Solve -9+{-6*[-3+(-2-5)-6]+2} Step-by-Step

by Mei Lin 43 views

Hey guys! Ever stumbled upon a math problem that looks like it belongs in a cryptic puzzle rather than a textbook? Well, I recently tackled one that fits the bill perfectly: -9+{-6[-3+(-2-5)-6]+2}*. It's got parentheses, brackets, braces, and a whole lot of negative signs – a recipe for potential confusion! But fear not, we're going to break it down step-by-step, making sure everyone understands the logic behind each operation. So, grab your pencils, your thinking caps, and let's dive into this mathematical adventure together!

Unpacking the Problem: -9+{-6*[-3+(-2-5)-6]+2}

Before we even think about crunching numbers, let's take a good, hard look at the expression: -9+{-6[-3+(-2-5)-6]+2}*. The key to conquering any complex math problem is to understand the order of operations. Remember the acronym PEMDAS (or BODMAS, depending on where you learned math)? It stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is our roadmap for solving this equation. We need to peel away the layers of parentheses and brackets like an onion, working our way from the inside out. Ignoring this order can lead to drastically incorrect answers, and we definitely want to avoid that! Think of it like building a house – you need to lay the foundation before you start putting up walls, right? Math is the same way; each step builds upon the previous one. So, let's get started with the innermost layer and work our way out, carefully following PEMDAS to ensure accuracy.

Step 1: Tackling the Innermost Parentheses (-2-5)

Our first mission, as dictated by PEMDAS, is to simplify the innermost parentheses: (-2-5). This might seem simple enough, but it's a crucial step. Remember, subtracting a positive number is the same as adding a negative number. So, (-2-5) is the same as (-2 + (-5)). When adding two negative numbers, we simply add their absolute values and keep the negative sign. In this case, 2 + 5 = 7, so -2 + (-5) = -7. We have successfully conquered the first layer of complexity! This might seem like a small victory, but it's a vital step towards simplifying the entire expression. Imagine trying to solve the whole thing at once – it would be overwhelming! By breaking it down into manageable chunks, we make the problem much less daunting. This also reduces the chance of making errors along the way. Math is all about precision, and taking it step-by-step helps us maintain that precision.

Step 2: Simplifying the Brackets [-3+(-7)-6]

Now that we've dealt with the innermost parentheses, let's move on to the brackets: [-3+(-7)-6]. We've already simplified (-2-5) to -7, so we can substitute that into the expression. This gives us [-3 + (-7) - 6]. Again, let's take it one step at a time. Adding -3 and -7 gives us -10. So now we have [-10 - 6]. Subtracting 6 from -10 is the same as adding -6, so we have -10 + (-6), which equals -16. We've successfully simplified the brackets! Notice how each step builds upon the previous one, making the overall problem more manageable. This is the beauty of the order of operations – it provides a clear path to the solution. By consistently applying PEMDAS, we can tackle even the most complex expressions with confidence. Think of each bracket and parenthesis as a mini-puzzle within the larger puzzle. Once we solve each mini-puzzle, the bigger picture starts to become much clearer.

Step 3: Handling the Braces {-6*[-16]+2}

With the brackets taken care of, we now focus on the braces: **-6*[-16]+2}**. We've simplified the expression inside the brackets to -16, so we can substitute that in. Now we have {-6 * -16 + 2}. According to PEMDAS, multiplication comes before addition. So, we first multiply -6 by -16. Remember, a negative times a negative is a positive! 6 multiplied by 16 is 96. So, -6 * -16 = 96. Now our expression looks like this {96 + 2. Adding 96 and 2 is straightforward: 96 + 2 = 98. We've simplified the braces to 98! This step highlights the importance of remembering the rules of multiplying and dividing negative numbers. A simple sign error can throw off the entire calculation. By carefully applying the rules, we ensure accuracy and maintain the integrity of our solution. Think of this as the bridge between the inner layers and the final answer. We're getting closer to the finish line!

Step 4: The Final Calculation -9 + 98

We've reached the final step! Our expression has been simplified to -9 + 98. This is a simple addition problem. When adding numbers with different signs, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. In this case, 98 is larger than 9, so the answer will be positive. 98 - 9 = 89. Therefore, -9 + 98 = 89. We have successfully solved the problem! It might seem like a long journey, but by breaking it down into smaller, manageable steps, we were able to conquer this mathematical challenge. This final step is where all our previous work pays off. It's the culmination of careful application of PEMDAS, attention to detail, and a systematic approach. And the feeling of arriving at the correct answer? Totally worth it!

