Understanding the Correct Order of Operations for 6/221

The problem of evaluating the expression 6/221 can often stump students and challenge even experienced mathematicians. This article aims to clarify the correct order of operations and demonstrate how to approach such expressions using the BODMAS (or PEMDAS) rule. Let's delve into the details and explore the different interpretations.

1. The BODMAS Rule

The acronym BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. This mnemonic guide ensures that operations are performed in the correct order to achieve the right result.

BODMAS Explained with 6/221

Given the expression 6/221, let's break it down using the BODMAS rule:

Brackets: There are no brackets in this expression. Orders: There are no exponents or powers involved. Division: The division operation is clearly defined in the expression. Multiplication: No multiplication is explicitly visible in the expression. Addition: No addition is present in the expression. Subtraction: No subtraction is visible in the expression.

Based on the BODMAS rule, we need to perform the division operation next. Here's how it works:

6 ÷ (2 * 3)  6 ÷ 6  1

Therefore, the correct answer is 1 when applying the BODMAS rule correctly, which respects the order of operations in the expression.

2. Alternative Interpretations and Confusion

However, the expression can be misinterpreted, leading to different results. Let's explore alternative interpretations and address the confusion:

Example 1: 1/2 Can Be Divided by Any Whole Number

A common misconception is that 1/2 can be divided by any whole number. While this may seem intuitive, it is not mathematically correct. Let's consider the expression:

6 ÷ 212  (6 ÷ 2) * 3  3 * 3  9

In this case, the expression is simplified as follows:

6 ÷ 2 3 3 * 3 9

So, the answer is 9 if we consider the expression in this manner.

Example 2: Order of Operations Matters

When solving the expression 6 ÷ 2(1 2), the order of operations (BODMAS) dictates that we first perform the operation within the parentheses:

1 2 3 6 ÷ 2 3 3 * 3 9

Thus, the correct answer is 9 using the standard order of operations.

3. Conclusion

The correct order of operations for the expression 6/221 is determined by the BODMAS rule, and the result greatly depends on how the expression is interpreted. When strictly following the rule, the answer is 1. However, when considering alternative interpretations and operation sequences, the answer can range from 1 to 9 depending on the context and the order in which operations are performed.

To prevent such ambiguity, it's always recommended to clearly define the expression and use parentheses to specify the intended order of operations. This clarity avoids confusion and ensures accurate results.

References

Math is Fun - Order of Operations

Mathway - Order of Operations