$$4{\frac{5}{9}} : {\frac{7}{9}} = {\frac{4 \cdot 9 + 5}{9}} : {\frac{7}{9}} = {\frac{41}{9}} : {\frac{7}{9}} = {\frac{41}{9}} \cdot {\frac{9}{7}} = {\frac{41}{7}} = 5{\frac{6}{7}}$$
Ответ: $$5{\frac{6}{7}}$$