Ответы
Ответ дал:
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((4 8/9-1 5/6):(2/3+5/9):(1 1/6+2,5):(3,8-2 1/3)*(0,75+5/6-3/8):(5 1/8-1 1/2))+2/3=((44/9-11/6):(2/3+5/9):(7/6+2,5):(3,8-7/3)*(0,75+5/6-3,8):(41/8-3/2))+2/3
Посчитаем находящееся в скобках:
1)![frac{44}{9} - frac{11}{6} =frac{(2*44-3*11)}{18}= frac{55}{18} frac{44}{9} - frac{11}{6} =frac{(2*44-3*11)}{18}= frac{55}{18}](https://tex.z-dn.net/?f=+frac%7B44%7D%7B9%7D+-+frac%7B11%7D%7B6%7D+%3Dfrac%7B%282%2A44-3%2A11%29%7D%7B18%7D%3D+frac%7B55%7D%7B18%7D+)
2)![frac{2}{3} + frac{5}{9} =frac{(3*2+1*5)}{9}= frac{11}{9} frac{2}{3} + frac{5}{9} =frac{(3*2+1*5)}{9}= frac{11}{9}](https://tex.z-dn.net/?f=+frac%7B2%7D%7B3%7D+%2B+frac%7B5%7D%7B9%7D+%3Dfrac%7B%283%2A2%2B1%2A5%29%7D%7B9%7D%3D+frac%7B11%7D%7B9%7D+)
3)![frac{7}{6} +2,5= frac{7}{6}+ frac{5}{2} =frac{(1*7+3*5}{6}= frac{22}{6} = frac{11}{3} frac{7}{6} +2,5= frac{7}{6}+ frac{5}{2} =frac{(1*7+3*5}{6}= frac{22}{6} = frac{11}{3}](https://tex.z-dn.net/?f=+frac%7B7%7D%7B6%7D+%2B2%2C5%3D+frac%7B7%7D%7B6%7D%2B+frac%7B5%7D%7B2%7D++%3Dfrac%7B%281%2A7%2B3%2A5%7D%7B6%7D%3D+frac%7B22%7D%7B6%7D+%3D+frac%7B11%7D%7B3%7D+)
4)![3,8-frac{7}{3} = frac{38}{10} - frac{7}{3} = frac{19}{5} - frac{7}{3} = frac{(3*19-5*7)}{15} = frac{22}{15} 3,8-frac{7}{3} = frac{38}{10} - frac{7}{3} = frac{19}{5} - frac{7}{3} = frac{(3*19-5*7)}{15} = frac{22}{15}](https://tex.z-dn.net/?f=+3%2C8-frac%7B7%7D%7B3%7D+%3D+frac%7B38%7D%7B10%7D+-+frac%7B7%7D%7B3%7D+%3D+frac%7B19%7D%7B5%7D+-+frac%7B7%7D%7B3%7D+%3D+frac%7B%283%2A19-5%2A7%29%7D%7B15%7D+%3D+frac%7B22%7D%7B15%7D+)
5)![0,75+frac{5}{6} - frac{3}{8} = frac{75}{100} + frac{5}{6}- frac{3}{8} = frac{3}{4} + frac{5}{6} - frac{3}{8} = frac{(6*3+4*5-3*3)}{24} = frac{29}{24} 0,75+frac{5}{6} - frac{3}{8} = frac{75}{100} + frac{5}{6}- frac{3}{8} = frac{3}{4} + frac{5}{6} - frac{3}{8} = frac{(6*3+4*5-3*3)}{24} = frac{29}{24}](https://tex.z-dn.net/?f=+0%2C75%2Bfrac%7B5%7D%7B6%7D+-+frac%7B3%7D%7B8%7D+%3D+frac%7B75%7D%7B100%7D+%2B+frac%7B5%7D%7B6%7D-+frac%7B3%7D%7B8%7D++%3D+frac%7B3%7D%7B4%7D+%2B+frac%7B5%7D%7B6%7D+-+frac%7B3%7D%7B8%7D+%3D+frac%7B%286%2A3%2B4%2A5-3%2A3%29%7D%7B24%7D+%3D+frac%7B29%7D%7B24%7D+)
