1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and find its value when $$n = 10$$. 2. **Write the expression:** $$\frac{n \times n + n}{n}$$. 3. **Apply algebraic rules:** Use the distributive property to factor the numerator: $$n \times n + n = n(n + 1)$$. 4. **Rewrite the expression:** $$\frac{n(n + 1)}{n}$$. 5. **Simplify the fraction:** Since $$n \neq 0$$, cancel $$n$$ in numerator and denominator: $$n + 1$$. 6. **Evaluate for $$n = 10$$:** $$10 + 1 = 11$$. **Final answer:** $$11$$.