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Теория: Умножение трехзначных чисел

Задание

Перемножить числа:

    \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\)
   x   
    \(\displaystyle 7\)\(\displaystyle 1\)\(\displaystyle 0\)

    
\(\displaystyle +\)      
    
\(\displaystyle +\)      
   

 

 

Решение

1. Умножаем единицы числа \(\displaystyle 71{\underline 0} \) (это число \(\displaystyle 0 \)) на число \(\displaystyle 461{\small,}\) получаем:

 

\(\displaystyle 0 \cdot 461=0{\small.}\)

Записываем результат в первую строку:

 

    \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\)
   x   
    \(\displaystyle 7\)\(\displaystyle 1\)\(\displaystyle \bf0\)

    \(\displaystyle \bf0\)\(\displaystyle \bf0\)\(\displaystyle \bf0\)

\(\displaystyle +\)

 

      
   \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\) 
\(\displaystyle +\)      
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  

 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

2. Умножаем десятки числа \(\displaystyle 7{\underline 1}0 \) (это число \(\displaystyle 1 \)) на число \(\displaystyle 461{\small,}\) получаем:

 

\(\displaystyle 1 \cdot 461=461{\small.} \)

Записываем результат во вторую строку:

 

    \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\)
   x   
    \(\displaystyle 7\)\(\displaystyle \bf1\)\(\displaystyle 0\)

    \(\displaystyle 0\)\(\displaystyle 0\)\(\displaystyle 0\)
\(\displaystyle +\)      
   \(\displaystyle \bf4\)\(\displaystyle \bf6\)\(\displaystyle \bf1\) 
\(\displaystyle +\)      
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  

 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

3. Умножаем сотни числа \(\displaystyle {\underline 7}10 \) (это число \(\displaystyle 7 \)) на число \(\displaystyle 461{\small,}\) получаем:

 

\(\displaystyle 7 \cdot 461=3227{\small.} \)

Записываем результат в третью строку:

 

    \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\)
   x   
    \(\displaystyle \bf7\)\(\displaystyle 1\)\(\displaystyle 0\)

    \(\displaystyle 0\)\(\displaystyle 0\)\(\displaystyle 0\)
\(\displaystyle +\)      
   \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\) 
\(\displaystyle +\)      
 \(\displaystyle \bf3\)\(\displaystyle \bf2\)\(\displaystyle \bf2\)\(\displaystyle \bf7\)  

 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

4. Складываем числа:

    \(\displaystyle 0\)\(\displaystyle 0\)\(\displaystyle 0\)
\(\displaystyle +\)      
   \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\) 
\(\displaystyle +\)      
 \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)  

 \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 3\)\(\displaystyle 1\)\(\displaystyle 0\)

 

В итоге получаем:

    \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\)
   x   
    \(\displaystyle 7\)\(\displaystyle 1\)\(\displaystyle 0\)

    \(\displaystyle 0\)\(\displaystyle 0\)\(\displaystyle 0\)
\(\displaystyle +\)      
   \(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 1\) 
\(\displaystyle +\)      
 \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)  

 \(\displaystyle 3\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 3\)\(\displaystyle 1\)\(\displaystyle 0\)

 

Ответ: \(\displaystyle 327310{\small.} \)