Interpreting Mathematical Expressions: The Case of 100/4 2 3
The expression 100/4 2 3 can be confusing due to the lack of explicit operators, leading to multiple interpretations. This article provides a detailed analysis and offers clarity on how to solve such expressions, emphasizing the importance of understanding the order of operations.
Introduction
Mathematics requires precision, and the ambiguity in the expression '100/4 2 3' can lead to different interpretations. This expression has sparked debate, with some treating it as a fraction and others as individual terms. This article aims to clarify the correct approach to solving this expression using the order of operations (PEMDAS).
Expression Analysis
The expression '100/4 2 3' can be interpreted in two primary ways:
Interpretation as a Fraction
The expression '100/4 2 3' can be seen as a fraction where 100 is the numerator and '4 2 3' is the denominator. This can be written as '100/(4*2 3)'. Let's break it down:
First, solve the denominator: 4*2 3 8 3 11. Then, solve the fraction: 100/11 ≈ 9.09 (rounded to two decimal places).
Interpretation as Terms
A more common interpretation is to treat '4 2 3' as a single term, making the expression '100/4*2 3'. Using the order of operations (PEMDAS), we get:
First, handle the division and multiplication: 100/4 25, then 25*2 50. Next, perform the addition: 50 3 53.
Order of Operations (PEMDAS)
The order of operations (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) simplifies such expressions. Here is the step-by-step process using PEMDAS:
Parentheses: There are no parentheses in the expression. Exponents: There are no exponents in the expression. Multiplication and Division: Solve from left to right. 100/4 25, then 25*2 50. Next, 50 3 53. Addition and Subtraction: The expression has no addition or subtraction.
Conclusion
The correct interpretation and solution of the expression '100/4 2 3' is 53, following the order of operations (PEMDAS). It is crucial to be aware of the context in which such expressions are presented, as they can sometimes be poorly written or intentionally misleading to test understanding.
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