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Теория: Умножение трехзначных и двузначных чисел

Задание

Перемножить числа:

   \(\displaystyle 4\)\(\displaystyle 3\)\(\displaystyle 7\)
  \(\displaystyle \times\)   
    \(\displaystyle 7\)\(\displaystyle 5\)
 
  
\(\displaystyle +\)     
  
 
 

 

Решение

1. Умножаем единицы числа \(\displaystyle 7\underline{5}\) (это цифра \(\displaystyle 5 \)) на число \(\displaystyle 437{\small:}\)

 

\(\displaystyle 5 \cdot 437=2185 {\small.}\)

 

   \(\displaystyle \bf4\)\(\displaystyle \bf3\)\(\displaystyle \bf7\)
  \(\displaystyle \times\)   
    \(\displaystyle 7\)\(\displaystyle \bf5\)
 
  \(\displaystyle \bf2\)\(\displaystyle \bf1\)\(\displaystyle \bf8\)\(\displaystyle \bf5\)
\(\displaystyle +\)     
 \(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\) 
 
 \(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)

 

2. Умножаем десятки числа \(\displaystyle \underline{7}5\) (это цифра \(\displaystyle 7 \)) на число \(\displaystyle 437{\small:}\)

 

\(\displaystyle 7 \cdot 437=3059 {\small.}\)

 

Записываем результат так, чтобы единицы  \(\displaystyle 3059\) шли под той цифрой на которую мы умножали; в нашем случае это десятки числа \(\displaystyle \underline{7}5\) (то есть цифра \(\displaystyle 7 \)):

 

   \(\displaystyle \bf4\)\(\displaystyle \bf3\)\(\displaystyle \bf7\)
  \(\displaystyle \times\)   
    \(\displaystyle \bf7\)\(\displaystyle 5\)
 
  \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 8\)\(\displaystyle 5\)
\(\displaystyle +\)     
 \(\displaystyle \bf3\)\(\displaystyle \bf0\)\(\displaystyle \bf5\)\(\displaystyle \bf9\) 
 
 \(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)\(\displaystyle ?\)

 

3. Складываем числа:

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

 

В итоге получаем:

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

 

Ответ: \(\displaystyle 32775{\small.}\)