Exercițiul 223

Metoda 1: Notăm $\overline{a,b(cd)} = x \quad | \times10$
$\overline{ab,(cd)} = 10x \quad | \times100$
$\overline{abcd,(cd)} = 1000x \quad | -10x$
$\overline{abcd,(cd)} - \overline{ab,(cd)} = 990x$
$\overline{abcd} - \overline{ab} = 990x \Rightarrow \boxed{x=\dfrac{\overline{abcd}-\overline{ab}}{990}}.$

Metoda 2: Ne folosimm de formula demonstrată anterior pentru $\overline{0,(ab)}.$
$\overline{a,b(cd)} = \dfrac{1}{10} \cdot \overline{ab,(cd)} = \dfrac{1}{10} \cdot (\overline{ab} + \overline{0,(cd)} = \dfrac{1}{10} \cdot \Big(\overline{ab} + \dfrac{\overline{cd}}{99}\Big) =$

$= \dfrac{1}{10} \cdot \dfrac{100 \cdot \overline{ab} + \overline{cd} - \overline{ab}}{99} = \dfrac{\overline{abcd}-\overline{ab}}{990}.$