Упражнение 639

Решение:

• $${\largeа)}\ \frac{4}{9}:\frac{3}{8}=\frac{4}{9}\cdot\frac{8}{3}=\frac{4\cdot8}{9\cdot3}=\frac{32}{27}=1\frac{5}{27}$$

• $${\largeб)}\ \frac{3}{7}:\frac{9}{14}=\frac{3}{7}\cdot\frac{14}{9}=\frac{\cancel3^{\backslash1}\cdot\cancel{14}^{\backslash2}}{\cancel7^{\backslash1}\cdot\cancel9^{\backslash3}}=\frac{2}{3}$$

• $${\largeв)}\ \frac{86}{113}:\frac{43}{51}=\frac{86}{113}\cdot\frac{51}{43}=\frac{\cancel{86}^{\backslash2}\cdot51}{113\cdot\cancel{43}^{\backslash1}}=\frac{102}{113}$$

• $${\largeг)}\ \frac{27}{64}:9=\frac{27}{64}:\frac{9}{1}=\frac{27}{64}\cdot\frac{1}{9}=\frac{\cancel{27}^{\backslash3}\cdot1}{64\cdot\cancel9^{\backslash1}}=\frac{3}{64}$$

• $${\largeд)}\ 8:\frac{2}{3}=\frac{8}{1}:\frac{2}{3}=\frac{8}{1}\cdot\frac{3}{2}=\frac{\cancel8^{\backslash4}\cdot3}{1\cdot\cancel2^{\backslash1}}=12$$

• $${\largeе)}\ 7:3=\frac{7}{1}:\frac{3}{1}=\frac{7}{1}\cdot\frac{1}{3}=\frac{7\cdot1}{1\cdot3}=\frac{7}{3}=2\frac{1}{3}$$

• $${\largeж)}\ 2\frac{1}{7}:1\frac{11}{14}=\frac{15}{7}:\frac{25}{14}=\frac{15}{7}\cdot\frac{14}{25}=\frac{\cancel{15}^{\backslash3}\cdot\cancel{14}^{\backslash2}}{\cancel7^{\backslash1}\cdot\cancel{25}^{\backslash5}}=\frac{6}{5}=1\frac{1}{5}$$

• $${\largeз)}\ 3\frac{3}{5}:1\frac{11}{25}=\frac{18}{5}:\frac{36}{25}=\frac{18}{5}\cdot\frac{25}{36}=\frac{\cancel{18}^{\backslash1}\cdot\cancel{25}^{\backslash5}}{\cancel5^{\backslash1}\cdot\cancel{36}^{\backslash2}}=\frac{5}{2}=2\frac{1}{2}$$