The Grand Finale: Solution and Summary

So, after all that mathematical maneuvering, we've arrived at our final answer: 89. The solution to -9+{-6*[-3+(-2-5)-6]+2} is 89. Remember, the key to tackling complex problems like this is to break them down into smaller, more manageable steps. By diligently following the order of operations (PEMDAS), we can avoid confusion and ensure accuracy. Math might seem intimidating at times, but with a systematic approach and a little patience, we can conquer any challenge! Let's recap the steps we took:

  1. Simplified the innermost parentheses: (-2-5) = -7
  2. Simplified the brackets: [-3+(-7)-6] = -16
  3. Simplified the braces: {-6*[-16]+2} = 98
  4. Performed the final addition: -9 + 98 = 89

Each step was crucial in leading us to the correct answer. And more importantly, understanding the process behind each step is what truly solidifies our mathematical skills. So, the next time you encounter a complex equation, remember the power of breaking it down and following the order of operations. You've got this!

Common Pitfalls and How to Avoid Them

Navigating complex mathematical expressions like -9+{-6[-3+(-2-5)-6]+2}* can be tricky, and it's easy to stumble into common pitfalls. Recognizing these potential errors is half the battle! One of the biggest culprits is forgetting the order of operations (PEMDAS/BODMAS). Jumping the gun and performing operations out of order can lead to wildly incorrect answers. Another frequent mistake is mishandling negative signs. It's crucial to remember the rules for multiplying and adding negative numbers. A single sign error can derail the entire calculation. Also, rushing through the steps can lead to careless mistakes. It's always better to take your time, double-check your work, and ensure accuracy at each stage. Another common oversight is failing to simplify expressions fully before moving on to the next step. Make sure each set of parentheses, brackets, and braces is completely simplified before tackling the outer layers. So, how can we avoid these pitfalls? First and foremost, always write out each step clearly and methodically. This helps you keep track of your progress and reduces the chance of making errors. Secondly, double-check your work at each step. It's much easier to catch a mistake early on than to try and backtrack later. And finally, practice makes perfect! The more you work with complex expressions, the more comfortable and confident you'll become in navigating them. Let’s highlight the key strategies:

  • Stick to PEMDAS: Always follow the order of operations religiously.
  • Mind the signs: Pay close attention to negative signs and their interactions.
  • Go slow and steady: Don't rush through the steps; take your time and be thorough.
  • Simplify fully: Ensure each layer is completely simplified before moving on.
  • Practice, practice, practice: The more you practice, the better you'll become.

By being aware of these common pitfalls and implementing strategies to avoid them, you'll be well-equipped to tackle even the most challenging mathematical expressions.

Practice Problems to Sharpen Your Skills

Now that we've dissected the problem -9+{-6[-3+(-2-5)-6]+2}* and discussed common pitfalls, it's time to put your skills to the test! Practice is the key to mastering any mathematical concept. So, let's dive into some similar problems that will help you sharpen your understanding of the order of operations and working with negative numbers. Remember, the goal is not just to get the right answer, but to understand the process behind it. Work through each problem step-by-step, showing your work clearly, and double-checking your calculations along the way. This will help you identify any areas where you might be struggling and reinforce the concepts we've discussed. Don't be afraid to make mistakes – that's how we learn! The important thing is to analyze your errors, understand why they occurred, and adjust your approach accordingly. And if you get stuck, don't hesitate to review the steps we took to solve the original problem or seek help from a teacher, tutor, or fellow student. Math is a collaborative endeavor, and we can all learn from each other. So, grab your pencils, your notebooks, and let's get practicing! Here are a few problems to get you started:

  1. -5 + {4 * [-2 + (1 - 3) - 5] + 10}
  2. 12 - { -3 * [ 7 + (-4 - 2) + 1] - 8 }
  3. -10 + {-2 * [-5 + (-1 - 4) - 3] + 6}

Remember to apply the same principles we used in the original problem: break it down step-by-step, follow PEMDAS, and pay close attention to negative signs. As you work through these problems, you'll start to develop a sense of confidence in your ability to tackle complex mathematical expressions. And that's a feeling worth celebrating!

Conclusion: Mastering the Art of Order of Operations

We've reached the end of our mathematical journey through the expression -9+{-6[-3+(-2-5)-6]+2}*! We started with a seemingly complex problem, but by breaking it down step-by-step and diligently following the order of operations, we were able to arrive at the solution: 89. Along the way, we discussed the importance of PEMDAS, the pitfalls of mishandling negative signs, and the value of consistent practice. Mastering the order of operations is not just about solving specific problems; it's about developing a fundamental skill that will serve you well in all areas of mathematics and beyond. It's about learning to think systematically, to approach challenges methodically, and to persevere even when faced with complexity. So, as you continue your mathematical adventures, remember the lessons we've learned today. Break down problems into smaller steps, follow the rules, double-check your work, and never be afraid to ask for help. Math can be challenging, but it can also be incredibly rewarding. And with a little effort and the right approach, you can conquer any mathematical mountain! Remember guys, keep practicing, keep exploring, and keep challenging yourselves. The world of mathematics is vast and fascinating, and there's always something new to learn. And who knows, maybe you'll even discover a new way to solve a problem that no one has ever thought of before! That's the beauty of mathematics – it's a journey of endless discovery.