08 Найдите частное: a) 4/7 : 16/49 = 6) 5/9 : 1/2 = B) 12/25 : 8/15 = a) 9/14 : 18/35 =

Решение:

1. \( \frac{4}{7} : \frac{16}{49} = \frac{4}{7} \cdot \frac{49}{16} = \frac{4 \cdot 49}{7 \cdot 16} = \frac{4 \cdot (7 \cdot 7)}{(7) \cdot (4 \cdot 4)} = \frac{7}{4} = 1\frac{3}{4} \)
2. \( \frac{5}{9} : \frac{1}{2} = \frac{5}{9} \cdot \frac{2}{1} = \frac{5 \cdot 2}{9 \cdot 1} = \frac{10}{9} = 1\frac{1}{9} \)
3. \( \frac{12}{25} : \frac{8}{15} = \frac{12}{25} \cdot \frac{15}{8} = \frac{12 \cdot 15}{25 \cdot 8} = \frac{(4 \cdot 3) \cdot (3 \cdot 5)}{(5 \cdot 5) \cdot (4 \cdot 2)} = \frac{3 \cdot 3}{5 \cdot 2} = \frac{9}{10} \)
4. \( \frac{9}{14} : \frac{18}{35} = \frac{9}{14} \cdot \frac{35}{18} = \frac{9 \cdot 35}{14 \cdot 18} = \frac{9 \cdot (5 \cdot 7)}{(2 \cdot 7) \cdot (2 \cdot 9)} = \frac{5}{2 \cdot 2} = \frac{5}{4} = 1\frac{1}{4} \)

Ответ: а) \( 1\frac{3}{4} \), б) \( 1\frac{1}{9} \), в) \( \frac{9}{10} \), г) \( 1\frac{1}{4} \).