To solve the expression \( \frac{27}{3} \times 9 + 1 \), we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. **Division**: First, divide 27 by 3:
   \[
   \frac{27}{3} = 9
   \]

2. **Multiplication**: Next, multiply the result by 9:
   \[
   9 \times 9 = 81
   \]

3. **Addition**: Finally, add 1:
   \[
   81 + 1 = 82
   \]

So, the final answer is **82**.

Would you like more details or have any questions?

Here are 8 related questions:

1. What is PEMDAS, and why is it important in solving math problems?
2. How do parentheses affect the order of operations?
3. What happens if you perform the operations in a different order?
4. Can the division in this problem be replaced by multiplication with a reciprocal? How would that work?
5. How do you solve expressions with multiple levels of parentheses?
6. What is the difference between the floor and ceiling functions, and how are they applied?
7. How would this expression change if there was a subtraction instead of addition at the end?
8. How would you solve the expression if it had a fraction in it?

**Tip:** Always solve multiplication and division from left to right, regardless of the order they appear in.

Learn how to solve the mathematical expression 27 divided by 3 times 9 plus 1 step-by-step. Understand the order of operations (PEMDAS) and the arithmetic operations involved. Suitable for students in Grades 6-8.

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