To solve the expression:

$3 \times 3 + 3 - \frac{3}{3}$

Follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

1. Perform the multiplication and division first: $3 \times 3 = 9, \quad \frac{3}{3} = 1$

   The expression becomes: $9 + 3 - 1$

2. Perform addition and subtraction from left to right: $9 + 3 = 12, \quad 12 - 1 = 11$

Final Answer:

$\boxed{11}$

Would you like to explore the steps further or have similar questions solved?

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Related Questions:

1. What is the value of $4 \times 4 + 4 - \frac{4}{4}$?
2. How does the order of operations affect complex expressions?
3. What happens if parentheses are introduced, e.g., $3 \times (3 + 3) - 3/3$?
4. Can you simplify $5 \times 5 + 5 - 5/5$ using the same method?
5. How is division prioritized when mixed with subtraction and addition?

Tip:

Always handle division and multiplication first in the absence of parentheses to avoid common calculation mistakes!