П.78 Вычислите: а) 0,46 : 3/23; б) 5/8 - 0,73; в) 0,289 : 17/18; г) 17,17 : 1 5/12; д) 5,53 : 7/9; е) 343,4 : 14 3/7

Решение:

• а) 0,46 : 3/23
  • \[ 0.46 : rac{3}{23} = rac{46}{100} imes rac{23}{3} = rac{23}{50} imes rac{23}{3} = rac{529}{150} = 3rac{79}{150} \]
• б) 5/8 - 0,73
  • \[ rac{5}{8} - 0.73 = 0.625 - 0.73 = -0.105 \]
• в) 0,289 : 17/18
  • \[ 0.289 : rac{17}{18} = rac{289}{1000} imes rac{18}{17} = rac{17 imes 17}{1000} imes rac{18}{17} = rac{17 imes 18}{1000} = rac{306}{1000} = 0.306 \]
• г) 17,17 : 1 5/12
  • \[ 17.17 : 1rac{5}{12} = 17.17 : rac{17}{12} = rac{1717}{100} imes rac{12}{17} = rac{101 imes 17}{100} imes rac{12}{17} = rac{101 imes 12}{100} = rac{1212}{100} = 12.12 \]
• д) 5,53 : 7/9
  • \[ 5.53 : rac{7}{9} = rac{553}{100} imes rac{9}{7} = rac{553 imes 9}{700} = rac{4977}{700} = 7rac{77}{700} = 7rac{11}{100} = 7.11 \]
• е) 343,4 : 14 3/7
  • \[ 343.4 : 14rac{3}{7} = 343.4 : rac{101}{7} = rac{3434}{10} imes rac{7}{101} = rac{34 imes 101 + 34}{10} imes rac{7}{101} = rac{3434}{10} imes rac{7}{101} \]
  • \[ rac{3434}{101} = 34 \]
  • \[ 34 imes rac{7}{10} = rac{238}{10} = 23.8 \]

Ответ: а) 3 150 79 ; б) -0,105; в) 0,306; г) 12,12; д) 7,11; е) 23,8.