1. Выполните действия a) \(\frac{4}{7}:\frac{5}{9}\) б) \(\frac{3}{8}:\frac{9}{16}\) в) \(7\frac{11}{12}:3\frac{1}{6}\) г) \(48:\frac{12}{13}\) д) \(\frac{15}{16}:5\)

Выполним действия:

1. а) \(\frac{4}{7}:\frac{5}{9} = \frac{4}{7} \cdot \frac{9}{5} = \frac{4 \cdot 9}{7 \cdot 5} = \frac{36}{35} = 1\frac{1}{35}\)
2. б) \(\frac{3}{8}:\frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{48}{72} = \frac{2}{3}\)
3. в) \(7\frac{11}{12}:3\frac{1}{6} = \frac{7 \cdot 12 + 11}{12} : \frac{3 \cdot 6 + 1}{6} = \frac{84+11}{12} : \frac{18+1}{6} = \frac{95}{12} : \frac{19}{6} = \frac{95}{12} \cdot \frac{6}{19} = \frac{95 \cdot 6}{12 \cdot 19} = \frac{5 \cdot 1}{2 \cdot 1} = \frac{5}{2} = 2\frac{1}{2}\)
4. г) \(48:\frac{12}{13} = 48 \cdot \frac{13}{12} = \frac{48 \cdot 13}{12} = \frac{4 \cdot 13}{1} = 52\)
5. д) \(\frac{15}{16}:5 = \frac{15}{16} \cdot \frac{1}{5} = \frac{15 \cdot 1}{16 \cdot 5} = \frac{3}{16}\)

Ответ: а) \(1\frac{1}{35}\); б) \(\frac{2}{3}\); в) \(2\frac{1}{2}\); г) \(52\); д) \(\frac{3}{16}\)