Solving 17 X (-155) - 6000 Divided By 4 A Step-by-Step Guide

Hey guys! Ever get those math problems that look like a jumbled mess of numbers and operations? Well, today we're going to tackle one head-on: 17 x (-155) - 6,000 : 4. Don't worry, it's not as scary as it looks! We'll break it down step-by-step, using the order of operations (PEMDAS/BODMAS) to guide us. Think of it like following a recipe – if you follow the steps in the right order, you'll get the perfect result. We will make sure that by the end of this guide, you'll not only be able to solve this specific problem but also feel more confident tackling similar calculations in the future. Remember, math is like building with LEGOs – each step builds upon the previous one. So, let's grab our math tools and dive in! First, we have to understand the basic principles that govern how we approach these calculations. The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), is our guiding star. This tells us the sequence in which we must perform the operations to arrive at the correct answer. Ignoring this order is like trying to build a house without a foundation – it just won't stand! Now, let’s delve deeper into each of these operations and how they play out in our specific problem. Multiplication and division hold a higher precedence over addition and subtraction. This means we need to tackle the multiplication and division parts of our equation before we even think about subtracting. Think of it as clearing the ground before you start building – these initial operations set the stage for the final calculation. Understanding this hierarchy is crucial for getting the right answer, and it’s a principle that applies across all kinds of mathematical problems, making it a valuable tool in your problem-solving toolkit.

Step 1: Multiplication – 17 x (-155)

Alright, let's kick things off with the multiplication part: 17 multiplied by -155. Now, remember that multiplying a positive number by a negative number always results in a negative number. This is a crucial rule to keep in mind, as it affects the sign of our intermediate result. We're dealing with 17 multiplied by -155, so we know our answer for this step will be negative. Let's set up the multiplication, and we'll go through it together. Take your time, and don't rush. Accuracy is key here! This is the foundational block upon which we'll build the rest of our solution, so let’s make sure we get it right. Think of it as laying the first brick in a building – a solid start ensures a stable structure. Now, when you multiply 17 by 155, you'll get 2635. But don't forget the negative sign! So, 17 x (-155) = -2635. That's our first major step completed! We've successfully navigated the multiplication part of our equation, and we have a solid number to work with moving forward. This negative sign is like a little flag reminding us of the direction we're heading in, so let’s keep it in mind as we move to the next stage. We’ve overcome the first hurdle, and the rest of the problem should feel a little less daunting now. Remember, breaking down a complex problem into smaller, manageable steps is a powerful strategy, not just in math, but in all areas of life. Let’s carry this momentum forward as we move on to the division part of our equation.

Step 2: Division – 6,000 : 4

Okay, next up we have the division: 6,000 divided by 4. This one's a bit more straightforward, right? We're figuring out how many times 4 fits into 6,000. Think of it as splitting a large sum equally among four friends. How much does each friend get? Division is the process of breaking a whole into equal parts, and in this case, we’re dividing the whole of 6,000 into four equal portions. This is a common operation in everyday life, from splitting the bill at a restaurant to calculating unit prices at the grocery store. Mastering division is not just about solving math problems; it's about understanding how things are distributed and shared. Now, let's do the math. When you divide 6,000 by 4, you get 1,500. So, 6,000 : 4 = 1,500. Great job! We've handled the division part of our problem, and we now have another crucial piece of the puzzle. This positive result will be used in the next step when we combine it with the negative result from our multiplication. Remember, in math, each operation builds upon the previous one, and having a clear, accurate result at each step is essential for reaching the final answer. We're making excellent progress, and we’re just one step away from solving the entire problem. We’ve successfully navigated both multiplication and division, and now it’s time to bring it all together with subtraction. Let’s move on to the final operation and see how these numbers interact.

Step 3: Subtraction – (-2635) - 1,500

Alright, we're in the home stretch! Now we need to subtract: -2635 minus 1,500. This is where things get a little tricky with negative numbers, so let's take it slow. Remember, subtracting a positive number from a negative number is like moving further into the negative side of the number line. Think of it as owing $2635 and then owing another $1500 – your debt is just getting bigger! This concept of negative numbers and how they interact with subtraction is a fundamental part of understanding math, and it’s something that you’ll encounter in various contexts, from temperature scales to financial calculations. So, let’s make sure we grasp it firmly here. Now, let's do the calculation. When you subtract 1,500 from -2635, you're essentially adding their absolute values and keeping the negative sign. This is because you're moving further to the left on the number line. So, we add 2635 and 1500, which gives us 4135. But remember, we're dealing with negative numbers, so our final answer is -4135. And there you have it! We've successfully solved the problem. We’ve taken a complex-looking equation and broken it down into manageable steps, using the principles of order of operations to guide us. This final step of subtraction brought everything together, and we arrived at the correct answer. We’re not just about getting the right answer, though; it’s also about understanding the process. So, let’s take a moment to review what we’ve done.

Final Answer: -4135

Boom! The final answer is -4135. Give yourself a pat on the back – you tackled a multi-step math problem like a champ! We started with a complex-looking equation and, by methodically applying the order of operations, we arrived at the solution. This process of breaking down a complex problem into smaller, more manageable steps is a key skill in mathematics and in life. It allows us to approach challenges with confidence and clarity, knowing that we can tackle any hurdle by taking it one step at a time. Remember, math is not about memorizing formulas; it’s about understanding the underlying principles and applying them in a logical, step-by-step manner. We started with multiplication, moved on to division, and finally completed the subtraction, each step building upon the previous one. Along the way, we paid close attention to the signs of the numbers, ensuring that our calculations were accurate and our final answer reflected the correct magnitude and direction. Now, take a moment to reflect on the journey we’ve taken together. We’ve not only solved a math problem; we’ve also honed our problem-solving skills and reinforced our understanding of mathematical principles. This experience will serve you well in future challenges, both in and out of the classroom. So, congratulations on your success! You’ve demonstrated the power of step-by-step problem-solving, and you’ve added another tool to your mathematical toolkit. Keep practicing, keep exploring, and keep pushing your boundaries – you’ve got this!

Practice Makes Perfect: Keep Honing Your Skills

So, guys, now that we've conquered this problem, the best way to solidify your understanding is to practice! Try tackling similar problems, playing around with different numbers and operations. You can even create your own problems to challenge yourself and your friends. The more you practice, the more confident you'll become in your math skills. Think of it like learning a musical instrument – you wouldn't expect to play a concerto after just one lesson, right? Math is the same way. Each problem you solve is like a practice session, strengthening your understanding and building your skills. So, don’t be afraid to make mistakes – they’re just opportunities to learn and grow! Embrace the challenge, and remember that every step you take is a step closer to mastery. You might even find that you enjoy the process of problem-solving, the satisfaction of unraveling a complex equation and arriving at the correct answer. Math is not just about numbers; it’s about logic, reasoning, and critical thinking. These are skills that will serve you well in all aspects of life, from making informed decisions to solving real-world problems. So, keep practicing, keep exploring, and keep challenging yourself. You're on a journey of continuous learning, and the more you invest in your skills, the more rewarding the journey will be. And remember, if you ever get stuck, there are plenty of resources available to help you – from online tutorials to textbooks to your classmates and teachers. You’re not alone on this journey, and there’s a whole community of learners ready to support you. So, keep going, keep growing, and keep conquering those math challenges!