Найдите частное:
\(\displaystyle 1:4=\),
Поделим \(\displaystyle 1\) на \(\displaystyle 4\) в столбик:
| \(\displaystyle 1\) | \(\displaystyle 4\) |
| \(\displaystyle ?\) |
Первое действие.
Так как \(\displaystyle 1<4\) и больше разрядов у числа нет, то пишем нуль первым числом в частном, ставим запятую после него:
| \(\displaystyle 1\) | \(\displaystyle 4\) | ||
| \(\displaystyle \color{blue}{0}\) | \(\displaystyle \color{red}{,}\) | \(\displaystyle ?\) |
и добавляем нуль к делимому справа (то есть к \(\displaystyle 1\) справа):
| \(\displaystyle 1\) | \(\displaystyle \color{red}{0}\) | \(\displaystyle 4\) | ||
| \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle ?\) |
Второе действие.
Делим \(\displaystyle 10\) на \(\displaystyle 4\):
\(\displaystyle 10= \color{green}{2}·4+2=\color{blue}{8}+2\).
| \(\displaystyle 1\) | \(\displaystyle 0\) | \(\displaystyle 4\) | ||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle \color{green}{2}\) | \(\displaystyle ?\) | ||
| \(\displaystyle \color{blue}{8}\) |
Вычитаем \(\displaystyle 10-\color{blue}{8}=\bf2\):
| \(\displaystyle 1\) | \(\displaystyle 0\) | \(\displaystyle 4\) | ||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle \color{green}{2}\) | \(\displaystyle ?\) | ||
| \(\displaystyle \color{blue}{8}\) | ||||||
| \(\displaystyle \bf2\) |
Третье действие.
Добавляем нуль к разности справа:
| \(\displaystyle 1\) | \(\displaystyle 0\) | \(\displaystyle 4\) | |||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 2\) | \(\displaystyle ?\) | |||
| \(\displaystyle 8\) | |||||||
| \(\displaystyle 2\) | \(\displaystyle \color{red}{0}\) |
Четвертое действие.
Делим \(\displaystyle 20\) на \(\displaystyle 4\):
\(\displaystyle 20= \color{green}{5}·4=\color{blue}{20}\).
Пишем \(\displaystyle \color{green}{5}\) в частном и вычитаем \(\displaystyle 20-\color{blue}{20}=\bf0\):
| \(\displaystyle 1\) | \(\displaystyle 0\) | \(\displaystyle 4\) | |||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 2\) | \(\displaystyle \color{green}{5}\) | |||
| \(\displaystyle 8\) | |||||||
| \(\displaystyle 2\) | \(\displaystyle 0\) | ||||||
| \(\displaystyle -\) | |||||||
| \(\displaystyle \color{blue}{2}\) | \(\displaystyle \color{blue}{0}\) | ||||||
| \(\displaystyle \bf0\) |
Таким образом, \(\displaystyle 1:4=0,25\).
Ответ: \(\displaystyle 0,25\).