To solve \(9 \times 9 - 3 \div 3 + 1\), we follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and then addition and subtraction (from left to right), also known as PEMDAS/BODMAS.

### Solution:
1. **Multiplication** and **division** first:
   - \(9 \times 9 = 81\)
   - \(3 \div 3 = 1\)

2. Substitute back:
   \[
   81 - 1 + 1
   \]

3. **Addition and subtraction** from left to right:
   - \(81 - 1 = 80\)
   - \(80 + 1 = 81\)

### Final Answer:
\[
81
\]

Would you like a more detailed explanation, or have any questions? 

Here are some related problems you may find interesting:
1. Evaluate \(8 \times 8 + 4 \div 2 - 1\).
2. Simplify \(6 \times 6 - 12 \div 4 + 2\).
3. Solve \(7 + 5 \times 3 - 4 \div 2\).
4. Calculate \(10 \times 10 - 5 + 3\).
5. Find the value of \(12 \div 4 \times 3 + 7\).

**Tip:** Always remember to perform multiplication and division before addition and subtraction, moving from left to right.

Solve the expression 9 x 9 - 3 ÷ 3 + 1 using order of operations (PEMDAS/BODMAS). This arithmetic problem helps students in Grades 5-7 understand multiplication, division, addition, and subtraction in sequence.

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