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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 \(\displaystyle 945{\small:}\)

 

\(\displaystyle 3 \cdot 945=2835 {\small.}\)

 

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

 

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

 

\(\displaystyle 2 \cdot 945=1890 {\small.}\)

 

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: \(\displaystyle 21735{\small.}\)