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Теория: Умножение трехзначных и двузначных чисел

Задание

Перемножить числа:

      \(\displaystyle 9\) \(\displaystyle 4\) \(\displaystyle 5\)
    \(\displaystyle \times\)      
        \(\displaystyle 2\) \(\displaystyle 3\)
 
   
\(\displaystyle +\)          
   
 
 

 

Решение

1. Умножаем единицы числа \(\displaystyle 2\underline{3} \) (это цифра \(\displaystyle 3 \)) на число \(\displaystyle 945\):

 

\(\displaystyle 3 \cdot 945=2835 \).

 

      \(\displaystyle \bf9\) \(\displaystyle \bf4\) \(\displaystyle \bf5\)
    \(\displaystyle \times\)      
        \(\displaystyle 2\) \(\displaystyle \bf3\)
 
    \(\displaystyle \bf2\) \(\displaystyle \bf8\) \(\displaystyle \bf3\) \(\displaystyle \bf5\)
\(\displaystyle +\)          
  \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\)  
 
  \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\)

 

2. Умножаем десятки числа \(\displaystyle \underline{2}3 \) (это цифра \(\displaystyle 2 \)) на число \(\displaystyle 945\):

 

\(\displaystyle 2 \cdot 945=1890 \).

 

Записываем результат так, чтобы единицы \(\displaystyle 1890\) шли под той цифрой, на которую мы умножали; в нашем случае это десятки числа \(\displaystyle \underline{2}3 \) (то есть цифра \(\displaystyle 2 \)):

 

      \(\displaystyle \bf9\) \(\displaystyle \bf4\) \(\displaystyle \bf5\)
    \(\displaystyle \times\)      
        \(\displaystyle \bf2\) \(\displaystyle 3\)
 
    \(\displaystyle 2\) \(\displaystyle 8\) \(\displaystyle 3\) \(\displaystyle 5\)
\(\displaystyle +\)          
  \(\displaystyle \bf1\) \(\displaystyle \bf8\) \(\displaystyle \bf9\) \(\displaystyle \bf0\)  
 
  \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\) \(\displaystyle ?\)

 

3. Складываем числа:

    \(\displaystyle 2\) \(\displaystyle 8\) \(\displaystyle 3\) \(\displaystyle 5\)
\(\displaystyle +\)          
  \(\displaystyle 1\) \(\displaystyle 8\) \(\displaystyle 9\) \(\displaystyle 0\)  
 
  \(\displaystyle \bf2\) \(\displaystyle \bf1\) \(\displaystyle \bf7\) \(\displaystyle \bf3\) \(\displaystyle \bf5\)

 

В итоге получаем:

      \(\displaystyle 9\) \(\displaystyle 4\) \(\displaystyle 5\)
    \(\displaystyle \times\)      
        \(\displaystyle 2\) \(\displaystyle 3\)
 
    \(\displaystyle 2\) \(\displaystyle 8\) \(\displaystyle 3\) \(\displaystyle 5\)
\(\displaystyle +\)          
  \(\displaystyle 1\) \(\displaystyle 8\) \(\displaystyle 9\) \(\displaystyle 0\)  
 
  \(\displaystyle 2\) \(\displaystyle 1\) \(\displaystyle 7\) \(\displaystyle 3\) \(\displaystyle 5\)

 

Ответ: \(\displaystyle 21735\).