Решение:

а) $$\frac{4}{7} : \frac{5}{9} = \frac{4}{7} \cdot \frac{9}{5} = \frac{4 \cdot 9}{7 \cdot 5} = \frac{36}{35} = 1\frac{1}{35}$$ б) $$\frac{3}{8} : \frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{48}{72} = \frac{2}{3}$$ в) $$7\frac{11}{12} : 3\frac{1}{6} = \frac{7 \cdot 12 + 11}{12} : \frac{3 \cdot 6 + 1}{6} = \frac{84 + 11}{12} : \frac{18 + 1}{6} = \frac{95}{12} : \frac{19}{6} = \frac{95}{12} \cdot \frac{6}{19} = \frac{95 \cdot 6}{12 \cdot 19} = \frac{570}{228} = \frac{5 \cdot 19 \cdot 6}{2 \cdot 6 \cdot 19} = \frac{5}{2} = 2\frac{1}{2}$$ г) $$48 : \frac{12}{13} = 48 \cdot \frac{13}{12} = \frac{48 \cdot 13}{12} = \frac{4 \cdot 12 \cdot 13}{12} = 4 \cdot 13 = 52$$ д) $$\frac{15}{16} : 5 = \frac{15}{16} : \frac{5}{1} = \frac{15}{16} \cdot \frac{1}{5} = \frac{15 \cdot 1}{16 \cdot 5} = \frac{15}{80} = \frac{3 \cdot 5}{16 \cdot 5} = \frac{3}{16}$$