4. Упростите выражение р-11P+222р и найдите его значение 3 15 19 при р = 125.

$$p - \frac{3}{11}p + 2\frac{15}{22}p = p(1 - \frac{3}{11} + \frac{2\cdot 22 + 15}{22}) = p(1 - \frac{3}{11} + \frac{44 + 15}{22}) = p(1 - \frac{3}{11} + \frac{59}{22}) = p(\frac{22}{22} - \frac{3 \cdot 2}{11 \cdot 2} + \frac{59}{22}) = p(\frac{22}{22} - \frac{6}{22} + \frac{59}{22}) = p(\frac{22-6+59}{22}) = p(\frac{75}{22}) = \frac{75}{22}p$$

$$p = 1\frac{19}{25} = \frac{1\cdot 25 + 19}{25} = \frac{25+19}{25} = \frac{44}{25}$$

$$\frac{75}{22} \cdot \frac{44}{25} = \frac{3 \cdot 25}{2 \cdot 11} \cdot \frac{4 \cdot 11}{25} = \frac{3 \cdot \cancel{25}}{2 \cdot \cancel{11}} \cdot \frac{4 \cdot \cancel{11}}{\cancel{25}} = \frac{3 \cdot 4}{2} = 3 \cdot 2 = 6$$

Ответ: $$6$$