$$12 \frac{3}{8} - 5 \frac{1}{4} + 7 \frac{1}{2} = \frac{99}{8} - \frac{21}{4} + \frac{15}{2} = \frac{99}{8} - \frac{21 \cdot 2}{4 \cdot 2} + \frac{15 \cdot 4}{2 \cdot 4} = \frac{99}{8} - \frac{42}{8} + \frac{60}{8} = \frac{99 - 42 + 60}{8} = \frac{117}{8} = 14 \frac{5}{8}$$
Ответ: $$\boxed{14 \frac{5}{8}}$$