To solve the expression \( 8 \div 2(2+2) \), we need to carefully follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:
1. **Parentheses first**: Simplify inside the parentheses.
   \[
   2 + 2 = 4
   \]
   So, the expression becomes:
   \[
   8 \div 2(4)
   \]

2. **Multiplication and Division**: We proceed from left to right. First, handle the division and multiplication:
   \[
   8 \div 2 = 4
   \]
   Now, we multiply the result by 4:
   \[
   4 \times 4 = 16
   \]

Thus, the final answer is:
\[
\boxed{16}
\]

Would you like more details or clarification on any step? 

Here are some related questions:
1. How does the order of operations (PEMDAS) affect solving expressions?
2. What are the common mistakes when dealing with parentheses in equations?
3. How would adding exponents or roots change the solution process?
4. Could grouping symbols (like brackets) change the outcome of similar expressions?
5. What is the difference between implicit and explicit multiplication?

**Tip**: Always handle multiplication or division from left to right, especially when parentheses are involved, to avoid misinterpretation.

Learn how to solve the mathematical expression 8 ÷ 2(2+2) using the order of operations (PEMDAS). This step-by-step solution simplifies the expression and helps avoid common mistakes, such as misinterpreting parentheses and multiplication. Perfect for students in Grades 5-7.

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