Вопрос:

Вычислите: А) \(\left(\frac45-\frac13\right)\cdot15\); Б) \(\left(\frac27+\frac5{21}\right)\cdot21\); В) \(\left(\frac7{12}-\frac59\right)\cdot12\); Г) \(\left(\frac38+\frac5{12}\right)\cdot24\); Д) \(\left(\frac8{11}-\frac3{22}\right)\cdot44\); Е) \(6\frac15\cdot4\); Ё) \(10\cdot5\frac25\); Ж) \(12\frac9{13}\cdot13\); З) \(\left(4\frac23+5\frac12\right)\cdot6\); И) \(\left(8-1\frac19\right)\cdot9\); Й) \(\left(3\frac35-2\frac1{15}\right)\cdot5\); К) \(\left(1\frac{14}{17}-1\frac1{34}\right)\cdot34\); Л) \(\left(2\frac34+4\frac18\right)\cdot1\frac5{11}\); М) \(1\frac25\cdot\left(1\frac1{14}-\frac57\right)\); Н) \(4\frac38\cdot\left(1\frac37-\frac{34}{35}\right)\).

Ответ:

  1. А) \(\left(\frac45-\frac13\right)\cdot15=\frac7{15}\cdot15=7\).
  2. Б) \(\left(\frac27+\frac5{21}\right)\cdot21=\frac{11}{21}\cdot21=11\).
  3. В) \(\left(\frac7{12}-\frac59\right)\cdot12=\frac1{36}\cdot12=\frac13\).
  4. Г) \(\left(\frac38+\frac5{12}\right)\cdot24=\frac{19}{24}\cdot24=19\).
  5. Д) \(\left(\frac8{11}-\frac3{22}\right)\cdot44=\frac{13}{22}\cdot44=26\).
  6. Е) \(6\frac15\cdot4=\frac{31}{5}\cdot4=\frac{124}{5}=24\frac45\).
  7. Ё) \(10\cdot5\frac25=10\cdot\frac{27}{5}=54\).
  8. Ж) \(12\frac9{13}\cdot13=\frac{165}{13}\cdot13=165\).
  9. З) \(\left(4\frac23+5\frac12\right)\cdot6=\left(\frac{14}{3}+\frac{11}{2}\right)\cdot6=\frac{61}{6}\cdot6=61\).
  10. И) \(\left(8-1\frac19\right)\cdot9=\frac{62}{9}\cdot9=62\).
  11. Й) \(\left(3\frac35-2\frac1{15}\right)\cdot5=\left(\frac{54}{15}-\frac{31}{15}\right)\cdot5=\frac{23}{15}\cdot5=\frac{23}{3}=7\frac23\).
  12. К) \(\left(1\frac{14}{17}-1\frac1{34}\right)\cdot34=\left(\frac{48}{34}-\frac{35}{34}\right)\cdot34=13\).
  13. Л) \(\left(2\frac34+4\frac18\right)\cdot1\frac5{11}=\left(\frac{11}{4}+\frac{33}{8}\right)\cdot\frac{16}{11}=\frac{55}{8}\cdot\frac{16}{11}=10\).
  14. М) \(1\frac25\cdot\left(1\frac1{14}-\frac57\right)=\frac75\cdot\left(\frac{15}{14}-\frac{10}{14}\right)=\frac75\cdot\frac5{14}=\frac12\).
  15. Н) \(4\frac38\cdot\left(1\frac37-\frac{34}{35}\right)=\frac{35}{8}\cdot\left(\frac{50}{35}-\frac{34}{35}\right)=\frac{35}{8}\cdot\frac{16}{35}=2\).

Ответ: А) 7; Б) 11; В) \(\frac13\); Г) 19; Д) 26; Е) \(24\frac45\); Ё) 54; Ж) 165; З) 61; И) 62; Й) \(7\frac23\); К) 13; Л) 10; М) \(\frac12\); Н) 2.