To solve the expression $3 \div 3 \times 3 - 3 + 3$, we follow the order of operations, often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Division and Multiplication (from left to right): $3 \div 3 = 1$ Now the expression is: $1 \times 3 - 3 + 3$ Next, we perform the multiplication: $1 \times 3 = 3$ Now the expression becomes: $3 - 3 + 3$

2. Subtraction and Addition (from left to right): $3 - 3 = 0$ $0 + 3 = 3$

So, the final answer is: $3$

Would you like further details or have any questions?

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Here are some related questions:

1. How does the order of operations affect solving complex expressions?
2. What are some examples where people often make mistakes with PEMDAS?
3. How would the solution change if parentheses were added to the expression?
4. Can PEMDAS rules be applied differently in other countries or mathematical conventions?
5. How can we represent this expression graphically?

Tip: Always handle multiplication and division from left to right before addition and subtraction for accurate results.