Упражнение 701

Решение:

• $${\largeа)}\ \frac{3{,}2}{12{,}8}=\frac{\frac{32}{10}}{\frac{128}{10}}=\frac{32}{10}:\frac{128}{10}=\frac{32}{10}\cdot\frac{10}{128}=\frac{\cancel{32}^{\backslash1}\cdot\cancel{10}^{\backslash1}}{\cancel{10}^{\backslash1}\cdot\cancel{128}^{\backslash4}}=\frac{1}{4}=0{,}25$$

• $${\largeб)}\ \frac{1{,}2}{0{,}15}=\frac{\frac{12}{10}}{\frac{15}{100}}=\frac{12}{10}:\frac{15}{100}=\frac{12}{10}\cdot\frac{100}{15}=\frac{6}{5}\cdot\frac{20}{3}=\frac{\cancel6^{\backslash2}\cdot\cancel{20}^{\backslash4}}{\cancel5^{\backslash1}\cdot\cancel3^{\backslash1}}=8$$

• $${\largeв)}\ \frac{1\frac{1}{3}}{2\frac{1}{6}}=\frac{\frac{4}{3}}{\frac{13}{6}}=\frac{4}{3}:\frac{13}{6}=\frac{4}{3}\cdot\frac{6}{13}=\frac{4\cdot\cancel6^{\backslash2}}{\cancel3^{\backslash1}\cdot13}=\frac{8}{13}$$

• $${\largeг)}\ \frac{5\frac{1}{2}}{1\frac{3}{5}}=\frac{\frac{11}{2}}{\frac{8}{5}}=\frac{11}{2}:\frac{8}{5}=\frac{11}{2}\cdot\frac{5}{8}=\frac{11\cdot5}{2\cdot8}=\frac{55}{16}=3\frac{7}{16}$$

• $${\largeд)}\ \frac{\cancel{2{,}4}^{\backslash1}\cdot\cancel{12{,}6}^{\backslash2}\cdot\cancel{3{,}5}^{\backslash1}}{\cancel{6{,}3}^{\backslash1}\cdot\cancel{4{,}8}^{\backslash2}\cdot\cancel{31{,}5}^{\backslash9}}=\frac{2}{18}=\frac{1}{9}$$

• $${\largeе)}\ \frac{\cancel{1{,}7}^{\backslash1}\cdot\cancel{4{,}92}^{\backslash6}\cdot\cancel{7{,}2}^{\backslash3}}{\cancel{4{,}8}^{\backslash2}\cdot\cancel{0{,}82}^{\backslash1}\cdot\cancel{5{,}1}^{\backslash3}}=\frac{18}{6}=3$$

• $${\largeж)}\ \frac{8{,}4\cdot2\frac{1}{2}\cdot12{,}1}{1{,}25\cdot4\cdot1{,}1}=\frac{\cancel{8{,}4}^{\backslash2{,}1}\cdot\cancel{2{,}5}^{\backslash1}\cdot\cancel{12{,}1}^{\backslash11}}{\cancel{1{,}25}^{\backslash0{,}5}\cdot\cancel4^{\backslash1}\cdot\cancel{1{,}1}^{\backslash1}}=\frac{23{,}1}{0{,}5}=46{,}2$$

• $${\largeз)}\ \frac{2\frac{1}{3}\cdot1\frac{1}{7}\cdot1\frac{1}{5}}{3\frac{3}{5}\cdot4\frac{2}{3}\cdot6\frac{5}{7}}=\frac{\frac{7}{3}\cdot\frac{8}{7}\cdot\frac{6}{5}}{\frac{18}{5}\cdot\frac{14}{3}\cdot\frac{47}{7}}=\frac{\cancel7^{\backslash1}\cdot8\cdot\cancel6^{\backslash2}}{\cancel3^{\backslash1}\cdot\cancel7^{\backslash1}\cdot5}:\frac{\cancel{18}^{\backslash6}\cdot\cancel{14}^{\backslash2}\cdot47}{5\cdot\cancel3^{\backslash1}\cdot\cancel7^{\backslash1}}=\frac{16}{5}:\frac{564}{5}=\frac{16}{5}\cdot\frac{5}{564}=\frac{\cancel{16}^{\backslash4}\cdot\cancel5^{\backslash1}}{\cancel5^{\backslash1}\cdot\cancel{564}^{\backslash141}}=\frac{4}{141}$$