1. Stating the problem: Solve the equation $d + \frac{5}{8} = \frac{7}{8}$ for $d$. 2. Formula and rules: To isolate $d$, subtract $\frac{5}{8}$ from both sides of the equation. 3. Subtracting $\frac{5}{8}$ from both sides: $$d + \frac{5}{8} - \frac{5}{8} = \frac{7}{8} - \frac{5}{8}$$ 4. Simplify both sides: $$d + \cancel{\frac{5}{8}} - \cancel{\frac{5}{8}} = \frac{7 - 5}{8}$$ $$d = \frac{2}{8}$$ 5. Simplify the fraction $\frac{2}{8}$ by dividing numerator and denominator by 2: $$d = \frac{\cancel{2}^1}{\cancel{8}^4}$$ 6. Final answer: $$d = \frac{1}{4}$$ So, the solution to the equation is $d = \frac{1}{4}$.