Вопрос:

4. Вычислите: А) (4/5 − 1/3)·15; Б) (2/7 + 5/21)·21; В) (7/12 − 5/9)·12; Г) (3/8 + 5/12)·24; Д) (8/11 − 3/22)·44; Е) 6 1/5·4; Ё) 10·5 2/5; Ж) 12 9/13·13; З) (4 2/3 + 5 1/2)·6; И) (8 − 1 1/9)·9; Й) (3 3/5 − 2 1/15)·5; К) (1 14/17 − 1 1/34)·34; Л) (2 3/4 + 4 1/8)·1 5/11; М) 1 2/5·(1 1/14 − 5/7); Н) 4 3/8·(1 3/7 − 34/35).

Ответ:

  1. \( (\frac45-\frac13)\cdot15=\frac7{15}\cdot15=7 \).
  2. \( (\frac27+\frac5{21})\cdot21=\frac{11}{21}\cdot21=11 \).
  3. \( (\frac7{12}-\frac59)\cdot12=\frac1{36}\cdot12=\frac13 \).
  4. \( (\frac38+\frac5{12})\cdot24=\frac{19}{24}\cdot24=19 \).
  5. \( (\frac8{11}-\frac3{22})\cdot44=\frac{13}{22}\cdot44=26 \).
  6. \(6\frac15\cdot4=\frac{31}{5}\cdot4=\frac{124}{5}=24\frac45\).
  7. \(10\cdot5\frac25=10\cdot\frac{27}{5}=54\).
  8. \(12\frac9{13}\cdot13=\frac{165}{13}\cdot13=165\).
  9. \( (4\frac23+5\frac12)\cdot6=(\frac{14}{3}+\frac{11}{2})\cdot6=\frac{61}{6}\cdot6=61 \).
  10. \( (8-1\frac19)\cdot9=(8-\frac{10}{9})\cdot9=\frac{62}{9}\cdot9=62 \).
  11. \( (3\frac35-2\frac1{15})\cdot5=(\frac{18}{5}-\frac{31}{15})\cdot5=\frac{23}{15}\cdot5=\frac{23}{3}=7\frac23 \).
  12. \( (1\frac{14}{17}-1\frac1{34})\cdot34=(\frac{48}{34}-\frac{35}{34})\cdot34=13 \).
  13. \( (2\frac34+4\frac18)\cdot1\frac5{11}=(\frac{11}{4}+\frac{33}{8})\cdot\frac{16}{11}=\frac{55}{8}\cdot\frac{16}{11}=10 \).
  14. \(1\frac25\cdot(1\frac1{14}-\frac57)=\frac75\cdot(\frac{15}{14}-\frac{10}{14})=\frac75\cdot\frac5{14}=\frac12\).
  15. \(4\frac38\cdot(1\frac37-\frac{34}{35})=\frac{35}{8}\cdot(\frac{38}{35}-\frac{34}{35})=\frac{35}{8}\cdot\frac4{35}=\frac12\).

Ответ: А) 7; Б) 11; В) 1/3; Г) 19; Д) 26; Е) 24 4/5; Ё) 54; Ж) 165; З) 61; И) 62; Й) 7 2/3; К) 13; Л) 10; М) 1/2; Н) 1/2.

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