Условие:

Вычисли и объясни, почему значения выражений, записанных в каждом столбике, равны.
1728 : 54 + 4482 : 54;
(1728 + 4482) : 54.
 
702 * 69 + 702 * 18;
702 * (69 + 18).

1728 : 54 + 4482 : 54 = 32 + 83 = 115;
1) $\begin{array}{cc}\begin{array}{l}\underset{¯}{\phantom{0}}1728\\ \phantom{0}\underset{¯}{162}\\ \phantom{0}\underset{¯}{\phantom{0}}108\\ \phantom{00}\underset{¯}{108}\\ \phantom{0000}0\end{array}& \begin{array}{l}\overline{)54}\\ \overline{\overline{)32}}\end{array}\end{array}$;
2) $\begin{array}{cc}\begin{array}{l}\underset{¯}{\phantom{0}}4482\\ \phantom{0}\underset{¯}{432}\\ \phantom{0}\underset{¯}{\phantom{0}}162\\ \phantom{00}\underset{¯}{162}\\ \phantom{0000}0\end{array}& \begin{array}{l}\overline{)54}\\ \overline{\overline{)83}}\end{array}\end{array}$;
3) 32 + 83 = 115.
 
(1728 + 4482) : 54 = 6210 : 54 = 115
1) $\begin{array}{r}\begin{array}{r}+\end{array}\underline{\begin{array}{r}1728\\ 4482\end{array}}\\ \begin{array}{r}6210\end{array}\end{array}$;
2) $\begin{array}{cc}\begin{array}{l}\underset{¯}{\phantom{0}}6210\\ \phantom{0}\underset{¯}{54}\\ \phantom{0}\underset{¯}{\phantom{0}}81\\ \phantom{00}\underset{¯}{54}\\ \phantom{0}\underset{¯}{\phantom{0}}270\\ \phantom{00}\underset{¯}{270}\\ \phantom{0000}0\end{array}& \begin{array}{l}\overline{)54}\\ \overline{\overline{)115}}\end{array}\end{array}$.
Значения выражений равны так как (a + b) : c = a : c + b : c.
702 * 69 + 702 * 18 = 48438 + 12636 = 61074
 
 
702 * 69 + 702 * 18 = 48438 + 12636 = 61074
1) $\begin{array}{r}\times \underset{¯}{\begin{array}{r}702\\ 69\end{array}}\\ 6318\\ 4212\phantom{0}\\ \overline{48438}\end{array}$;
2) $\begin{array}{r}\times \underset{¯}{\begin{array}{r}702\\ 18\end{array}}\\ 5616\\ 702\phantom{0}\\ \overline{12636}\end{array}$;
3) $\begin{array}{r}\begin{array}{r}+\end{array}\underline{\begin{array}{r}48438\\ 12636\end{array}}\\ \begin{array}{r}61074\end{array}\end{array}$.
 
702 * (69 + 18) = 702 * 87 = 61074
1) 69 + 18 = 87;
2) $\begin{array}{r}\times \underset{¯}{\begin{array}{r}702\\ 87\end{array}}\\ 4914\\ 5616\phantom{0}\\ \overline{61074}\end{array}$.
Значения выражений равны так как a * (b + c) = a * b + a * c.
702 * (69 + 18) = 702 * 69 + 702 * 18 = 61074