Great! Let’s carefully analyze this expression step-by-step:
[
8 \div 2(2+2)
]
Step 1: Evaluate inside the parentheses
[
2 + 2 = 4
]
So the expression becomes:
[
8 \div 2(4)
]
Step 2: Clarify the expression
This now reads:
[
8 \div 2 \times 4
]
Because multiplication by parentheses is implied multiplication, and division and multiplication have the same precedence.
Step 3: Apply the order of operations (PEMDAS/BODMAS)
- Parentheses: done
- Exponents: none
- MD (Multiplication and Division): from left to right
- AS Addition and Subtraction
Step 4: Calculate division and multiplication from left to right
- First: (8 \div 2 = 4)
- Then: (4 \times 4 = 16)
Final Answer: 16
Why the controversy?
Some people interpret (2(4)) as a single denominator (like (8 \div [2 \times 4])), which would change the order:
[
8 \div (2 \times 4) = 8 \div 8 = 1
]
This comes from different conventions in writing implicit multiplication next to division, but according to standard modern algebraic conventions, division and multiplication have equal precedence and are evaluated left to right.
Summary:
- If interpreted strictly as written, answer = 16.
- If parentheses are added around (2(4)), answer = 1.
If you want, I can walk through other similar tricky problems or show how different notation can change outcomes.
