1. **State the problem:** We need to subtract the fractions $\frac{7}{8}$ and $\frac{3}{4}$.\n\n2. **Formula and rules:** To subtract fractions, they must have a common denominator. The formula is:\n$$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$\nwhere $a$, $b$, $c$, and $d$ are integers and $b, d \neq 0$.\n\n3. **Find a common denominator:** The denominators are 8 and 4. The least common denominator (LCD) is 8.\n\n4. **Convert fractions to have the same denominator:**\n$\frac{7}{8}$ stays the same.\n$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$\n\n5. **Subtract the numerators:**\n$$\frac{7}{8} - \frac{6}{8} = \frac{7 - 6}{8} = \frac{1}{8}$$\n\n6. **Final answer:**\n$$\frac{7}{8} - \frac{3}{4} = \frac{1}{8}$$