1. **State the problem:** Simplify the expression $\frac{1}{1}$. 2. **Recall the rule:** Any number divided by itself (except zero) equals 1. 3. **Apply the rule:** Since numerator and denominator are both 1, the fraction simplifies directly. 4. **Intermediate step showing cancellation:** $$\frac{\cancel{1}}{\cancel{1}} = 1$$ 5. **Final answer:** The simplified value of $\frac{1}{1}$ is $1$.