\cdot5\cdot21\cdot3}{5\cdot21\cdot3\cdot21} = 1\]
• \[\frac{56\cdot169\cdot225}{100\cdot64\cdot15} = \frac{8\cdot7\cdot13\cdot13\cdot15\cdot15}{4\cdot25\cdot8\cdot8\cdot15} = \frac{7\cdot13\cdot13\cdot15}{4\cdot25\cdot8} = \frac{7\cdot169\cdot3}{4\cdot5\cdot8} = \frac{3549}{160}\]

№2. Найдите значение x:

• a) \[\frac{9}{x} = \frac{45}{55}\] \(45x = 9 \cdot 55\) \(x = \frac{9 \cdot 55}{45} = \frac{9 \cdot 5 \cdot 11}{9 \cdot 5} = 11\)
• б) \[\frac{8}{9} = \frac{72}{x}\] \(8x = 9 \cdot 72\) \(x = \frac{9 \cdot 72}{8} = \frac{9 \cdot 9 \cdot 8}{8} = 81\)

Ответ: a) x = 11, б) x = 81