Вопрос:

5. Вычислите: А) \(\frac58\cdot\frac13+\frac38:3\); Б) \(\frac{11}{17}\cdot9-\frac2{11}\cdot\frac19\); В) \(\frac67\cdot\frac14-\frac27:4\); Г) \(\frac{17}{19}:5+\frac2{19}\cdot\frac15\); Д) \(79\cdot11-69:\frac1{11}\); Е) \(87:\frac1{15}+13\cdot15\); Ё) \(\frac78\cdot10+\frac18:0{,}1\); З) \(\frac5{12}:0{,}2+\frac7{12}\cdot5\); И) \(19\cdot\frac5{17}+81:3\frac25\); Й) \(57:\frac9{11}+33\cdot1\frac29\); К) \(\frac78\cdot9+\frac58:\frac19-\frac12\cdot9\); Л) \(\frac79:9+\frac59\cdot\frac11-\frac19\cdot\frac19\); М) \(\frac2{43}\cdot\frac16+\frac2{43}\cdot1\frac23+\frac{41}{43}:\frac{24}{37}\); Н) \(\frac5{63}\cdot2\frac3{14}+\frac5{63}\cdot\frac5{21}+\frac{58}{63}:\frac{42}{97}\); О) \(\frac{87\cdot35-81\cdot35}{37\cdot28-28^2}\).

Ответ:

  1. А) \(\frac58\cdot\frac13+\frac38:3=\frac5{24}+\frac18=\frac13\).
  2. Б) \(\frac{11}{17}\cdot9-\frac2{11}\cdot\frac19=\frac{99}{17}-\frac2{99}=\frac{9673}{1683}\).
  3. В) \(\frac67\cdot\frac14-\frac27:4=\frac3{14}-\frac1{14}=\frac17\).
  4. Г) \(\frac{17}{19}:5+\frac2{19}\cdot\frac15=\frac{17}{95}+\frac2{95}=\frac15\).
  5. Д) \(79\cdot11-69:\frac1{11}=869-759=110\).
  6. Е) \(87:\frac1{15}+13\cdot15=1305+195=1500\).
  7. Ё) \(\frac78\cdot10+\frac18:0.1=\frac{35}{4}+\frac54=\frac{45}{4}=11\frac14\).
  8. З) \(\frac5{12}:0.2+\frac7{12}\cdot5=\frac{25}{12}+\frac{35}{12}=5\).
  9. И) \(19\cdot\frac5{17}+81:3\frac25=\frac{95}{17}+\frac{405}{17}=\frac{500}{17}=29\frac7{17}\).
  10. Й) \(57:\frac9{11}+33\cdot1\frac29=\frac{209}{3}+\frac{110}{3}=\frac{319}{3}=106\frac13\).
  11. К) \(\frac78\cdot9+\frac58:\frac19-\frac12\cdot9=\frac{63}{8}+\frac{45}{8}-\frac{36}{8}=9\).
  12. Л) \(\frac79:9+\frac59\cdot\frac11-\frac19\cdot\frac19=\frac7{81}+\frac5{99}-\frac1{81}=\frac2{27}+\frac5{99}=\frac{71}{891}\).
  13. М) \(\frac2{43}\cdot\frac16+\frac2{43}\cdot1\frac23+\frac{41}{43}:\frac{24}{37}=\frac1{129}+\frac2{129}+\frac{1517}{1032}=\frac{49}{32}\).
  14. Н) \(\frac5{63}\cdot2\frac3{14}+\frac5{63}\cdot\frac5{21}+\frac{58}{63}:\frac{42}{97}=\frac{55}{126}+\frac{25}{1323}+\frac{2813}{1323}=\frac{16}{7}\).
  15. О) \(\frac{87\cdot35-81\cdot35}{37\cdot28-28^2}=\frac{(87-81)\cdot35}{28(37-28)}=\frac{210}{252}=\frac56\).

Ответ: А) \(\frac13\); Б) \(\frac{9673}{1683}\); В) \(\frac17\); Г) \(\frac15\); Д) 110; Е) 1500; Ё) \(11\frac14\); З) 5; И) \(29\frac7{17}\); Й) \(106\frac13\); К) 9; Л) \(\frac{71}{891}\); М) \(\frac{49}{32}\); Н) \(\frac{16}{7}\); О) \(\frac56\).