### Теорія:

Виконаємо ділення тризначного числа $$420$$ на двозначне число $$35:$$

$\begin{array}{l}\begin{array}{ll}\begin{array}{l}{}_{-}420\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{35}\end{array}& \left|\begin{array}{l}\underset{¯}{35}\\ 12\end{array}\right\end{array}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\begin{array}{l}{}_{-}70\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ \begin{array}{l}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{70}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}0\end{array}\end{array}\end{array}$

Поділимо $$42$$ десятки на $$35.$$ Отримаємо $$1$$ десяток у частці та $$7$$ десятків у залишку.

$$7$$ десятків і $$0$$ одиниць разом дадуть $$70$$ одиниць.

Поділимо $$70$$ одиниць на $$35,$$ отримаємо $$2$$ одиниці в частці.

Зробимо перевірку:

$35\cdot 12\phantom{\rule{0.147em}{0ex}}=420$

$\begin{array}{l}{}_{×}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}35\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}12}\\ {}_{+}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.294em}{0ex}}70\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{\phantom{\rule{0.147em}{0ex}}35\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.588em}{0ex}}420\end{array}$

Отже, $$12$$ — частка при діленні $$420$$ на $$35.$$