The mathematical expression in the image is:

$9 - 3 \div \frac{1}{3} + 1 = ?$

Steps to solve:

1. Apply the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

2. Division first:

$3 \div \frac{1}{3} = 3 \times 3 = 9$

This is because dividing by a fraction is the same as multiplying by its reciprocal.

3. Substitute the result back into the equation:

$9 - 9 + 1$

4. Perform subtraction and addition:

$0 + 1 = 1$

Thus, the final result is:

$\boxed{1}$

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the general rule for dividing by fractions?
2. How does the order of operations impact the result?
3. What happens if you change the division sign to multiplication in this equation?
4. Can you solve a similar equation with different numbers, such as $8 - 4 \div \frac{2}{3} + 2$?
5. How would adding parentheses around part of the expression change the outcome?

Tip: Always perform division and multiplication from left to right when both are present in an expression, following the order of operations.