6)![frac{41}{8} - frac{3}{2} = frac{(1*41-4*3)}{8} = frac{29}{8} frac{41}{8} - frac{3}{2} = frac{(1*41-4*3)}{8} = frac{29}{8}](https://tex.z-dn.net/?f=+frac%7B41%7D%7B8%7D+-+frac%7B3%7D%7B2%7D+%3D+frac%7B%281%2A41-4%2A3%29%7D%7B8%7D+%3D+frac%7B29%7D%7B8%7D+)
Теперь впишем в скобки полученное:
![(frac{55}{18} : frac{11}{9} : frac{11}{3} : frac{22}{15} * frac{29}{24} : frac{29}{8}) + frac{2}{3} (frac{55}{18} : frac{11}{9} : frac{11}{3} : frac{22}{15} * frac{29}{24} : frac{29}{8}) + frac{2}{3}](https://tex.z-dn.net/?f=%28frac%7B55%7D%7B18%7D+%3A+frac%7B11%7D%7B9%7D+%3A+frac%7B11%7D%7B3%7D+%3A+frac%7B22%7D%7B15%7D+%2A+frac%7B29%7D%7B24%7D+%3A+frac%7B29%7D%7B8%7D%29+%2B+frac%7B2%7D%7B3%7D+)
Теперь, всё делим по порядку:
![frac{55}{18} :frac{11}{9}= frac{55}{18}* frac{9}{18} = frac{55*9}{18*11} = frac{5*1}{2*1} = frac{5}{2} frac{55}{18} :frac{11}{9}= frac{55}{18}* frac{9}{18} = frac{55*9}{18*11} = frac{5*1}{2*1} = frac{5}{2}](https://tex.z-dn.net/?f=+frac%7B55%7D%7B18%7D+%3Afrac%7B11%7D%7B9%7D%3D+frac%7B55%7D%7B18%7D%2A+frac%7B9%7D%7B18%7D+%3D+frac%7B55%2A9%7D%7B18%2A11%7D+%3D+frac%7B5%2A1%7D%7B2%2A1%7D+%3D+frac%7B5%7D%7B2%7D+)
Впишем:
![(frac{5}{2} : frac{11}{3} : frac{22}{15} * frac{29}{24} : frac{29}{8} )+ frac{2}{3} (frac{5}{2} : frac{11}{3} : frac{22}{15} * frac{29}{24} : frac{29}{8} )+ frac{2}{3}](https://tex.z-dn.net/?f=+%28frac%7B5%7D%7B2%7D+%3A+frac%7B11%7D%7B3%7D+%3A+frac%7B22%7D%7B15%7D+%2A+frac%7B29%7D%7B24%7D+%3A+frac%7B29%7D%7B8%7D+%29%2B+frac%7B2%7D%7B3%7D+)
Делим:
![frac{5}{2} : frac{11}{3} = frac{5}{2} * frac{11}{3} = frac{5*11}{2*3} = frac{55}{6} frac{5}{2} : frac{11}{3} = frac{5}{2} * frac{11}{3} = frac{5*11}{2*3} = frac{55}{6}](https://tex.z-dn.net/?f=+frac%7B5%7D%7B2%7D+%3A+frac%7B11%7D%7B3%7D+%3D+frac%7B5%7D%7B2%7D+%2A+frac%7B11%7D%7B3%7D+%3D+frac%7B5%2A11%7D%7B2%2A3%7D+%3D+frac%7B55%7D%7B6%7D+)
Впишем:
![(frac{55}{6} : frac{22}{15} * frac{29}{24} : frac{29}{8} )+ frac{2}{3} (frac{55}{6} : frac{22}{15} * frac{29}{24} : frac{29}{8} )+ frac{2}{3}](https://tex.z-dn.net/?f=+%28frac%7B55%7D%7B6%7D+%3A+frac%7B22%7D%7B15%7D+%2A+frac%7B29%7D%7B24%7D+%3A+frac%7B29%7D%7B8%7D+%29%2B+frac%7B2%7D%7B3%7D+)
Делим:
