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The Correct Answer to 60÷5(7-5) Explained
The math equation 60÷5(7-5) has gone viral, sparking debates and confusion about the correct answer. While many calculators and online tools produce different results, there’s a clear explanation based on mathematical conventions and the order of operations.
Understanding the Order of Operations
The order of operations, often remembered by the acronym PEMDAS or BODMAS, dictates the sequence in which mathematical operations are performed:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Solving the Equation
Following PEMDAS, we first solve the expression inside the parentheses:
- 60÷5(7-5) = 60÷5(2)
Next, we perform the division, as multiplication and division have equal precedence and are evaluated from left to right:
- 60÷5(2) = 12(2)
Finally, we multiply to get the final answer:
- 12(2) = 24
Historical Context and Notation
The confusion often arises from historical mathematical notation and the ambiguity of the ÷ symbol. In older mathematical texts, the ÷ symbol was sometimes used to represent a fraction, which could lead to different interpretations of the equation. However, modern mathematical conventions clearly define the ÷ symbol as representing division, and the expression 60÷5(7-5) should be interpreted as division followed by multiplication.
Binary Expression Trees
For a more visual understanding, we can use binary expression trees. These trees represent the structure of mathematical expressions, with each node representing an operation and its operands. The tree for 60÷5(7-5) would look like this:
The tree clearly shows that the division operation is performed before the multiplication, leading to the correct answer of 24.
Conclusion
While the equation 60÷5(7-5) may appear ambiguous, the correct answer is 24 based on the established order of operations and modern mathematical conventions. Understanding these conventions is crucial for accurately interpreting and solving mathematical expressions. Remember, always follow PEMDAS (or BODMAS) to ensure you arrive at the correct solution.