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Теория: Десятичная дробь как частное при делении натуральных чисел

Задание

Найдите частное:

\(\displaystyle 9:8=\),

Решение

Поделим \(\displaystyle 9\) на \(\displaystyle 8\) в столбик:

 

\(\displaystyle 9\) \(\displaystyle 8\)
  \(\displaystyle ?\)

Первое действие.

Поделим \(\displaystyle 9\) на \(\displaystyle 8\) с остатком:

 

\(\displaystyle 9= \color{green}{1}·8+1=\color{blue}{8}+1\).

 

Пишем \(\displaystyle \color{blue}{8}\) под \(\displaystyle 9\) и \(\displaystyle \color{green}{1}\)в частном:

 

  \(\displaystyle 9\) \(\displaystyle 8\)  
\(\displaystyle -\)   \(\displaystyle \color{green}{1}\) \(\displaystyle ?\)
  \(\displaystyle \color{blue}{8}\)    

 

Вычитаем \(\displaystyle 9-\color{blue}{8}=\bf1\):

 

  \(\displaystyle 9\) \(\displaystyle 8\)  
\(\displaystyle -\)   \(\displaystyle \color{green}{1}\) \(\displaystyle ?\)
  \(\displaystyle \color{blue}{8}\)    
  \(\displaystyle \bf1\)    

 

Второе действие.

Так как \(\displaystyle 1<8\) и больше разрядов у числа нет, то ставим запятую в частном, добавляем нуль к разности справа (то есть к \(\displaystyle 1\) справа):

 

  \(\displaystyle 9\)   \(\displaystyle 8\)    
\(\displaystyle -\)     \(\displaystyle 1\) \(\displaystyle \color{red}{,}\) \(\displaystyle ?\)
  \(\displaystyle 8\)        
  \(\displaystyle 1\) \(\displaystyle \color{blue}{0}\)      

Делим \(\displaystyle 10\) на \(\displaystyle 8\):

\(\displaystyle 10= \color{green}{1}·8+2=\color{blue}{8}+2\).

 

Пишем \(\displaystyle \color{green}{1}\) в частном и вычитаем \(\displaystyle 10-\color{blue}{8}=\bf2\):

 

  \(\displaystyle 9\)   \(\displaystyle 8\)      
\(\displaystyle -\)     \(\displaystyle 1\) \(\displaystyle ,\) \(\displaystyle \color{green}{1}\) \(\displaystyle ?\)
  \(\displaystyle 8\)          
  \(\displaystyle 1\) \(\displaystyle 0\)        
\(\displaystyle -\)            
    \(\displaystyle \color{blue}{8}\)        
    \(\displaystyle \bf2\)        

Третье действие.

Добавляем нуль к разности справа:

  \(\displaystyle 9\)     \(\displaystyle 8\)      
\(\displaystyle -\)       \(\displaystyle 1\) \(\displaystyle ,\) \(\displaystyle 1\) \(\displaystyle ?\)
  \(\displaystyle 8\)            
  \(\displaystyle 1\) \(\displaystyle 0\)          
\(\displaystyle -\)              
    \(\displaystyle 8\)          
    \(\displaystyle 2\) \(\displaystyle \color{red}{0}\)        

 

Делим \(\displaystyle 20\) на \(\displaystyle 8\):

\(\displaystyle 20= \color{green}{2}·8+4=\color{blue}{16}+4\).

 

Пишем \(\displaystyle \color{green}{2}\)в частном и вычитаем \(\displaystyle 20-\color{blue}{16}=\bf4\):

 

  \(\displaystyle 9\)     \(\displaystyle 8\)        
\(\displaystyle -\)       \(\displaystyle 1\) \(\displaystyle ,\) \(\displaystyle 1\) \(\displaystyle \color{green}{2}\) \(\displaystyle ?\)
  \(\displaystyle 8\)              
  \(\displaystyle 1\) \(\displaystyle 0\)            
\(\displaystyle -\)                
    \(\displaystyle 8\)            
    \(\displaystyle 2\) \(\displaystyle 0\)          
  \(\displaystyle -\)              
    \(\displaystyle \color{blue}{1}\) \(\displaystyle \color{blue}{6}\)          
      \(\displaystyle \bf4\)          

 

Четвертое действие.

Добавляем нуль к разности справа:

  \(\displaystyle 9\)       \(\displaystyle 8\)        
\(\displaystyle -\)         \(\displaystyle 1\) \(\displaystyle ,\) \(\displaystyle 1\) \(\displaystyle 2\) \(\displaystyle ?\)
  \(\displaystyle 8\)                
  \(\displaystyle 1\) \(\displaystyle 0\)              
\(\displaystyle -\)                  
    \(\displaystyle 8\)              
    \(\displaystyle 2\) \(\displaystyle 0\)            
  \(\displaystyle -\)                
    \(\displaystyle 1\) \(\displaystyle 6\)            
      \(\displaystyle 4\) \(\displaystyle \color{red}{0}\)          

 

Делим \(\displaystyle 40\) на \(\displaystyle 8\):

 

\(\displaystyle 40= \color{green}{5}·8=\color{blue}{40}\).

 

Пишем \(\displaystyle \color{green}{5}\) в частном и вычитаем \(\displaystyle 40-\color{blue}{40}=\bf0\):

 

  \(\displaystyle 9\)       \(\displaystyle 8\)        
\(\displaystyle -\)         \(\displaystyle 1\) \(\displaystyle ,\) \(\displaystyle 1\) \(\displaystyle 2\) \(\displaystyle \color{green}{5}\)
  \(\displaystyle 8\)                
  \(\displaystyle 1\) \(\displaystyle 0\)              
\(\displaystyle -\)                  
    \(\displaystyle 8\)              
    \(\displaystyle 2\) \(\displaystyle 0\)            
  \(\displaystyle -\)                
    \(\displaystyle 1\) \(\displaystyle 6\)            
      \(\displaystyle 4\) \(\displaystyle 0\)          
    \(\displaystyle -\)              
      \(\displaystyle \color{blue}{4}\) \(\displaystyle \color{blue}{0}\)          
        \(\displaystyle \bf0\)          

 

Таким образом, \(\displaystyle 9:8=1,125\).

Ответ: \(\displaystyle 1,125\).