![frac{55}{6} : frac{22}{15} = frac{55}{6} * frac{15}{22} = frac{55*15}{6*22} = frac{55*5}{2*22} = frac{275}{44} frac{55}{6} : frac{22}{15} = frac{55}{6} * frac{15}{22} = frac{55*15}{6*22} = frac{55*5}{2*22} = frac{275}{44}](https://tex.z-dn.net/?f=+frac%7B55%7D%7B6%7D+%3A+frac%7B22%7D%7B15%7D+%3D+frac%7B55%7D%7B6%7D+%2A+frac%7B15%7D%7B22%7D+%3D++frac%7B55%2A15%7D%7B6%2A22%7D+%3D+frac%7B55%2A5%7D%7B2%2A22%7D+%3D+frac%7B275%7D%7B44%7D+)
Впишем:
![( frac{275}{44} * frac{29}{24} : frac{29}{8} )+ frac{2}{3} ( frac{275}{44} * frac{29}{24} : frac{29}{8} )+ frac{2}{3}](https://tex.z-dn.net/?f=%28+frac%7B275%7D%7B44%7D+%2A+frac%7B29%7D%7B24%7D+%3A+frac%7B29%7D%7B8%7D+%29%2B+frac%7B2%7D%7B3%7D+)
![frac{275}{44} * frac{29}{24} = frac{275*29}{44*24} frac{275}{44} * frac{29}{24} = frac{275*29}{44*24}](https://tex.z-dn.net/?f=+frac%7B275%7D%7B44%7D+%2A+frac%7B29%7D%7B24%7D+%3D+frac%7B275%2A29%7D%7B44%2A24%7D+)
Снова вписываем:
![(frac{275*29}{44*24} ): frac{29}{8} + frac{2}{3} (frac{275*29}{44*24} ): frac{29}{8} + frac{2}{3}](https://tex.z-dn.net/?f=+%28frac%7B275%2A29%7D%7B44%2A24%7D+%29%3A+frac%7B29%7D%7B8%7D+%2B+frac%7B2%7D%7B3%7D+)
Делим:
![( frac{275*29}{44*24} ): frac{29}{8} = (frac{275*29}{44*24} )* frac{8}{29} = frac{275*29*8}{44*24*29} = frac{275}{3*44} ( frac{275*29}{44*24} ): frac{29}{8} = (frac{275*29}{44*24} )* frac{8}{29} = frac{275*29*8}{44*24*29} = frac{275}{3*44}](https://tex.z-dn.net/?f=%28+frac%7B275%2A29%7D%7B44%2A24%7D+%29%3A+frac%7B29%7D%7B8%7D+%3D+%28frac%7B275%2A29%7D%7B44%2A24%7D+%29%2A+frac%7B8%7D%7B29%7D+%3D+frac%7B275%2A29%2A8%7D%7B44%2A24%2A29%7D+%3D+frac%7B275%7D%7B3%2A44%7D+)
Впишем:
![frac{275}{3*44}+ frac{2}{3} = frac{275+44*2}{3*44} = frac{363}{132} = frac{11*33}{33*4} = frac{11}{4} =2,75 frac{275}{3*44}+ frac{2}{3} = frac{275+44*2}{3*44} = frac{363}{132} = frac{11*33}{33*4} = frac{11}{4} =2,75](https://tex.z-dn.net/?f=+frac%7B275%7D%7B3%2A44%7D%2B+frac%7B2%7D%7B3%7D+%3D+frac%7B275%2B44%2A2%7D%7B3%2A44%7D+%3D+frac%7B363%7D%7B132%7D+%3D+frac%7B11%2A33%7D%7B33%2A4%7D+%3D+frac%7B11%7D%7B4%7D+%3D2%2C75)
Ответ: 2,75 или
.
Посчитаем находящееся в скобках:
1)
2)
3)
4)
5)
6)
Теперь впишем в скобки полученное:
Теперь, всё делим по порядку:
Впишем:
Делим:
Впишем:
Делим:
Впишем:
Снова вписываем:
Делим:
Впишем:
Ответ: 2,75 или
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