### Теория:

Выполним деление трёхзначного числа $$420$$на двузначное число $$35$$.

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

Разделим $$42$$ дес. на $$35$$ получим $$1$$ дес. в частном и $$7$$ дес. в остатке.

$$7$$ дес. и $$0$$ ед. вместе $$70$$ ед.

Делим $$70$$ ед. на $$35$$, получаем $$2$$ ед. в частном.

Выполним проверку.

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

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

Значит,  $$12$$— частное при делении $$420$$ на $$35$$.