1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and find its value when $$n = 10$$. 2. **Write the expression:** $$\frac{n \times n + n}{n} = \frac{n^2 + n}{n}$$. 3. **Use algebraic rules:** We can split the fraction as $$\frac{n^2}{n} + \frac{n}{n}$$. 4. **Simplify each term:** $$\frac{n^2}{n} = n$$ and $$\frac{n}{n} = 1$$ (since any nonzero number divided by itself is 1). 5. **Combine the simplified terms:** $$n + 1$$. 6. **Substitute $$n = 10$$:** $$10 + 1 = 11$$. **Final answer:** $$11$$.