1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and evaluate it for $$n = 10$$. 2. **Write the expression:** The given expression is $$\frac{n^2 + n}{n}$$. 3. **Simplify the expression:** Use the property that $$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$$. $$\frac{n^2 + n}{n} = \frac{n^2}{n} + \frac{n}{n}$$ 4. **Simplify each term:** $$\frac{n^2}{n} = n$$ because dividing powers with the same base subtracts exponents: $$n^{2-1} = n$$. $$\frac{n}{n} = 1$$ because any nonzero number divided by itself is 1. 5. **Combine the simplified terms:** $$n + 1$$ 6. **Evaluate for $$n = 10$$:** $$10 + 1 = 11$$ **Final answer:** $$11$$