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Теория: Деление натуральных чисел на трехзначные числа

Задание

Выполните деление:

 

 \(\displaystyle 3\)\(\displaystyle 0\)\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle 7\)\(\displaystyle 5\)\(\displaystyle 6\)\(\displaystyle 9\)
\(\displaystyle –\)        
   
     
 \(\displaystyle –\)       
     
     \(\displaystyle 0\)   

 

Решение

1. Выбираем первые три цифры и делим число \(\displaystyle 301\) на \(\displaystyle 569\) с остатком, но \(\displaystyle 301<569\) поэтому мы сносим следующий разряд числа \(\displaystyle 301{\bf5}7\) (это цифра \(\displaystyle 5\)).

Делим число \(\displaystyle 3015\) на \(\displaystyle 569\) с остатком:

 

\(\displaystyle 3015=2845+170=569\cdot {\bf 5}+ 170{\small.}\)

 

Пишем \(\displaystyle \bf 5\) первой цифрой в частном и число \(\displaystyle 2845\) под числом \(\displaystyle 3015{\small:}\)

 

 \(\displaystyle 3\)\(\displaystyle 0\)\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle 7\)\(\displaystyle 5\)\(\displaystyle 6\)\(\displaystyle 9\)
\(\displaystyle –\)        
 \(\displaystyle \bf 2\)\(\displaystyle \bf 8\)\(\displaystyle \bf 4\)\(\displaystyle \bf 5\) \(\displaystyle \bf 5\)\(\displaystyle {\small?}\) 
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)   
 \(\displaystyle –\)       
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)   
     \(\displaystyle 0\)   

 

2. Вычитаем  \(\displaystyle 3015-2845={\bf 170}{\small:}\)

 

 \(\displaystyle 3\)\(\displaystyle 0\)\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle 7\)\(\displaystyle 5\)\(\displaystyle 6\)\(\displaystyle 9\)
\(\displaystyle –\)        
 \(\displaystyle 2\)\(\displaystyle 8\)\(\displaystyle 4\)\(\displaystyle 5\) \(\displaystyle 5\)\(\displaystyle {\small?}\) 
  \(\displaystyle \bf 1\)\(\displaystyle \bf 7\)\(\displaystyle \bf 0\)\(\displaystyle {\small?}\)   
 \(\displaystyle –\)       
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)   
     \(\displaystyle 0\)   

 

3. Сносим единицы числа \(\displaystyle 3015{\bf 7}\) (это цифра \(\displaystyle 7 \)):

 

 \(\displaystyle 3\)\(\displaystyle 0\)\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle \bf 7\)\(\displaystyle 5\)\(\displaystyle 6\)\(\displaystyle 9\)
\(\displaystyle –\)        
 \(\displaystyle 2\)\(\displaystyle 8\)\(\displaystyle 4\)\(\displaystyle 5\) \(\displaystyle 5\)\(\displaystyle {\small?}\) 
  \(\displaystyle 1\)\(\displaystyle 7\)\(\displaystyle 0\)\(\displaystyle \bf 7\)   
 \(\displaystyle –\)       
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)   
     \(\displaystyle 0\)   

 

4. Делим число \(\displaystyle 1707\) на \(\displaystyle 569{\small:}\)

\(\displaystyle 1707=569 \cdot {\bf 3}{\small.}\)

 

Пишем \(\displaystyle \bf 3\) второй цифрой в частном и \(\displaystyle 1707\) под \(\displaystyle 1707{\small:}\)

 

 \(\displaystyle 3\)\(\displaystyle 0\)\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle 7\)\(\displaystyle 5\)\(\displaystyle 6\)\(\displaystyle 9\)
\(\displaystyle –\)        
 \(\displaystyle 2\)\(\displaystyle 8\)\(\displaystyle 4\)\(\displaystyle 5\) \(\displaystyle 5\)\(\displaystyle \bf 3\) 
  \(\displaystyle 1\)\(\displaystyle 7\)\(\displaystyle 0\)\(\displaystyle 7\)   
 \(\displaystyle –\)       
  \(\displaystyle 1\)\(\displaystyle 7\)\(\displaystyle 0\)\(\displaystyle 7\)   
     \(\displaystyle 0\)