Упражнение 852

Решение:

• $${\largeа)}\ \frac{10\frac{10}{11}:12}{2\frac{21}{22}}\cdot6\frac{1}{2}=\frac{\frac{120}{11}:12}{\frac{65}{22}}\cdot\frac{13}{2}=\frac{120}{11}:\frac{12}{1}\cdot\frac{13}{2}:\frac{65}{22}=\frac{\cancel{120}^{\backslash10}}{\cancel{11}^{\backslash1}}\cdot\frac{1\phantom{^{\backslash1}}}{\cancel{12}^{\backslash1}}\cdot\frac{\cancel{13}^{\backslash1}}{2\phantom{^{\backslash1}}}\cdot\frac{\cancel{22}^{\backslash2}}{\cancel{65}^{\backslash5}}=\frac{20}{10}=2$$

• $${\largeб)}\ \frac{8:2\frac{2}{5}}{5\frac{1}{4}:7}:\frac{2\frac{1}{7}:\frac{5}{7}}{4:\frac{8}{9}}=\frac{8:\frac{12}{5}}{\frac{21}{4}:7}:\frac{\frac{15}{7}:\frac{5}{7}}{4:\frac{8}{9}}=\frac{\cancel8^{\backslash2}\cdot\frac{5\phantom{^{\backslash3}}}{\cancel{12}^{\backslash3}}}{\frac{\cancel{21}^{\backslash3}}{4\phantom{^{\backslash3}}}\cdot\frac{1\phantom{^{\backslash1}}}{\cancel7^{\backslash1}}}:\frac{\frac{\cancel{15}^{\backslash3}}{\cancel7^{\backslash1}}\cdot\frac{\cancel7^{\backslash1}}{\cancel5^{\backslash1}}}{\cancel4^{\backslash1}\cdot\frac{9\phantom{^{\backslash2}}}{\cancel8^{\backslash2}}}=\frac{\frac{10}{3}}{\frac{3}{4}}:\frac{3}{\frac{9}{2}}=\left(\frac{10}{3}:\frac{3}{4}\right):\left(3:\frac{9}{2}\right)=\left(\frac{10}{3}\cdot\frac{4}{3}\right):\left(\cancel3^{\backslash1}\cdot\frac{2\phantom{^{\backslash3}}}{\cancel9^{\backslash3}}\right)=\frac{40}{9}:\frac{2}{3}=\frac{\cancel{40}^{\backslash20}}{\cancel9^{\backslash3}}\cdot\frac{\cancel3^{\backslash1}}{\cancel2^{\backslash1}}=\frac{20}{3}=6\frac{2}{3}$$