Resolving Mathematical Expressions with PEMDAS: A Guide to 12-4÷2/62
Understanding the order of operations is fundamental in mathematics, and for those familiar with acronyms such as PEMDAS (in the United States) or BODMAS (in the United Kingdom), this topic can be particularly interesting. This guide will walk you through the resolution of the mathematical expression 12-4÷2/62, illustrating various interpretations and their outcomes based on different orders of operations.
PEMDAS vs. BODMAS: An Overview
PEMDAS and BODMAS are acronyms used to remember the order of operations in mathematics. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS stands for Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Solving the Expression: 12-4÷2/62
Let's start by solving the expression 12 - 4 ÷ 2 ÷ 62. The key to solving this expression lies in understanding the order of operations. We will follow the PEMDAS/BODMAS principle to ensure accuracy.
Step-by-Step Solution
Division from left to right: 4 ÷ 2 2 2 ÷ 62 1/31 Substitution back into the expression: 12 - 1/31 Perform the subtraction: 12 - 1/31 372 - 1 371/31 ≈ 11.97The final answer, when properly followed, is 11.97 or approximately 12, as shown in the example 12 - 4 ÷ 2 ÷ 62 12 - 2/62 12 - 1/32 11.875. This illustrates the importance of correct interpretation and application of the order of operations.
However, curiosity often leads to different interpretations, such as:
12 - 4 ÷ 2/62 12 - 2/8 12 - 1/4 11.75 12 - 4 ÷ 2/62 12 - 2/62 12 - 1/32 12 - 0.03125 11.96875 12 - 4 ÷ 2/62 8 ÷ 1/32 8 × 32 256 12 - 4 ÷ 2/62 12 - 4 ÷ 1/32 42 - 1/3 41 2/3These variations demonstrate the need for clear and consistent application of the order of operations to avoid ambiguity.
Golden Principle of BODMAS
The BODMAS rule dictates that operations within brackets should be done first, followed by orders (or exponents), then division and multiplication from left to right, and finally addition and subtraction from left to right. Applying this rule to the given expression 12 - 4 ÷ 2/62:
Division first: 4 ÷ 1/32 4 × 32 128 12 - 128/2 12 - 64 Final subtraction: 12 - 64 -52Thus, following the correct order yields the result of -52. It is essential to note that any result other than 2 or -52 would be incorrect based on the standard interpretation of the order of operations.
Conclusion
Understanding and applying the principles of PEMDAS and BODMAS is crucial in solving mathematical expressions accurately. Clear and consistent application ensures that the answer is consistent with established mathematical standards. In the case of 12 - 4 ÷ 2 ÷ 62, the correct interpretation and solution is 11.97 or approximately 12. Any deviation could lead to misunderstandings or incorrect results depending on the interpretation of the order of operations.