Math Problem Solved: A Step-by-Step Guide
Hey everyone! Let's dive into a cool math problem: (589 + 146) / 15 + (287 - 269) / 3. Don't worry, it looks a bit intimidating, but we'll break it down step by step to make it super easy. This is a classic example of using the order of operations (PEMDAS/BODMAS), which is a fundamental concept in mathematics. Understanding this is key to solving various arithmetic expressions and equations. We'll focus on clarity and a methodical approach so that you can confidently tackle similar problems in the future. We are going to do this together, so grab your calculators (or don't, if you want to practice mental math!), and let's get started! This guide is designed to be user-friendly for everyone, whether you're a math whiz or just brushing up on your skills. The aim is to not just solve the problem but also to understand why each step is taken, reinforcing your grasp of mathematical principles. The core idea behind this problem is to ensure we follow the correct sequence of mathematical operations to arrive at the accurate solution. Failing to adhere to the order of operations could lead to significant errors. This problem provides a fantastic exercise in practicing this crucial skill. It requires us to balance addition, subtraction, division, and the use of parentheses. So, let's get down to it. We'll start by simplifying what's inside the parentheses, as per the order of operations. This is to ensure that we tackle the problem systematically and without confusion. This is more than just finding an answer; it's about building a solid understanding of mathematical principles. By the end, you'll have a clear understanding of how to solve this kind of problem and will be ready to tackle similar ones with confidence. So, are you ready? Let's get started and make math fun!
Step-by-Step Solution
Alright, let's get down to business! First things first, remember the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). We're going to break down the problem (589 + 146) / 15 + (287 - 269) / 3 into manageable parts. This way, we'll avoid making any silly mistakes. This structured approach makes the entire process less daunting. Think of it like a recipe; you follow the steps in order to get the desired outcome. By breaking the problem down, it makes it easier to check each step for accuracy, which is essential to avoid any errors. The first step is to address what's inside the parentheses. This is a critical step because it determines the sequence of computations that follow. Let's take it slow, step by step, okay? We'll handle the operations within the parentheses first, then move on to the division and addition. So, let's begin: The primary goal here is to eliminate the complexity that's often associated with math problems. We'll see how easy it is when we break everything down. This approach also helps in developing your problem-solving skills. By following the given instructions, we'll get the correct answer. This approach is crucial for solving more complex problems in the future. So, get ready, because this will teach you how to approach other more advanced math problems.
Solving the Parentheses
Let's begin by solving the expressions within the parentheses. This is our first major step, so pay close attention! We have two sets of parentheses in the problem: (589 + 146) and (287 - 269). First, calculate 589 + 146. This is a simple addition problem. You can use a calculator, do it by hand, or even use mental math if you're feeling confident. The answer is 735. Now, let's move to the second set of parentheses: (287 - 269). This is a straightforward subtraction problem. Solve it and you'll find that 287 - 269 = 18. The results we just obtained are critical, as they simplify the initial problem into something that is easier to handle. Now we'll simplify the original expression, replacing the parenthesis-based expressions with their simplified values. Remember, these steps are essential to ensuring we follow the correct order of operations. By methodically solving the problems within the parentheses, we prepare for the subsequent steps which require division and addition. The overall objective is to simplify the problem so that we can easily compute the final answer. It is very important to meticulously follow these steps to avoid making any mistakes. Thus, let's proceed to the next part, where we perform division and addition. This will help us get closer to the solution. Remember that we must handle these operations in the order that they appear in the expression. Let’s go!
Performing Division
Great job, guys! Now that we've handled the parentheses, it's time to move on to division. Our expression now looks like this: 735 / 15 + 18 / 3. We need to divide 735 by 15 first. Grab your calculator, or do it longhand – the result of 735 / 15 is 49. Awesome! Next, we need to divide 18 by 3. This is super easy, and you probably already know that 18 / 3 = 6. The importance of division is clearly shown in this step. Now, we have greatly simplified our expression. We have reduced a more complex problem into a sequence of manageable arithmetic operations. We're getting closer to the final answer! The next stage involves addition, which will bring us home. After all, division comes before addition in the order of operations. Ensure that the order of operations is followed meticulously to achieve the correct result. Our objective is to apply mathematical rules and principles step by step. This builds on previous steps, and we finally get closer to the final answer. So, make sure you understand each step as we go along; you're doing great so far! By following the correct steps, we're gradually simplifying the equation, getting closer to the solution step by step. The key here is to break down the problem into the simpler components. This allows us to efficiently execute each computation without missing anything. Are you ready for the last step?
Final Addition
Alright, we're in the home stretch! Our problem has been simplified to 49 + 6. Now it is time for the final operation, which is addition. Adding these two numbers together is a piece of cake: 49 + 6 = 55. And there you have it! The answer to the math problem (589 + 146) / 15 + (287 - 269) / 3 is 55. Congratulations! You've successfully solved the equation. This is a testament to the power of following the order of operations and breaking down complex problems into simple steps. You've now mastered the crucial skill of simplifying a mathematical expression. We have successfully completed the math problem! The solution isn't just about the answer; it is also about understanding the process. So pat yourself on the back, because now you know how to solve this type of problem. From start to finish, this entire process highlights the significance of structured problem-solving. By breaking down the problem and following the correct order of operations, we were able to find the correct answer. Now, you can confidently tackle similar problems, knowing that you have a solid grasp of the underlying principles. Good job!
Recap and Conclusion
So, to recap, here’s what we did: First, we addressed the expressions inside the parentheses. Then, we performed the division operations. Finally, we added the two results together. This step-by-step process ensures that we followed the correct order of operations. Remember, the order of operations (PEMDAS/BODMAS) is your best friend when it comes to solving math problems. Always start with parentheses, then exponents, followed by multiplication and division (from left to right), and finish with addition and subtraction (from left to right). Following these steps consistently helps you avoid making errors. Now, you're all set to tackle similar math problems with confidence. Always remember to break down complex problems into smaller parts. Practice makes perfect, so try solving similar problems to solidify your understanding. This kind of structured approach not only helps you solve problems but also improves your critical thinking skills. By practicing more, you can easily memorize and recall the steps needed for the order of operations. The more problems you solve, the more comfortable you'll become with the process. So, keep practicing, and you will become a math whiz! We believe in you. You now have the tools to conquer any math problem that comes your way. And remember, math can be fun when approached in a step-by-step manner. Keep practicing, keep learning, and never be afraid to ask for help. You’ve got this!