1. **State the problem:** Solve the equation $$\frac{1}{8} + c = \frac{4}{5}$$ for $c$. 2. **Isolate $c$:** To find $c$, subtract $\frac{1}{8}$ from both sides: $$c = \frac{4}{5} - \frac{1}{8}$$ 3. **Find a common denominator:** The denominators are 5 and 8. The least common denominator (LCD) is 40. 4. **Rewrite fractions with denominator 40:** $$\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}$$ $$\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}$$ 5. **Subtract the fractions:** $$c = \frac{32}{40} - \frac{5}{40} = \frac{32 - 5}{40} = \frac{27}{40}$$ 6. **Simplify the fraction:** $\frac{27}{40}$ is already in simplest form because 27 and 40 have no common factors other than 1. **Final answer:** $$c = \frac{27}{40}$$