Деление обыкновенных дробей и смешанных чисел 6 6 18 1. : 7. 35 49 7 : 28 25 2 3 9 2. 6: 二7 8. 3:25 5 4 1 3. 6:7 9. 12:24 4 9 1 4. 1: 10. 20 2:12 4 5. 1:3 11. 16:56 6 9 14 6. : 1 12. 0:817 20

Решим примеры на деление обыкновенных дробей и смешанных чисел.

1. $$\frac{6}{35} : \frac{18}{49} = \frac{6}{35} \cdot \frac{49}{18} = \frac{6 \cdot 49}{35 \cdot 18} = \frac{6 \cdot 7 \cdot 7}{5 \cdot 7 \cdot 6 \cdot 3} = \frac{7}{5 \cdot 3} = \frac{7}{15}$$
2. $$6 : \frac{2}{7} = 6 \cdot \frac{7}{2} = \frac{6 \cdot 7}{2} = \frac{2 \cdot 3 \cdot 7}{2} = 3 \cdot 7 = 21$$
3. $$6 : \frac{4}{7} = 6 \cdot \frac{7}{4} = \frac{6 \cdot 7}{4} = \frac{2 \cdot 3 \cdot 7}{2 \cdot 2} = \frac{3 \cdot 7}{2} = \frac{21}{2} = 10\frac{1}{2}$$
4. $$1 : \frac{9}{20} = 1 \cdot \frac{20}{9} = \frac{20}{9} = 2\frac{2}{9}$$
5. $$1 : \frac{4}{3} = 1 \cdot \frac{3}{4} = \frac{3}{4}$$
6. $$\frac{9}{20} : 1 = \frac{9}{20} \cdot 1 = \frac{9}{20}$$
7. $$\frac{7}{25} : 28 = \frac{7}{25} \cdot \frac{1}{28} = \frac{7 \cdot 1}{25 \cdot 28} = \frac{7 \cdot 1}{25 \cdot 7 \cdot 4} = \frac{1}{25 \cdot 4} = \frac{1}{100}$$
8. $$3\frac{3}{5} : \frac{9}{25} = \frac{3 \cdot 5 + 3}{5} : \frac{9}{25} = \frac{15 + 3}{5} : \frac{9}{25} = \frac{18}{5} : \frac{9}{25} = \frac{18}{5} \cdot \frac{25}{9} = \frac{18 \cdot 25}{5 \cdot 9} = \frac{9 \cdot 2 \cdot 5 \cdot 5}{5 \cdot 9} = 2 \cdot 5 = 10$$
9. $$12 : 2\frac{1}{4} = 12 : \frac{2 \cdot 4 + 1}{4} = 12 : \frac{8 + 1}{4} = 12 : \frac{9}{4} = 12 \cdot \frac{4}{9} = \frac{12 \cdot 4}{9} = \frac{3 \cdot 4 \cdot 4}{3 \cdot 3} = \frac{4 \cdot 4}{3} = \frac{16}{3} = 5\frac{1}{3}$$
10. $$2\frac{1}{4} : 12 = \frac{2 \cdot 4 + 1}{4} : 12 = \frac{8 + 1}{4} : 12 = \frac{9}{4} : 12 = \frac{9}{4} \cdot \frac{1}{12} = \frac{9 \cdot 1}{4 \cdot 12} = \frac{3 \cdot 3}{4 \cdot 3 \cdot 4} = \frac{3}{4 \cdot 4} = \frac{3}{16}$$
11. $$16\frac{1}{3} : 5\frac{5}{6} = \frac{16 \cdot 3 + 1}{3} : \frac{5 \cdot 6 + 5}{6} = \frac{48 + 1}{3} : \frac{30 + 5}{6} = \frac{49}{3} : \frac{35}{6} = \frac{49}{3} \cdot \frac{6}{35} = \frac{49 \cdot 6}{3 \cdot 35} = \frac{7 \cdot 7 \cdot 3 \cdot 2}{3 \cdot 7 \cdot 5} = \frac{7 \cdot 2}{5} = \frac{14}{5} = 2\frac{4}{5}$$
12. $$0 : 8\frac{14}{17} = 0 : \frac{8 \cdot 17 + 14}{17} = 0 : \frac{136 + 14}{17} = 0 : \frac{150}{17} = 0 \cdot \frac{17}{150} = 0$$

Ответ: 1) $$\frac{7}{15}$$; 2) 21; 3) $$10\frac{1}{2}$$; 4) $$2\frac{2}{9}$$; 5) $$\frac{3}{4}$$; 6) $$\frac{9}{20}$$; 7) $$\frac{1}{100}$$; 8) 10; 9) $$5\frac{1}{3}$$; 10) $$\frac{3}{16}$$; 11) $$2\frac{4}{5}$$; 12) 0