1. Выполни действие: a) 4 5/7 : 7/9; б) 3 9/8 : 5 10/27; в) 4 4/9 : 2 2/3; г) 32: 8/9; д) 12/13 : 6/18.

1. Выполним действия:

1. a) $$4 \frac{5}{7} : \frac{7}{9} = \frac{4 \cdot 7 + 5}{7} : \frac{7}{9} = \frac{33}{7} : \frac{7}{9} = \frac{33}{7} \cdot \frac{9}{7} = \frac{33 \cdot 9}{7 \cdot 7} = \frac{297}{49} = 6 \frac{3}{49}$$
2. б) $$3 \frac{9}{8} : 5 \frac{10}{27} = \frac{3 \cdot 8 + 9}{8} : \frac{5 \cdot 27 + 10}{27} = \frac{33}{8} : \frac{145}{27} = \frac{33}{8} \cdot \frac{27}{145} = \frac{33 \cdot 27}{8 \cdot 145} = \frac{891}{1160}$$
3. в) $$4 \frac{4}{9} : 2 \frac{2}{3} = \frac{4 \cdot 9 + 4}{9} : \frac{2 \cdot 3 + 2}{3} = \frac{40}{9} : \frac{8}{3} = \frac{40}{9} \cdot \frac{3}{8} = \frac{40 \cdot 3}{9 \cdot 8} = \frac{120}{72} = \frac{5}{3} = 1 \frac{2}{3}$$
4. г) $$32 : \frac{8}{9} = 32 \cdot \frac{9}{8} = \frac{32}{1} \cdot \frac{9}{8} = \frac{32 \cdot 9}{1 \cdot 8} = \frac{288}{8} = 36$$
5. д) $$\frac{12}{13} : \frac{6}{18} = \frac{12}{13} : \frac{1}{3} = \frac{12}{13} \cdot \frac{3}{1} = \frac{12 \cdot 3}{13 \cdot 1} = \frac{36}{13} = 2 \frac{10}{13}$$

Ответ: a) $$6 \frac{3}{49}$$, б) $$\frac{891}{1160}$$, в) $$1 \frac{2}{3}$$, г) $$36$$, д) $$2 \frac{10}{13}$$