Найдите частное:
\(\displaystyle 3:2=\),
Поделим \(\displaystyle 3\) на \(\displaystyle 2\) в столбик:
| \(\displaystyle 3\) | \(\displaystyle 2\) |
| \(\displaystyle ?\) |
Первое действие.
Поделим \(\displaystyle 3\) на \(\displaystyle 2\) с остатком:
\(\displaystyle 3= \color{green}{1}·2+1=\color{blue}{2}+1\).
Пишем \(\displaystyle \color{blue}{2}\) под \(\displaystyle 3\) и \(\displaystyle \color{green}{1}\) в частном:
| \(\displaystyle 3\) | \(\displaystyle 2\) | |
| \(\displaystyle -\) | \(\displaystyle \color{green}{1}\) | |
| \(\displaystyle \color{blue}{2}\) |
и вычитаем \(\displaystyle 3-\color{blue}{2}=1\):
| \(\displaystyle 3\) | \(\displaystyle 2\) | ||
| \(\displaystyle -\) | \(\displaystyle \color{green}{1}\) | \(\displaystyle ?\) | |
| \(\displaystyle \color{blue}{2}\) | |||
| \(\displaystyle 1\) |
Второе действие.
Так как \(\displaystyle 1<2\) и больше разрядов у числа нет, то ставим запятую частном, добавляем нуль к разности справа (то есть к \(\displaystyle 1\) справа):
| \(\displaystyle 3\) | \(\displaystyle 2\) | ||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle ?\) | ||
| \(\displaystyle 2\) | |||||
| \(\displaystyle 1\) | \(\displaystyle \color{red}{0}\) |
Третье действие.
Делим \(\displaystyle 10\) на \(\displaystyle 2\):
\(\displaystyle 10= \color{green}{5}·2=\color{blue}{10}\).
Пишем \(\displaystyle \color{green}{5}\) в частном и вычитаем \(\displaystyle 10-\color{blue}{10}=0\):
| \(\displaystyle 3\) | \(\displaystyle 2\) | |||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle \color{green}{5}\) | |||
| \(\displaystyle 2\) | ||||||
| \(\displaystyle 1\) | \(\displaystyle 0\) | |||||
| \(\displaystyle -\) | ||||||
| \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{0}\) | |||||
| \(\displaystyle 0\) |
Таким образом, \(\displaystyle 3:2=1,5\).
Ответ: \(\displaystyle 1,5\).