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!