Untangling the Math Debate: Solving 6 ÷ 2(1 2) with BODMAS

Mathematics can be a nuanced and sometimes controversial subject, especially when it comes to the order of operations. The expression 6 ÷ 2(1 2) has sparked considerable debate, with different interpretations leading to seemingly conflicting answers. In this article, we'll explore the correct answer using the BODMAS method, which stands for Brackets, Orders, Division/Multiplication, Addition, and Subtraction.

The Expression Explained

The expression in question is:

```plaintext 6 ÷ 2(1 2) ```
Some people interpret this as a fully bracketed expression, leading to different interpretations. However, the correct approach using the BODMAS method is as follows:

Solving 6 ÷ 2(1 2) with BODMAS

First, let's simplify the expression step by step using the BODMAS method:

Step 1: Order of Operations

According to BODMAS:

Brackets Orders (powers and square roots, etc.) Division and Multiplication (left to right) Addition and Subtraction (left to right)

Let's start with the Brackets:

```plaintext 6 ÷ 2(1 2) ```
6 ÷ 2(3) (since 1 2 3)

Now, the expression is:

```plaintext 6 ÷ 2 × 3 ```
According to BODMAS, we next handle the Division and Multiplication from left to right:

Step 2: Division

```plaintext 6 ÷ 2 ```
3 (since 6 ÷ 2 3)

Now our expression is:

```plaintext 3 × 3 ```

Step 3: Multiplication

```plaintext 3 × 3 ```
9 (since 3 × 3 9)

Therefore, the correct answer is 9, not 8 as some might claim.

It's important to note that the expression provided initially (6 ÷ 2(1 2)) could be misleading. If the intention was to write (6 ÷ 2)(1 2), then the answer would indeed be 8, as shown in the following breakdown:

Alternative Interpretation: (6 ÷ 2)(1 2)

This alternative interpretation, while not explicitly stated, has gained traction due to common notational ambiguity:

Step 1: Order of Operations

Apply BODMAS:

```plaintext (6 ÷ 2)(1 2) ```
(3)(3) (since 6 ÷ 2 3 and 1 2 3)

Now, perform the Multiplication:

```plaintext 3 × 3 ```
9 (since 3 × 3 9)

However, if the notation is intended as implied multiplication, and the expression is actually 6 ÷ 2(1 2), then the grouping takes precedence where 2(1 2) is treated as a single term:

Step 1: Order of Operations (with brackets)

```plaintext 6 ÷ 2(1 2) ```
6 ÷ 2(3) (since 1 2 3)

According to BODMAS, treat this as:

```plaintext 6 ÷ 2 × 3 ```
3 × 3 (since 6 ÷ 2 3)

Now, perform the multiplication:

```plaintext 3 × 3 ```
9 (since 3 × 3 9)

Therefore, the correct answer according to BODMAS is 9.

In conclusion, the interpretation of mathematical expressions is crucial. Using the BODMAS method, the expression 6 ÷ 2(1 2) evaluates to 9, not 8. It's always advisable to be clear with your notation to avoid ambiguity and ensure your calculations are correct.

Have a mathematically enlightening day!