Let's solve the expression step by step, following the order of operations (PEMDAS/BODMAS):

Expression:
$3 \times 3 - 3 \div 3 + 3$

Step 1: Handle Multiplication and Division (from left to right)

1. $3 \times 3 = 9$
2. $3 \div 3 = 1$

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

Step 2: Handle Addition and Subtraction (from left to right)

1. $9 - 1 = 8$
2. $8 + 3 = 11$

Final Answer:

$11$

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Would you like additional details or have any questions?

Related Questions:

1. What is the order of operations, and why is it important in mathematics?
2. How do parentheses affect the outcome of an expression?
3. Can you explain more about the difference between subtraction and negative numbers in equations?
4. How would this expression change if it were written as $(3 \times 3) - (3 \div (3+3))$?
5. What are some common mistakes when solving such mixed operations?

Tip: Always work step by step, keeping the order of operations in mind to avoid errors.