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Теория: Умножение трехзначных чисел

Задание

Перемножить числа:

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
  x   
   \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 1\)
   
\(\displaystyle +\)     
   
\(\displaystyle +\)     
   
 

 

Решение

1. Умножаем единицы числа \(\displaystyle 32{\underline 1} \) (это число \(\displaystyle 1 \)) на число \(\displaystyle 211{\small,}\) получаем:

 

\(\displaystyle 1 \cdot 211=211 {\small.}\)

Записываем результат в первую строку:

 

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
  x   
   \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle \bf 1\)
   \(\displaystyle \bf 2\)\(\displaystyle \bf 1\)\(\displaystyle \bf 1\)
\(\displaystyle +\)     
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\) 
\(\displaystyle +\)     
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

2. Умножаем десятки числа \(\displaystyle 3{\underline 2}1 \) (это число \(\displaystyle 2 \)) на число \(\displaystyle 211{\small,}\) получаем:

 

\(\displaystyle 2 \cdot 211=422 {\small.}\)

Записываем результат во вторую строку:

 

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
  x   
   \(\displaystyle 3\)\(\displaystyle \bf 2\)\(\displaystyle 1\)
   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
\(\displaystyle +\)     
  \(\displaystyle \bf 4\)\(\displaystyle \bf 2\)\(\displaystyle \bf 2\) 
\(\displaystyle +\)     
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

3. Умножаем сотни числа \(\displaystyle {\underline 3}21 \) (это число \(\displaystyle 3 \)) на число \(\displaystyle 211{\small,}\) получаем:

 

\(\displaystyle 3 \cdot 211=633 {\small.}\)

Записываем результат в третью строку:

 

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
  x   
   \(\displaystyle \bf 3\)\(\displaystyle 2\)\(\displaystyle 1\)
   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
\(\displaystyle \)+     
  \(\displaystyle 4\)\(\displaystyle 2\)\(\displaystyle 2\) 
\(\displaystyle +\)     
 \(\displaystyle \bf 6\)\(\displaystyle \bf 3\)\(\displaystyle \bf 3\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

4. Складываем числа:

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
\(\displaystyle +\)     
  \(\displaystyle 4\)\(\displaystyle 2\)\(\displaystyle 2\) 
\(\displaystyle +\)     
 \(\displaystyle 6\)\(\displaystyle 3\)\(\displaystyle 3\)  
 \(\displaystyle 6\)\(\displaystyle 7\)\(\displaystyle 7\)\(\displaystyle 3\)\(\displaystyle 1\)

 

В итоге получаем:

   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
  x   
   \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 1\)
   \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 1\)
\(\displaystyle +\)     
  \(\displaystyle 4\)\(\displaystyle 2\)\(\displaystyle 2\) 
\(\displaystyle +\)     
 \(\displaystyle 6\)\(\displaystyle 3\)\(\displaystyle 3\)  
 \(\displaystyle \bf6\)\(\displaystyle \bf7\)\(\displaystyle \bf7\)\(\displaystyle \bf3\)\(\displaystyle \bf1\)

 

Ответ: \(\displaystyle 67731{\small.} \)