Your explanation of simplifying the expression is mostly clear, but let's go through it step by step carefully:

Problem:

$8 \div 2(2 + 2)$

Step 1: Simplify inside the parentheses

First, solve what's inside the parentheses:

$2 + 2 = 4$

Now the expression becomes:

$8 \div 2(4)$

Step 2: Division and Multiplication (Left to Right)

When dealing with division and multiplication, the order of operations (PEMDAS/BODMAS) states that you should handle these operations from left to right.

1. First, divide 8 by 2:

   $8 \div 2 = 4$

2. Now multiply the result by 4:

   $4 \times 4 = 16$

Final Answer:

$16$

The final result is 16, and this matches your conclusion. You applied the rules of the order of operations correctly by simplifying the parentheses first, and then performing division and multiplication left to right.

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Do you need more details on any step or have questions about the rules of operations?

Here are 5 related questions:

1. How would the expression change if it were written as $\frac{8}{2(2+2)}$?
2. Can you explain why division and multiplication must be done left to right?
3. What happens if there's an exponent involved in an expression like $8 \div 2^2(2+2)$?
4. How does PEMDAS help in organizing the order of operations?
5. What is the difference between evaluating $8 \div 2(4)$ and $8 \div (2 \times 4)$?

Tip:

Always handle multiplication and division as they appear from left to right after simplifying parentheses to avoid confusion.