To solve the expression $3 \times 3 - 3 \div 3 + 3$, we follow the order of operations (PEMDAS/BODMAS):

1. Multiplication and Division first, from left to right.

   • $3 \times 3 = 9$
   • $3 \div 3 = 1$

2. Now substitute these results back into the expression: $9 - 1 + 3$

3. Addition and Subtraction next, from left to right.

   • $9 - 1 = 8$
   • $8 + 3 = 11$

So, the final result is: $\boxed{11}$

Would you like more details or have any questions?

Here are five related questions to practice:

1. What is $4 \times 4 - 4 \div 4 + 4$?
2. Simplify $5 \times 5 - 5 \div 5 + 5$.
3. Calculate $2 \times 6 - 2 \div 2 + 6$.
4. Solve $10 \times 2 - 10 \div 2 + 10$.
5. Evaluate $7 \times 7 - 7 \div 7 + 7$.

Tip: Always handle multiplication and division before moving to addition and subtraction for accurate results.