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To solve the expression \( 9 - 3 \div \frac{1}{3} + 1 \), we need to follow the order of operations (PEMDAS/BODMAS):

1. **Division**: 
   \[
   3 \div \frac{1}{3} = 3 \times \frac{3}{1} = 9
   \]

2. **Subtraction**:
   \[
   9 - 9 = 0
   \]

3. **Addition**:
   \[
   0 + 1 = 1
   \]

So, the correct answer is \( 1 \).

Would you like more details or have any questions about this calculation?

Here are some related questions to further your understanding:

1. What is the order of operations and why is it important?
2. How would the answer change if the fraction were different?
3. Can you solve a similar expression with different numbers?
4. What happens if we change the division operation to multiplication?
5. How do parentheses affect the order of operations?

**Tip:** Always perform division and multiplication before addition and subtraction, unless there are parentheses that alter the order.

Learn how to solve the expression 9 - 3 ÷ 1/3 + 1 by applying the order of operations. This problem involves division of fractions, subtraction, and addition, suitable for students in Grades 5-7.

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