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Whether you are working on simple math problems or complex equations, the order of operations is crucial. The acronym PEMDAS helps remember this order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This ensures that everyone solves the equation in the same way and gets the same result. Let’s break down PEMDAS:

- **P** for Parentheses: Always solve expressions inside parentheses first.
- **E** for Exponents: Next, handle any exponents.
- **MD** for Multiplication and Division: Solve these from left to right.
- **AS** for Addition and Subtraction: Lastly, deal with addition and subtraction from left to right.

Using PEMDAS correctly means you won’t get tricked by complex expressions. It forms the backbone of many math problems and helps keep calculations orderly and predictable.

Division is one of the core operations in mathematics. It is the process of splitting a number into equal parts. When dividing numbers, always follow the order of operations. In the exercise, we start with the division:
The problem is: \[ 33 \div 3 + 8 \cdot 2 \]
As per PEMDAS, we handle the division first: \[ 33 \div 3 = 11 \]This means dividing 33 by 3 equals 11. Once division is complete, we can move on to the next operations. Remember that dividing must be done before addition in any mixed operation problem, following PEMDAS.

Next up is multiplication, another fundamental operation in math. Like division, multiplication takes priority over addition and subtraction in PEMDAS. In our specific problem:
After finishing division, we have: \[ 11 + 8 \cdot 2 \]Next, we must handle the multiplication:
\[ 8 \cdot 2 = 16 \]Multiplying 8 by 2 gives us 16. Multiplication simplifies multiple items into one quantity quickly and is crucial in solving math problems according to the order of operations. Now, with both division and multiplication done, the only remaining step is addition.

Addition is usually the final operation in the order of operations unless subtraction is present. It involves combining numbers to get their total. Returning to our example, after following PEMDAS, we are left with:
\[ 11 + 16 \]Adding 11 and 16 together:
\[ 11 + 16 = 27 \]So the final answer to the problem 33 divided by 3 plus 8 times 2 is 27. Addition is often the final closing step in many problems and provides the total sum after all other operations are completed.