Skip to main content

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:

 

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

 

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

 

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

 

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):

 

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

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 \(\displaystyle 10-\color{blue}{8}=\bf2\):

 

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

Третье действие.

Добавляем нуль к разности справа:

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

 

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 \(\displaystyle 20-\color{blue}{16}=\bf4\):

 

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

 

Четвертое действие.

Добавляем нуль к разности справа:

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

 

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

 

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

 

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

 

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

 

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

Ответ: \(\displaystyle 1,125\).