Упражнение 640

Решение:

• $${\largeа)}\ 7\frac{1}{8}:4\frac{3}{4}\cdot8=\frac{57}{8}:\frac{19}{4}\cdot\frac{8}{1}=\frac{57}{8}\cdot\frac{4}{19}\cdot\frac{8}{1}=\frac{\cancel{57}^{\backslash3}\cdot4\cdot\cancel8^{\backslash1}}{\cancel8^{\backslash1}\cdot\cancel{19}^{\backslash1}\cdot1}=12$$

• $${\largeб)}\ 11\frac{1}{3}:\frac{4}{21}:4\frac{1}{4}=\frac{34}{3}:\frac{4}{21}:\frac{17}{4}=\frac{34}{3}\cdot\frac{21}{4}\cdot\frac{4}{17}=\frac{\cancel{34}^{\backslash2}\cdot\cancel{21}^{\backslash7}\cdot\cancel4^{\backslash1}}{\cancel3^{\backslash1}\cdot\cancel4^{\backslash1}\cdot\cancel{17}^{\backslash1}}=14$$

• $${\largeв)}\ 1\frac{7}{9}\cdot2\frac{2}{5}:1\frac{3}{5}=\frac{16}{9}\cdot\frac{12}{5}:\frac{8}{5}=\frac{16}{9}\cdot\frac{12}{5}\cdot\frac{5}{8}=\frac{\cancel{16}^{\backslash2}\cdot\cancel{12}^{\backslash4}\cdot\cancel5^{\backslash1}}{\cancel9^{\backslash3}\cdot\cancel5^{\backslash1}\cdot\cancel8^{\backslash1}}=\frac{8}{3}=2\frac{2}{3}$$

• $${\largeг)}\ \frac{7}{8}\cdot\frac{8}{9}:1\frac{1}{9}=\frac{7}{8}\cdot\frac{8}{9}:\frac{10}{9}=\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}=\frac{7\cdot\cancel8^{\backslash1}\cdot\cancel9^{\backslash1}}{\cancel8^{\backslash1}\cdot\cancel9^{\backslash1}\cdot10}=\frac{7}{10}$$