1. **State the problem:** Simplify the fraction $\frac{1025}{200}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divisor (GCD). 3. **Find the GCD:** The prime factors of 1025 are $5^2 \times 41$, and for 200 are $2^3 \times 5^2$. The common factors are $5^2 = 25$. 4. **Divide numerator and denominator by 25:** $$\frac{\cancel{1025}^{25}}{\cancel{200}^{25}} = \frac{41}{8}$$ 5. **Final answer:** The simplified form of $\frac{1025}{200}$ is $\frac{41}{8}$.