Найдите частное:
\(\displaystyle 9:8=\),
Поделим \(\displaystyle 9\) на \(\displaystyle 8\) в столбик:
| \(\displaystyle 9\) | \(\displaystyle 8\) |
| \(\displaystyle ?\) |
Первое действие.
Поделим \(\displaystyle 9\) на \(\displaystyle 8\) с остатком:
\(\displaystyle 9= \color{green}{1}·8+1=\color{blue}{8}+1\).
Пишем \(\displaystyle \color{blue}{8}\) под \(\displaystyle 9\) и \(\displaystyle \color{green}{1}\)в частном:
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||
| \(\displaystyle -\) | \(\displaystyle \color{green}{1}\) | \(\displaystyle ?\) | |
| \(\displaystyle \color{blue}{8}\) |
Вычитаем \(\displaystyle 9-\color{blue}{8}=\bf1\):
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||
| \(\displaystyle -\) | \(\displaystyle \color{green}{1}\) | \(\displaystyle ?\) | |
| \(\displaystyle \color{blue}{8}\) | |||
| \(\displaystyle \bf1\) |
Второе действие.
Так как \(\displaystyle 1<8\) и больше разрядов у числа нет, то ставим запятую в частном, добавляем нуль к разности справа (то есть к \(\displaystyle 1\) справа):
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle \color{red}{,}\) | \(\displaystyle ?\) | ||
| \(\displaystyle 8\) | |||||
| \(\displaystyle 1\) | \(\displaystyle \color{blue}{0}\) |
Делим \(\displaystyle 10\) на \(\displaystyle 8\):
\(\displaystyle 10= \color{green}{1}·8+2=\color{blue}{8}+2\).
Пишем \(\displaystyle \color{green}{1}\) в частном и вычитаем \(\displaystyle 10-\color{blue}{8}=\bf2\):
| \(\displaystyle 9\) | \(\displaystyle 8\) | |||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle \color{green}{1}\) | \(\displaystyle ?\) | ||
| \(\displaystyle 8\) | ||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | |||||
| \(\displaystyle -\) | ||||||
| \(\displaystyle \color{blue}{8}\) | ||||||
| \(\displaystyle \bf2\) |
Третье действие.
Добавляем нуль к разности справа:
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle ?\) | |||
| \(\displaystyle 8\) | |||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | ||||||
| \(\displaystyle -\) | |||||||
| \(\displaystyle 8\) | |||||||
| \(\displaystyle 2\) | \(\displaystyle \color{red}{0}\) |
Делим \(\displaystyle 20\) на \(\displaystyle 8\):
\(\displaystyle 20= \color{green}{2}·8+4=\color{blue}{16}+4\).
Пишем \(\displaystyle \color{green}{2}\)в частном и вычитаем \(\displaystyle 20-\color{blue}{16}=\bf4\):
| \(\displaystyle 9\) | \(\displaystyle 8\) | |||||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle \color{green}{2}\) | \(\displaystyle ?\) | |||
| \(\displaystyle 8\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | |||||||
| \(\displaystyle -\) | ||||||||
| \(\displaystyle 8\) | ||||||||
| \(\displaystyle 2\) | \(\displaystyle 0\) | |||||||
| \(\displaystyle -\) | ||||||||
| \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{6}\) | |||||||
| \(\displaystyle \bf4\) |
Четвертое действие.
Добавляем нуль к разности справа:
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle ?\) | ||||
| \(\displaystyle 8\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle 8\) | |||||||||
| \(\displaystyle 2\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||
| \(\displaystyle 4\) | \(\displaystyle \color{red}{0}\) |
Делим \(\displaystyle 40\) на \(\displaystyle 8\):
\(\displaystyle 40= \color{green}{5}·8=\color{blue}{40}\).
Пишем \(\displaystyle \color{green}{5}\) в частном и вычитаем \(\displaystyle 40-\color{blue}{40}=\bf0\):
| \(\displaystyle 9\) | \(\displaystyle 8\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle \color{green}{5}\) | ||||
| \(\displaystyle 8\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle 8\) | |||||||||
| \(\displaystyle 2\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||
| \(\displaystyle 4\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle \color{blue}{4}\) | \(\displaystyle \color{blue}{0}\) | ||||||||
| \(\displaystyle \bf0\) |
Таким образом, \(\displaystyle 9:8=1,125\).
Ответ: \(\displaystyle 1,125\).