Finding The Missing Step In Evaluating The Expression [(-10+2)-1]+(2+3)

Jul 14, 2025 by ADMIN 72 views

The Missing Step in Evaluating the Expression: A Detailed Breakdown

Navigating the world of mathematical expressions often requires a systematic approach, breaking down complex problems into manageable steps. In this article, we'll dissect a specific mathematical expression, meticulously analyzing each step to pinpoint a missing link in the evaluation process. Our focus centers on the expression [(-10+2)-1]+(2+3), where we aim to identify the crucial step that bridges the gap between the initial expression and its subsequent simplification. This journey will not only enhance our understanding of order of operations but also sharpen our problem-solving skills in mathematics. Let's embark on this mathematical exploration, unraveling the intricacies of the expression and discovering the missing step.

Unveiling the Initial Expression: `[(-10+2)-1]+(2+3)`

At the heart of our exploration lies the expression [(-10+2)-1]+(2+3). This expression, at first glance, might seem daunting, but it's essentially a sequence of arithmetic operations patiently waiting to be executed. To effectively tackle this expression, we must adhere to the fundamental principles of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order serves as our roadmap, guiding us through the expression's simplification process.

Our initial focus will be on the parentheses, the innermost layers of the expression. Inside the brackets [], we encounter (-10+2), a simple addition operation. Performing this addition, we get -8. Now, our expression transforms into [-8-1]+(2+3). We continue working within the brackets, subtracting 1 from -8, which yields -9. This simplifies the bracketed portion to [-9]. Simultaneously, we address the parentheses (2+3), which straightforwardly adds up to 5. Thus, the expression undergoes a significant transformation, morphing into -9 + 5. This methodical reduction of the expression highlights the importance of meticulously following the order of operations, ensuring accuracy at each step. The initial expression, with its layers of operations, is gradually being unveiled, paving the way for the final solution. Understanding this initial breakdown is crucial, setting the stage for identifying the missing step and ultimately solving the expression.

The Given Steps: A Glimpse into the Solution

We are provided with two pivotal steps in the evaluation of our expression, offering a glimpse into the solution's progression. These steps act as guiding markers, helping us navigate the simplification process and pinpoint the missing link. Let's examine these steps closely:

Step 2: $-9 + 2 + 3$

This step presents a simplified form of the original expression. The brackets and parentheses have seemingly vanished, and we are left with a series of additions and subtractions. The appearance of -9 suggests that the operations within the brackets [(-10+2)-1] have been performed, resulting in this value. However, the presence of 2 + 3 indicates that the parentheses (2+3) might not have been fully resolved in the preceding step. This step serves as a crucial checkpoint, showcasing the intermediate stage of the simplification process.

Step 3: $-7 + 3$

In this final step, the expression is further simplified. The -9 and 2 from Step 2 have been combined to produce -7. This indicates that the addition operation -9 + 2 has been executed. The + 3 remains untouched, suggesting that the final addition is yet to be performed. This step brings us closer to the ultimate solution, leaving only one operation to complete. By analyzing these given steps, we gain valuable insights into the expression's simplification journey. We can trace the transformations, observe the operations being performed, and begin to formulate a hypothesis about the missing step that bridges the gap between the initial expression and Step 2. This analytical approach is key to unraveling the puzzle and completing the solution.

Identifying the Missing Step: Bridging the Gap

Our mission now is to reconstruct the missing step, the critical link that connects the initial expression [(-10+2)-1]+(2+3) to Step 2, which is $-9 + 2 + 3$. To accomplish this, we must meticulously analyze the transformations that occur between these two points. The initial expression presents us with nested operations, demanding a systematic approach following the order of operations (PEMDAS). We've already established that Step 2 reflects the simplification of the bracketed portion [(-10+2)-1] to -9. However, the parentheses (2+3) seem to be lingering, not yet fully resolved as a single value.

Therefore, the missing step must involve the execution of the operations within both the brackets and the parentheses. Let's break it down:

Brackets [(-10+2)-1]: As we discussed earlier, -10 + 2 equals -8. Then, subtracting 1 from -8 gives us -9. So, the bracketed portion simplifies to -9.
Parentheses (2+3): This is a straightforward addition, resulting in 5.

