A seemingly simple math problem intended for children has recently become the center of a heated debate among adults, with many unable to agree on the correct answer. The problem in question is:
8 ÷ 2(2 + 2) = ?
At first glance, this equation appears straightforward, but differing interpretations of the order of operations have led to two primary solutions: 1 and 16. Let’s explore how each answer is derived.
Solution Leading to 16:
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Parentheses First: Calculate the expression inside the parentheses.
2 + 2 = 4
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Rewrite the Equation: Substitute the result back into the equation.
8 ÷ 2(4)
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Interpret Multiplication: Recognize that 2(4) implies multiplication.
8 ÷ 2 × 4
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Perform Division and Multiplication from Left to Right:
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First, divide: 8 ÷ 2 = 4
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Then, multiply: 4 × 4 = 16
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Therefore, one interpretation yields an answer of 16.
Solution Leading to 1:
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Parentheses First: Calculate the expression inside the parentheses.
2 + 2 = 4
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Rewrite the Equation: Substitute the result back into the equation.
8 ÷ 2(4)
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Interpret as a Single Term: Some interpret 2(4) as a single term (2 × 4 = 8).
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Perform Division:
- Divide: 8 ÷ 8 = 1
Thus, another interpretation yields an answer of 1.
The Core of the Debate:
The crux of the disagreement lies in the interpretation of the expression 2(4) following the division. Traditional 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)), dictates that multiplication and division should be performed from left to right as they appear. However, the notation 2(4) can be perceived as implying a single entity, leading some to prioritize the multiplication differently.
Clarifying the Notation:
Mathematical notation can sometimes be ambiguous, and clarity is crucial to avoid misinterpretation. In this case, rewriting the original problem with explicit multiplication can help:
8 ÷ 2 × (2 + 2)
Following standard order of operations:
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Parentheses First: 2 + 2 = 4
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Rewrite: 8 ÷ 2 × 4
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Left to Right Calculation:
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First, divide: 8 ÷ 2 = 4
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Then, multiply: 4 × 4 = 16
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This approach supports the answer of 16.
Conclusion:
While the debate highlights how mathematical expressions can be interpreted differently based on notation and individual understanding, adhering to standard mathematical conventions leads to the answer of 16. This discussion underscores the importance of clear notation and a solid grasp of the order of operations to ensure consistency and accuracy in mathematical problem-solving.
