1. Выполните действия a) 5/7 : 3/8 b) 5/9 : 10/27 в) 4/9 : 2/3 г) 32/5 : 8/9 д) 12/13 : 6/5

Решение:

1. а)
   

   \[ \frac{5}{7} : \frac{3}{8} = \frac{5}{7} \times \frac{8}{3} = \frac{5 \times 8}{7 \times 3} = \frac{40}{21} \]

2. б)
   

   \[ \frac{5}{9} : \frac{10}{27} = \frac{5}{9} \times \frac{27}{10} = \frac{5 \times 27}{9 \times 10} = \frac{1 \times 3}{1 \times 2} = \frac{3}{2} \]

3. в)
   

   \[ \frac{4}{9} : \frac{2}{3} = \frac{4}{9} \times \frac{3}{2} = \frac{4 \times 3}{9 \times 2} = \frac{2 \times 1}{3 \times 1} = \frac{2}{3} \]

4. г)
   

   \[ \frac{32}{5} : \frac{8}{9} = \frac{32}{5} \times \frac{9}{8} = \frac{32 \times 9}{5 \times 8} = \frac{4 \times 9}{5 \times 1} = \frac{36}{5} \]

5. д)
   

   \[ \frac{12}{13} : \frac{6}{5} = \frac{12}{13} \times \frac{5}{6} = \frac{12 \times 5}{13 \times 6} = \frac{2 \times 5}{13 \times 1} = \frac{10}{13} \]