Therefore, the missing step should reflect these two simplifications. Combining these results, the missing step should be: $[-9] + 5$. However, since the brackets around a single number don't change its value, we can simply write it as $-9 + 5$. Now, let's compare this to Step 2, which is $-9 + 2 + 3$. We notice a discrepancy: 5 in our deduced step versus 2 + 3 in Step 2. This reveals that the missing step involves simplifying the brackets but not fully resolving the parentheses. The parentheses (2+3) are still present in their original form in Step 2. Thus, the correct missing step should be:

Step 1: $-9 + (2 + 3)$

This step perfectly bridges the gap. It shows the simplification of the brackets to -9 while retaining the parentheses (2+3). This logical deduction, based on the order of operations and a careful comparison of the given steps, allows us to confidently identify the missing link in the expression's evaluation.

Evaluating the Options: Identifying the Correct Expression

We are presented with two options for the missing expression:

A. $[8+1]+(2+3)$
B. $-9 + (2 + 3)$ (This is the expression we deduced)

By carefully comparing these options with our deduced missing step, we can easily identify the correct one. Option A, [8+1]+(2+3), bears no resemblance to the intermediate step we identified. It doesn't reflect the simplification of the original expression's brackets [(-10+2)-1] to -9. Therefore, Option A is incorrect.

Option B, $-9 + (2 + 3)$, perfectly aligns with our deduced missing step. It accurately represents the simplification of the brackets to -9 while maintaining the parentheses (2+3). This option demonstrates a clear understanding of the order of operations and the step-by-step simplification process.

Therefore, the correct missing expression is Option B: $-9 + (2 + 3)$. This confirms our analytical approach and reinforces the importance of meticulously following the order of operations in mathematical evaluations. By correctly identifying the missing step, we complete the logical flow of the solution and pave the way for the final calculation.

Completing the Solution: From Missing Step to Final Answer

Having successfully identified the missing step, we can now complete the solution and arrive at the final answer. Our journey began with the expression [(-10+2)-1]+(2+3), and we've meticulously navigated through the steps, including the crucial missing one. Let's recap the steps:

Step 1: $-9 + (2 + 3)$ (The missing step we identified)
Step 2: $-9 + 2 + 3$ (Given)
Step 3: $-7 + 3$ (Given)

Step 3 brings us to a point where only one operation remains: -7 + 3. This is a straightforward addition, and performing this operation, we get:

-7 + 3 = -4

Therefore, the final answer to the expression [(-10+2)-1]+(2+3) is -4. This result is the culmination of our methodical approach, highlighting the importance of breaking down complex expressions into manageable steps. By carefully following the order of operations and meticulously performing each calculation, we successfully navigated the expression's simplification process. This journey not only provides us with the final answer but also reinforces our understanding of mathematical principles and problem-solving strategies. The ability to dissect expressions, identify missing links, and systematically arrive at solutions is a valuable skill in mathematics and beyond. This exercise serves as a testament to the power of a structured approach in tackling complex problems.

Conclusion: Mastering the Art of Mathematical Evaluation

In this comprehensive exploration, we embarked on a journey to evaluate the expression [(-10+2)-1]+(2+3), focusing on identifying a crucial missing step in its simplification. We meticulously dissected the expression, emphasizing the paramount importance of adhering to the order of operations (PEMDAS). By analyzing the given steps and logically deducing the transformations occurring between them, we successfully identified the missing step as $-9 + (2 + 3)$. This step bridged the gap in the solution process, allowing us to seamlessly progress towards the final answer.

Furthermore, we evaluated the provided options, confidently selecting the expression that aligned perfectly with our deduced missing step. This reinforced the accuracy of our analytical approach and highlighted the significance of careful comparison and logical reasoning in mathematical problem-solving. Finally, we completed the solution, performing the remaining operations to arrive at the final answer of -4. This culmination demonstrated the effectiveness of our methodical approach and showcased the power of a structured strategy in tackling complex mathematical expressions.

This exercise underscores the importance of mastering the art of mathematical evaluation. It's not merely about arriving at the correct answer but also about understanding the underlying principles and developing a systematic approach. By breaking down complex problems into manageable steps, meticulously following the order of operations, and carefully analyzing each transformation, we can navigate the world of mathematics with confidence and precision. The skills honed in this exploration extend beyond the realm of mathematics, equipping us with valuable problem-solving abilities applicable to various aspects of life. This journey serves as a reminder that with a clear understanding of fundamental principles and a structured approach, we can conquer even the most challenging mathematical puzzles.