Solving the Equation 3 - 3 × 6 × 2 and Understanding the Order of Operations

When dealing with mathematical equations, it's crucial to follow the correct order of operations, often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) or BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). This article aims to clarify the correct solution to the equation 3 - 3 × 6 × 2 and explain the importance of the order of operations.

The Correct Solution According to PEMDAS/BODMAS

Let's break down the equation step by step to solve it correctly:

First, perform the multiplication as per the order of operations: 3 × 6 18 Substitute back into the equation: 3 - 18 × 2 Next, perform the remaining multiplication: 18 × 2 36 Substitute back into the equation: 3 - 36 Finally, perform the subtraction: 3 - 36 -33

Therefore, the correct answer based on the order of operations is -33, and not the commonly suggested -13.

Common Misunderstandings and Misinterpretations

There are several common misunderstandings that might lead to incorrect solutions. Let's explore a few of these:

Ignoring Order of Operations: One of the most common errors is failing to follow the order of operations. For example, the equation 3 - 3 × 6 × 2 is often mistakenly solved as:

FIRST: Subtract 3 from 3: 3 - 3 0

SECOND: Multiply by 6: 6 × 2 12

THIRD: Multiply the result by 2: 0 × 12 0

Clearly, this approach is incorrect as it disregards the multiplication that should have been done first. Incorrect Application of Brackets: Another frequent mistake is adding or missing brackets in the equation. For instance, someone might incorrectly write:

3 - 3 × 62 as 3 - (3 × 6) × 2 or 3 - 3 × (62).

Both of these interpretations are also incorrect due to the order of operations. Order of Operations Disregarded: Let's clarify an incorrect solution provided:

3 - 3 × 6 × 2

3 - 182

5 - 18

-13

This solution misses the multiplication step and the order of operations, leading to the incorrect answer of -13.

Conclusion

Understanding the order of operations is key to solving mathematical equations accurately. By following the correct sequence—Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)—we can ensure the right solution. Incorrectly solving the equation 3 - 3 × 6 × 2 results in -33 and not -13, as demonstrated by correctly applying the order of operations.

Key Points to Remember

Always follow the order of operations (PEMDAS/BODMAS). Multiplication and division come before addition and subtraction. Left to right is the order for operations with the same precedence level.

Keywords: order of operations, PEMDAS, BODMAS, equation solving.