Solving [-7-2-642-(2×3)]-(-8-9) A Step-by-Step Guide

Hey guys! Ever stumbled upon a math problem that looks like a cryptic code? Well, today we're going to crack one such puzzle: [-7-2-642-(2×3)]-(-8-9). This isn't just about finding the answer; it's about understanding the order of operations, simplifying complex expressions, and building a solid foundation in mathematics. So, grab your calculators (or your brains, if you're feeling extra sharp!) and let's dive in!

Breaking Down the Expression

At first glance, the expression [-7-2-642-(2×3)]-(-8-9) might seem intimidating. But don't worry, we'll tackle it step by step. The key to solving any mathematical expression is to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us the sequence in which we should perform the operations to arrive at the correct answer. Ignoring this order can lead to some seriously wonky results, and we definitely don't want that!

Our expression has parentheses within parentheses, which means we'll need to work from the innermost set outwards. This is like peeling an onion – we start with the core and work our way through the layers. First, we'll focus on the innermost parenthesis: (2×3). This is a simple multiplication operation that we can easily solve. Once we've dealt with that, we'll move on to the outer parenthesis and simplify the expression within it. Then, we'll handle the subtraction outside the brackets. Breaking the problem down into smaller, manageable chunks makes it less daunting and more solvable. So, let's get started with that innermost operation!

Step 1: Tackling the Innermost Parenthesis (2×3)

Okay, let's kick things off with the innermost parenthesis: (2×3). This is where things get nice and simple, guys. We're dealing with basic multiplication here, and we all know that 2 multiplied by 3 equals 6. So, we can confidently replace (2×3) with 6 in our expression. Our expression now looks like this: [-7-2-642-6]-(-8-9). See? We've already made progress! This is how we conquer complex problems – by breaking them down into smaller, easier-to-digest pieces. Now that we've handled the innermost parenthesis, we can move on to the next layer and continue simplifying. Remember, math is like building with LEGOs – we start with the basic blocks and gradually build something amazing. And in this case, we're building our way to the correct answer!

Step 2: Simplifying the Outer Brackets [-7-2-642-6]

Now that we've conquered the innermost parenthesis, let's turn our attention to the outer brackets: [-7-2-642-6]. This looks a bit more complex, but it's just a series of subtractions. We need to perform these subtractions from left to right to ensure we get the correct result. Think of it like reading a sentence – we start at the beginning and move sequentially to the end. So, let's begin by subtracting 2 from -7. This gives us -9. Our expression inside the brackets now becomes [-9-642-6]. We're making good progress, guys! We've reduced the number of operations we need to perform and are one step closer to simplifying the entire expression. Next, we'll subtract 642 from -9. This is where our understanding of negative numbers comes into play. Remember, subtracting a positive number from a negative number results in an even more negative number. So, let's tackle that next step!

Continuing the Subtraction: -9-642

Alright, let's keep the momentum going! We're at the stage where we need to subtract 642 from -9. This might seem a bit daunting, but it's actually quite straightforward. Think of a number line. You're starting at -9, and you're moving 642 steps further in the negative direction. That means you're going to end up with a larger negative number. To find the result, we simply add the absolute values of the two numbers (9 and 642) and keep the negative sign. So, 9 plus 642 equals 651. And since we're moving in the negative direction, our result is -651. Now our expression inside the brackets looks like this: [-651-6]. We're almost there! We've simplified the expression inside the brackets significantly. We just have one more subtraction to perform within the brackets, and then we can move on to the next part of the problem. Keep up the great work, guys! We're smashing it!

Final Subtraction Within the Brackets: -651-6

We're in the home stretch for simplifying the first set of brackets! We need to perform the final subtraction: -651-6. Just like before, we're subtracting a positive number from a negative number. This means we're moving further into the negative territory on the number line. So, we add the absolute values of the numbers (651 and 6) and keep the negative sign. 651 plus 6 equals 657. Therefore, -651 minus 6 equals -657. We've successfully simplified the expression inside the first set of brackets! Now we can replace [-7-2-642-(2×3)] with -657 in our original expression. Our expression now looks like this: -657-(-8-9). Wow, guys, we've come a long way! We've tackled the inner parenthesis and simplified the outer brackets. Now, we're ready to move on to the next set of parentheses and continue our journey towards the final answer. Let's keep this momentum going!

Step 3: Simplifying the Second Parenthesis (-8-9)

Okay, let's shift our focus to the second set of parentheses: (-8-9). This is another straightforward subtraction problem involving negative numbers. We're subtracting 9 from -8. Think of it like this: you're already 8 units to the left of zero on the number line, and now you're moving another 9 units to the left. So, we're going even further into the negative numbers. To find the result, we add the absolute values of the numbers (8 and 9) and keep the negative sign. 8 plus 9 equals 17. Therefore, -8 minus 9 equals -17. We've successfully simplified the second set of parentheses! We can now replace (-8-9) with -17 in our expression. Our expression now looks like this: -657-(-17). Notice that we have a double negative here. This is a crucial point, as subtracting a negative number is the same as adding a positive number. This is a common trick in math problems, and understanding it is key to getting the correct answer. So, let's tackle that double negative next!

Step 4: Handling the Double Negative -(-17)

Alright, guys, we've arrived at a crucial point in our problem: the double negative -(-17). This is where things get a little bit… well, positive! Remember, subtracting a negative number is the same as adding its positive counterpart. It's like saying "not not going" – which means you are going! So, -(-17) becomes +17. Our expression now transforms into -657+17. We've eliminated the double negative and simplified our expression even further. We're almost at the finish line! We just have one final addition to perform, and we'll have cracked this mathematical puzzle. This step highlights the importance of understanding the rules of negative numbers. They might seem a bit tricky at first, but once you grasp the concept, they become much easier to work with. So, let's move on to that final addition and claim our victory!

Step 5: The Final Calculation: -657 + 17

Here we are, guys, at the final step! We need to perform the addition: -657 + 17. We're adding a positive number to a negative number. Think of it as moving 17 steps to the right on the number line, starting from -657. Since the negative number has a larger absolute value than the positive number, our final answer will be negative. To find the result, we subtract the smaller absolute value (17) from the larger absolute value (657) and keep the sign of the number with the larger absolute value (which is negative in this case). So, 657 minus 17 equals 640. Therefore, -657 plus 17 equals -640. We've done it! We've successfully solved the expression [-7-2-642-(2×3)]-(-8-9), and the answer is -640. Give yourselves a pat on the back, guys! You've navigated through parentheses, brackets, negative numbers, and the order of operations like true mathematical pros!

Conclusion: Mastering the Order of Operations

So, guys, we've successfully tackled the math puzzle [-7-2-642-(2×3)]-(-8-9) and arrived at the answer: -640. But more importantly, we've reinforced the importance of understanding the order of operations (PEMDAS) and how to work with negative numbers. These are fundamental concepts in mathematics that will serve you well in more complex problems. Remember, math isn't just about getting the right answer; it's about the process of problem-solving and developing critical thinking skills. By breaking down complex expressions into smaller, manageable steps, we can conquer even the most challenging problems. So, keep practicing, keep exploring, and keep having fun with math! And remember, if you ever get stuck, just break it down, step by step, and you'll get there. You've got this!