Math Problem: Simplify The Expression

Hey math whizzes and curious minds of Plastik Magazine! Today, we're diving deep into a super interesting math problem that's sure to get your brains buzzing. We've got an expression that looks a little intimidating at first glance, but trust me, guys, once we break it down, it's as easy as pie. The question we're tackling is: What is the value of $\frac{-8(17-12)}{-2(8-(-2))}$? Let's get this party started and figure out the answer, shall we?

Breaking Down the Numerator: The Top Half of the Action

Alright, let's focus on the numerator first, which is the top part of our fraction: $-8(17-12)$. This is where the magic begins, and it's all about following the order of operations, or PEMDAS/BODMAS as you might remember it from school – Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). First, we need to deal with what's inside the parentheses: $(17-12)$. When you subtract 12 from 17, you get a nice, clean 5. So, our numerator simplifies to $-8(5)$. Now, all we have to do is multiply -8 by 5. Remember your rules for multiplying a negative number by a positive number? The result will be negative. So, $-8 \times 5 = -40$. Boom! The top half of our fraction is -40. Not too shabby, right? We've successfully navigated the first step, and the rest of the problem will be just as straightforward if we keep our cool and stick to the plan. This initial step is crucial because it sets the stage for the rest of the calculation. Getting the numerator right means we're halfway to the solution, and that's a great feeling in any math problem, big or small. Keep this -40 in mind as we move on to conquer the denominator!

Decoding the Denominator: The Bottom Half of the Equation

Now, let's move on to the denominator, which is the bottom part of our fraction: $-2(8-(-2))$. Just like with the numerator, we need to tackle the operations inside the parentheses first. Here, we have $(8-(-2))$. Subtracting a negative number is the same as adding its positive counterpart. So, $(8-(-2))$ is the same as $(8+2)$. And what's 8 plus 2? It's a friendly 10! So, our denominator simplifies to $-2(10)$. Now we just need to multiply -2 by 10. Again, remembering our rules for multiplying a negative number by a positive number, the result will be negative. So, $-2 \times 10 = -20$. And there you have it, guys! The bottom half of our fraction is -20. We've successfully simplified both the top and bottom parts of the expression, and now we're ready for the grand finale: dividing the simplified numerator by the simplified denominator. It's been a journey, but we're almost there. This denominator step, like the numerator, requires careful attention to the signs. Dealing with that double negative $\text{(-(-2))}$ is a common spot where mistakes can happen, but by treating it as addition, we've kept things on track. So far, we have $\frac{-40}{-20}$, and the final calculation awaits!

The Grand Finale: Division Time!

We've done the hard work, guys! We've simplified the numerator to -40 and the denominator to -20. Now, all that's left is to perform the division: $\frac{-40}{-20}$. This is where the final answer will reveal itself. When you divide a negative number by another negative number, the result is always positive. So, $\frac{-40}{-20}$ is the same as $\frac{40}{20}$. And what is 40 divided by 20? It's a simple 2! So, the value of the entire expression $\frac{-8(17-12)}{-2(8-(-2))}$ is 2. We nailed it! Looking back at the options provided (A. -4, B. -2, C. 2, D. 4), our calculated answer, 2, perfectly matches option C. It's incredibly satisfying when a complex-looking problem breaks down into such a clear and simple answer. This exercise really highlights the importance of meticulously following the order of operations and being careful with negative signs. Even small slips can send you down the wrong path, but with a methodical approach, you can conquer any mathematical challenge. We hope you found this breakdown helpful and maybe even a little fun. Keep practicing, keep questioning, and keep exploring the amazing world of mathematics! You've got this!

Conclusion: Celebrating the Correct Answer

So there you have it, math enthusiasts! We meticulously worked through the expression $\frac{-8(17-12)}{-2(8-(-2))}$, step by step. We first simplified the numerator, $-8(17-12)$, by calculating $(17-12) = 5$ and then multiplying $-8 \times 5 = -40$. Next, we tackled the denominator, $-2(8-(-2))$. We simplified $(8-(-2))$ to $(8+2) = 10$ and then multiplied $-2 \times 10 = -20$. Finally, we performed the division $\frac{-40}{-20}$. Because a negative divided by a negative yields a positive, the answer is $\frac{40}{20} = 2$. Therefore, the correct option is C. 2. This problem was a fantastic reminder of the power of order of operations (PEMDAS/BODMAS) and the importance of handling negative signs correctly. Each step, from simplifying parentheses to performing the final division, was critical. Remember, even when a problem looks daunting, breaking it down into smaller, manageable parts is the key to finding the solution. Keep that mathematical curiosity alive, and don't shy away from challenges like this. Whether you're a seasoned math whiz or just starting your journey, consistent practice and a willingness to understand each component will lead you to success. We encourage you to try similar problems and solidify your understanding. The world of mathematics is full of fascinating puzzles waiting to be solved, and you're well-equipped to tackle them! Keep up the great work, and we'll see you in the next math adventure!

Answer: C. 2