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Теория: Умножение трехзначных чисел

Задание

Перемножить числа:

    \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 4\)
   x   
    \(\displaystyle 7\)\(\displaystyle 4\)\(\displaystyle 5\)

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

 

 

Решение

1. Умножаем единицы числа \(\displaystyle 74{\underline 5} \) (это число \(\displaystyle 5 \)) на число \(\displaystyle 454{\small,}\) получаем:

 

\(\displaystyle 5 \cdot 454=2270{\small.} \)

Записываем результат в первую строку:

 

    \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 4\)
   x   
    \(\displaystyle 7\)\(\displaystyle 4\)\(\displaystyle \bf5\)

   \(\displaystyle \bf2\)\(\displaystyle \bf2\)\(\displaystyle \bf7\)\(\displaystyle \bf0\)
\(\displaystyle +\)      
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\) 
\(\displaystyle +\)      
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  

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

 

2. Умножаем десятки числа \(\displaystyle 7{\underline 4}5 \) (это число \(\displaystyle 4 \)) на число \(\displaystyle 454{\small,}\) получаем:

 

\(\displaystyle 4 \cdot 454=1816{\small.} \)

Записываем результат во вторую строку:

 

    \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 4\)
   x   
    \(\displaystyle 7\)\(\displaystyle \bf4\)\(\displaystyle 5\)

   \(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 0\)
\(\displaystyle +\)      
  \(\displaystyle \bf1\)\(\displaystyle \bf8\)\(\displaystyle \bf1\)\(\displaystyle \bf6\) 

\(\displaystyle +\)

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

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

 

3. Умножаем сотни числа \(\displaystyle {\underline 7}45 \) (это число \(\displaystyle 7 \)) на число \(\displaystyle 454{\small,}\) получаем:

 

\(\displaystyle 7 \cdot 454=3178 {\small.}\)

Записываем результат в третью строку:

 

    \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 4\)
   x   
    \(\displaystyle \bf7\)\(\displaystyle 4\)\(\displaystyle 5\)

   \(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 0\)
\(\displaystyle +\)      
  \(\displaystyle 1\)\(\displaystyle 8\)\(\displaystyle 1\)\(\displaystyle 6\) 
\(\displaystyle +\)      
 \(\displaystyle \bf3\)\(\displaystyle \bf1\)\(\displaystyle \bf7\)\(\displaystyle \bf8\)  

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

 

4. Складываем числа:

   \(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 0\)
\(\displaystyle +\)      
  \(\displaystyle 1\)\(\displaystyle 8\)\(\displaystyle 1\)\(\displaystyle 6\) 
\(\displaystyle +\)      
 \(\displaystyle 3\)\(\displaystyle 1\)\(\displaystyle 7\)\(\displaystyle 8\)  

 \(\displaystyle 3\)\(\displaystyle 3\)\(\displaystyle 8\)\(\displaystyle 2\)\(\displaystyle 3\)\(\displaystyle 0\)

 

В итоге получаем:

    \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 4\)
   x   
    \(\displaystyle 7\)\(\displaystyle 4\)\(\displaystyle 5\)

   \(\displaystyle 2\)\(\displaystyle 2\)\(\displaystyle 7\)\(\displaystyle 0\)
\(\displaystyle +\)      
  \(\displaystyle 1\)\(\displaystyle 8\)\(\displaystyle 1\)\(\displaystyle 6\) 
\(\displaystyle +\)      
 \(\displaystyle 3\)\(\displaystyle 1\)\(\displaystyle 7\)\(\displaystyle 8\)  

 \(\displaystyle \bf3\)\(\displaystyle \bf3\)\(\displaystyle \bf8\)\(\displaystyle \bf2\)\(\displaystyle \bf3\)\(\displaystyle \bf0\)

 

Ответ: \(\displaystyle 338230{\small.} \)