4. Упростите выражение \(p - \frac{3}{11}p + 2\frac{15}{22}p\) и найдите его значение при \(p = 1\frac{19}{25}\).

Решение:

1. \(p - \frac{3}{11}p + 2\frac{15}{22}p = p - \frac{6}{22}p + 2\frac{15}{22}p = (1 - \frac{6}{22} + 2\frac{15}{22})p = (\frac{22}{22} - \frac{6}{22} + 2\frac{15}{22})p = (\frac{16}{22} + 2\frac{15}{22})p = 2\frac{31}{22}p = 3\frac{9}{22}p\)
2. Если \(p = 1\frac{19}{25}\), то \(3\frac{9}{22}p = 3\frac{9}{22} \cdot 1\frac{19}{25} = \frac{75}{22} \cdot \frac{44}{25} = \frac{75 \cdot 44}{22 \cdot 25} = \frac{3 \cdot 2}{1 \cdot 1} = 6\)

Ответ: 6