Understanding the Expression 6 ÷ (2(21)) and Its Correct Solution
When solving mathematical expressions, it's crucial to follow the correct order of operations to arrive at the accurate result. The expression 6 ÷ (2(21)) can be particularly tricky due to its use of parentheses. Let's break it down step-by-step using the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, and Subtraction) to ensure clarity and accuracy.
Brackets (B): The first step is to solve the expression within the parentheses.
6 ÷ (2(21))
First, solve the operation inside the parentheses: 2(21).
2(21) 2 × 21 42
So the expression now becomes: 6 ÷ 42.
Division (D)
The next step is to perform the division operation.
6 ÷ 42 0.142857 (approximately)
It's important to note that the expression provided in the initial examples (6 ÷ 221 and 6 ÷ 22 1) can be misleading. These expressions do not require parentheses and should be solved differently.
Solving 6 ÷ 221
In the expression 6 ÷ 221, there are no parentheses or exponents. Therefore, we solve this step-by-step using the correct order of operations (BODMAS).
Step 1: No operations in parentheses.
The expression is: 6 ÷ 221
Step 2: Perform the division.
6 ÷ 221 0.02712 (approximately)
Solving 6 ÷ 2 21
The expression 6 ÷ 2 21 is ambiguous. To resolve ambiguity, we need to clarify the expression. Assuming the expression is 6 ÷ (2(21)), we have already found the solution to be approximately 0.142857.
Clarification: Why BODMAS is crucial.
BODMAS helps ensure that mathematical operations are performed in the correct order, preventing errors. For instance:
6 ÷ (2(21)):
1. Solve the parentheses: 2(21) 42
2. Perform the division: 6 ÷ 42 0.142857 (approximately)
Common Pitfalls and Correct Solutions
It's easy to make mistakes when not following the BODMAS rule. Here are a few common pitfalls and their correct solutions:
Pitfall: Not Solving Parentheses First
Example: 6 ÷ 2(21)
Incorrect Solution: 6 ÷ 2 3, then 3 × 21 63
Correct Solution: First, solve the parentheses: 2(21) 42, then 6 ÷ 42 0.142857 (approximately)
Pitfall: Incorrect Order of Division and Multiplication
Example: 6 ÷ 2 × 21
Incorrect Solution: 6 ÷ 2 3, then 3 × 21 63
Correct Solution: Perform division and multiplication from left to right: 6 ÷ 2 3, then 3 × 21 63
Conclusion
Understanding and correctly applying the BODMAS rule is essential for solving mathematical expressions accurately. From parentheses to division, multiplication, and beyond, each step is crucial. Misinterpretation or lack of adherence to the rule can lead to incorrect results, as seen in the ambiguous and misleading expressions provided. Always clarify any ambiguity in mathematical expressions to avoid errors.