2.419 Вычислите значение частного: a) $$5\frac{1}{4}:\frac{4}{5}$$; б) $$\frac{2}{13}:2\frac{2}{13}$$; в) $$2\frac{4}{7}:1\frac{3}{10}$$; г) $$10\frac{3}{5}:3\frac{3}{5}$$; д) $$5\frac{1}{4}:1\frac{3}{4}$$; ж) $$0:10\frac{7}{15}$$; е) $$5\frac{3}{7}:3$$; з) $$5\frac{1}{16}:1$$

a) $$5\frac{1}{4}:\frac{4}{5} = \frac{21}{4}:\frac{4}{5} = \frac{21}{4} \cdot \frac{5}{4} = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} = 6\frac{9}{16}$$ <p><strong>Ответ:</strong> $$6\frac{9}{16}$$</p> б) $$\frac{2}{13}:2\frac{2}{13} = \frac{2}{13}:\frac{28}{13} = \frac{2}{13} \cdot \frac{13}{28} = \frac{2 \cdot 13}{13 \cdot 28} = \frac{1 \cdot 1}{1 \cdot 14} = \frac{1}{14}$$ <p><strong>Ответ:</strong> $$\frac{1}{14}$$</p> в) $$2\frac{4}{7}:1\frac{3}{10} = \frac{18}{7}:\frac{13}{10} = \frac{18}{7} \cdot \frac{10}{13} = \frac{18 \cdot 10}{7 \cdot 13} = \frac{180}{91} = 1\frac{89}{91}$$ <p><strong>Ответ:</strong> $$1\frac{89}{91}$$</p> г) $$10\frac{3}{5}:3\frac{3}{5} = \frac{53}{5}:\frac{18}{5} = \frac{53}{5} \cdot \frac{5}{18} = \frac{53 \cdot 5}{5 \cdot 18} = \frac{53}{18} = 2\frac{17}{18}$$ <p><strong>Ответ:</strong> $$2\frac{17}{18}$$</p> д) $$5\frac{1}{4}:1\frac{3}{4} = \frac{21}{4}:\frac{7}{4} = \frac{21}{4} \cdot \frac{4}{7} = \frac{21 \cdot 4}{4 \cdot 7} = \frac{3 \cdot 1}{1 \cdot 1} = 3$$ <p><strong>Ответ:</strong> $$3$$</p> ж) $$0:10\frac{7}{15} = 0$$ <p><strong>Ответ:</strong> $$0$$</p> е) $$5\frac{3}{7}:3 = \frac{38}{7}:3 = \frac{38}{7} \cdot \frac{1}{3} = \frac{38}{21} = 1\frac{17}{21}$$ <p><strong>Ответ:</strong> $$1\frac{17}{21}$$</p> з) $$5\frac{1}{16}:1 = \frac{81}{16}:1 = \frac{81}{16} \cdot 1 = \frac{81}{16} = 5\frac{1}{16}$$ <p><strong>Ответ:</strong> $$5\frac{1}{16}$$</p>