Determining the Correct Answer to the Mathematical Expression 3 - 3x3 - 3

Introduction

Mathematical expressions can sometimes present a challenge, especially when it comes to the order of operations. The expression 3 - 3x3 - 3 is a prime example. Various interpretations and answer proposals have been made, but the correct interpretation hinges on understanding the order of operations and the specific rules surrounding multiplication and subtraction.

Understanding the Order of Operations (DMAS Rule)

The order of operations, often remembered by the acronym DMAS (Division, Multiplication, Addition, Subtraction), guides us on how to evaluate such expressions. According to this rule, multiplication takes precedence over subtraction. This is because multiplication is a higher priority operation in the order of operations. Let's break it down step-by-step.

Step-by-Step Solution

First, we perform the multiplication: 3 x 3 9. Next, we substitute the multiplication result back into the expression: 3 - 9 - 3. Finally, we perform the subtraction from left to right: 3 - 9 -6 -6 - 3 -3

Therefore, the correct answer to the expression 3 - 3 x 3 - 3 is -3.

Addressing Different Interpretations

It's important to note that the expression can be interpreted differently based on context and implied grouping. If the expression was meant to be evaluated differently, additional parentheses or brackets would be necessary. For instance, if the expression 3 - (3x3 - 3) were intended, the steps would be:

First, the expression inside the parentheses is evaluated: 3 x 3 - 3 9 - 3 6. Then, the result is substituted back into the original expression: 3 - 6. Finally, the subtraction is performed: 3 - 6 -3.

This interpretation still results in the same answer, but it's essential to recognize why.

Conclusion

The importance of the order of operations cannot be overstated. Applying the DMAS rule consistently ensures a correct and accurate evaluation of mathematical expressions. The expression 3 - 3x3 - 3, when evaluated correctly according to the order of operations, yields the result of -3.