Упр.188 Рабочая тетрадь №1 ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Найдите частное: 1) $$9:\frac{4}{5}$$; 2) $$12:\frac{6}{7}$$; 3) $$15:\frac{10}{11}$$; 4) $$1:\frac{16}{17}$$; 5) $$\frac{7}{13}:4$$; 6) $$\frac{12}{19}:3$$; 7) $$4\frac{1}{6}:\frac{5}{9}$$; 8) $$\frac{9}{16}:1\frac{1}{2}$$; 9) $$1\frac{5}{7}:3\frac{3}{4}$$; 10) $$5\frac{1}{2}:3\frac{2}{3}$$.

При делении на дробь умножаем на обратную дробь.

1. $$9 : \frac{4}{5} = 9 \cdot \frac{5}{4} = \frac{45}{4} = 11 \frac{1}{4}$$
2. $$12 : \frac{6}{7} = 12 \cdot \frac{7}{6} = \frac{12 \cdot 7}{6} = 2 \cdot 7 = 14$$
3. $$15 : \frac{10}{11} = 15 \cdot \frac{11}{10} = \frac{15 \cdot 11}{10} = \frac{3 \cdot 11}{2} = \frac{33}{2} = 16 \frac{1}{2}$$
4. $$1 : \frac{16}{17} = 1 \cdot \frac{17}{16} = \frac{17}{16} = 1 \frac{1}{16}$$
5. $$\frac{7}{13} : 4 = \frac{7}{13} \cdot \frac{1}{4} = \frac{7}{52}$$
6. $$\frac{12}{19} : 3 = \frac{12}{19} \cdot \frac{1}{3} = \frac{12}{19 \cdot 3} = \frac{4}{19}$$
7. $$4 \frac{1}{6} : \frac{5}{9} = \frac{25}{6} : \frac{5}{9} = \frac{25}{6} \cdot \frac{9}{5} = \frac{25 \cdot 9}{6 \cdot 5} = \frac{5 \cdot 3}{2 \cdot 1} = \frac{15}{2} = 7 \frac{1}{2}$$
8. $$\frac{9}{16} : 1 \frac{1}{2} = \frac{9}{16} : \frac{3}{2} = \frac{9}{16} \cdot \frac{2}{3} = \frac{9 \cdot 2}{16 \cdot 3} = \frac{3 \cdot 1}{8 \cdot 1} = \frac{3}{8}$$
9. $$1 \frac{5}{7} : 3 \frac{3}{4} = \frac{12}{7} : \frac{15}{4} = \frac{12}{7} \cdot \frac{4}{15} = \frac{12 \cdot 4}{7 \cdot 15} = \frac{4 \cdot 4}{7 \cdot 5} = \frac{16}{35}$$
10. $$5 \frac{1}{2} : 3 \frac{2}{3} = \frac{11}{2} : \frac{11}{3} = \frac{11}{2} \cdot \frac{3}{11} = \frac{3}{2} = 1 \frac{1}{2}$$

Ответ: 1) $$11 \frac{1}{4}$$; 2) $$14$$; 3) $$16 \frac{1}{2}$$; 4) $$1 \frac{1}{16}$$; 5) $$\frac{7}{52}$$; 6) $$\frac{4}{19}$$; 7) $$7 \frac{1}{2}$$; 8) $$\frac{3}{8}$$; 9) $$\frac{16}{35}$$; 10) $$1 \frac{1}{2}$$.