Solving the Mathematical Equation: 6 ÷ 2(1 2) Across Different Rules

Mathematics can often present confusing problems, especially when it comes to order of operations. The equation 6 ÷ 2(1 2) is a classic example that often leads to disagreements due to the interpretation of the order of operations. Let's explore this equation using BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) and PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) rules.

BODMAS Rule

Firstly, let's break down the equation 6 ÷ 2(1 2) using the BODMAS rule:

Brackets (1 2): Start by solving the expression within the parentheses. 1 2 3 After solving the bracket, the equation becomes 6 ÷ 2 × 3. Division and Multiplication: Perform the division and multiplication from left to right. 6 ÷ 2 3 3 × 3 9

According to this breakdown, the final answer is 9.

PEMDAS Rule

The PEMDAS rule also leads to the same breakdown as BODMAS:

Parentheses (1 2): Solve the expression within the parentheses. 1 2 3. The equation now becomes 6 ÷ 2 × 3. Multiplication and Division: Solve the division and multiplication from left to right. 6 ÷ 2 3. 3 × 3 9.

Thus, following the PEMDAS rule, the answer remains 9.

Alternative Interpretations

Some argue that without the multiplication sign, the equation 2(1 2) can be interpreted as 2 × (1 2).

Brackets (1 2): Solve the expression within the parentheses. 1 2 3. Multiplication (2 × 3): Multiply 2 by the result of the bracket. 2 × 3 6. 6 ÷ 6 1.

According to this interpretation, the answer is 1.

Conclusion

The equation 6 ÷ 2(1 2) can be solved using both BODMAS and PEMDAS to arrive at an answer of 9, provided that the equation is interpreted without the multiplication sign. However, if the multiplication sign is included or interpreted explicitly, the equation results in an answer of 1.

Understanding and applying the correct order of operations is crucial for solving complex mathematical equations. Whether you follow BODMAS or PEMDAS, the consistency in the steps ensures accurate results.