The Correct Answer to 86–4×4÷2 and the Role of BODMAS
When dealing with mathematical expressions, it is crucial to grasp the correct order of operations to ensure accurate results. Let's explore the expression 86 - 4×4 ÷ 2 and how to solve it correctly, emphasizing the importance of the BODMAS rule.
The Expression Explained
The given expression is 86 - 4×4 ÷ 2. It's important to note that the order of operations significantly impacts the final answer. Without adhering to the proper order, one can either obtain incorrect answers or delay the problem-solving process. Let's break it down step by step.
Understanding the BODMAS Rule
For clarity, let's first define the BODMAS rule, which
stands for:
According to BODMAS, we first perform operations inside brackets, then handle powers and roots, followed by division and multiplication from left to right, and finally addition and subtraction from left to right. In the absence of brackets or orders, we proceed with division and multiplication in the order they appear, then addition and subtraction.
Solving the Expression Correctly
Let's solve the expression following the BODMAS rule.
86 - 4×4 ÷ 2 86 - 16 ÷ 2 (4×4 16) 86 - 8 (16 ÷ 2 8) 78 (86 - 8 78)Therefore, the correct answer to the expression 86 - 4×4 ÷ 2 is 78.
Alternatives and Misconceptions
It is sometimes argued that the expression could be interpreted differently, such as:
4×4 16 16 ÷ 2 8 86 - 8 78 (Correct interpretation) 16 ÷ 2 8 86 - 4 x 8 78 (Correct interpretation under different grouping)However, from the BODMAS rule, the correct interpretation should be 78, not 20. The given interpretations of "10 x 4 ÷ 2" and "10 x 2" leading to 20 and 12 are incorrect because they do not follow the BODMAS rule.
Further Clarification - PEMDAS
For those familiar with the USA, the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is equivalent to BODMAS. Following either PEDMAS or BODMAS, the expression is solved in the same way, emphasizing:
Multiplication and Division before Addition and SubtractionTherefore, the final answer is consistent:
86 - 4×4 ÷ 2 86 - 16 ÷ 2 86 - 8 78Conclusion
Understanding the order of operations, whether through BODMAS or PEMDAS, is crucial in solving mathematical expressions accurately. The correct answer to the expression 86 - 4×4 ÷ 2 is 78, not 20 or 12, as the given alternative methods do not follow the proper order of operations.
By adhering to the BODMAS rule, you ensure consistency and correctness in your mathematical computations, avoiding common pitfalls and ensuring clarity in problem-solving.