Skip to main content

Теория: Умножение больших натуральных чисел

Задание

Найдите произведение чисел:

   \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)
  x     
     \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 2\)
   
\(\displaystyle +\)       
   
\(\displaystyle +\)       
   
 

 

Решение

1. Первое действие.

Умножаем единицы числа \(\displaystyle 21{\underline 2}\) (это цифра \(\displaystyle 2\)) на число \(\displaystyle 45974\):

 

\(\displaystyle 45974 \cdot 2=91948{\small.}\)

 

   \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)
  x     
     \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle \bf2\)
   \(\displaystyle \bf9\)\(\displaystyle \bf1\)\(\displaystyle \bf9\)\(\displaystyle \bf4\)\(\displaystyle \bf8\)
\(\displaystyle +\)       
  \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\) 
\(\displaystyle +\)       
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

2. Второе действие.

Умножаем десятки числа \(\displaystyle 2{\underline 1}2\) (это цифра \(\displaystyle 1\)) на число \(\displaystyle 45974{\small:}\)

 

\(\displaystyle 45974 \cdot 1=45974{\small.}\)

 

Записываем результат так, чтобы единицы \(\displaystyle 4597{\underline 4}\) шли под той цифрой, на которую мы умножали (в нашем случае это десятки числа \(\displaystyle 2{\underline 1}2{\small,} \) то есть цифра \(\displaystyle 1\)).

 

   \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)
  x     
     \(\displaystyle 2\)\(\displaystyle \bf1\)\(\displaystyle 2\)
   \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)
\(\displaystyle +\)       
  \(\displaystyle \bf4\)\(\displaystyle \bf5\)\(\displaystyle \bf9\)\(\displaystyle \bf7\)\(\displaystyle \bf4\) 
\(\displaystyle +\)       
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

3. Третье действие.

Умножаем сотни числа \(\displaystyle {\underline 2}12\) (это цифра \(\displaystyle 2\)) на число \(\displaystyle 45974{\small:}\)

 

\(\displaystyle 45974 \cdot 2=91948{\small.}\)

 

Записываем результат так, чтобы единицы \(\displaystyle 9194{\underline 8}\) шли под той цифрой, на которую мы умножали (в нашем случае это сотни числа \(\displaystyle {\underline 2}12{\small,}\) то есть цифра \(\displaystyle 2\)).

 

   \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)
  x     
     \(\displaystyle \bf2\)\(\displaystyle 1\)\(\displaystyle 2\)
   \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)
\(\displaystyle +\)       
  \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\) 
\(\displaystyle +\)       
 \(\displaystyle \bf9\)\(\displaystyle \bf1\)\(\displaystyle \bf9\)\(\displaystyle \bf4\)\(\displaystyle \bf8\)  
 \(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)\(\displaystyle {\small?}\)

 

4. Четвертое действие.

Складываем получившиеся числа:

 

   \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)
\(\displaystyle +\)       
  \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\) 
\(\displaystyle +\)       
 \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)  
 \(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 4\)\(\displaystyle 8\)\(\displaystyle 8\)

 

 

В итоге имеем:

   \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\)
  x     
     \(\displaystyle 2\)\(\displaystyle 1\)\(\displaystyle 2\)
   \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)
\(\displaystyle +\)       
  \(\displaystyle 4\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 7\)\(\displaystyle 4\) 
\(\displaystyle +\)       
 \(\displaystyle 9\)\(\displaystyle 1\)\(\displaystyle 9\)\(\displaystyle 4\)\(\displaystyle 8\)  
 \(\displaystyle \bf9\)\(\displaystyle \bf7\)\(\displaystyle \bf4\)\(\displaystyle \bf6\)\(\displaystyle \bf4\)\(\displaystyle \bf8\)\(\displaystyle \bf8\)

 

Ответ: \(\displaystyle 9746488{\small.}\)