4. Упростите выражение р-\frac{8}{11}p+\frac{2}{22}p+\frac{15}{22} и найдите его значение при р-\frac{19}{25}

4. Упростите выражение:

$$p-\frac{8}{11}p+\frac{2}{22}p+\frac{15}{22} = p(1-\frac{8}{11} + \frac{2}{22}) + \frac{15}{22} = p(1-\frac{16}{22}+\frac{2}{22})+\frac{15}{22} = p(1-\frac{14}{22})+\frac{15}{22} = p(\frac{22-14}{22}) + \frac{15}{22} = \frac{8}{22}p + \frac{15}{22} = \frac{4}{11}p + \frac{15}{22}$$

Найдите его значение при $$p = \frac{19}{25}$$:

$$\frac{4}{11} \cdot \frac{19}{25} + \frac{15}{22} = \frac{76}{275} + \frac{15}{22} = \frac{152 + 375}{550} = \frac{527}{550}$$

Ответ: $$\frac{527}{550}$$