Math Problem Solved: Step-by-Step Guide

Hey guys! Let's dive into solving the math problem: $45 ÷ (-9) × 24 - 81 ÷ 9 - 24 + 12 - 6 ÷ (-2)$. This might look a little intimidating at first, but trust me, we'll break it down step-by-step to make it super clear and easy to understand. We will be looking at order of operations and how to apply them. It's all about following the rules, and once you get the hang of it, you'll be solving these problems like a pro! So, grab your calculators (or just use your brainpower!), and let's get started. We'll make sure to explain everything in a way that's easy to follow, no matter your math background. It's like a fun puzzle, and we're here to put the pieces together. Get ready to boost your math skills and feel confident tackling similar problems in the future. Remember, practice makes perfect, and with each step, you'll get more comfortable and faster at solving these types of equations. Let’s unravel the mysteries of this equation and come out victorious. Let's make math fun and less scary, one step at a time.

Breaking Down the Equation: Order of Operations

Okay, before we jump in, let's quickly recap the order of operations. You might know it as PEMDAS or BODMAS. It stands for:

• Parentheses / Brackets
• Exponents / Orders
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This is the golden rule! It tells us the order in which we need to solve different parts of the equation. So, first, we tackle anything inside parentheses or brackets. Then, we look for exponents or orders (like powers and roots). After that, we do multiplication and division, working from left to right. Finally, we do addition and subtraction, also from left to right. Following this order ensures we get the right answer every time. Think of it as a roadmap; if you follow the directions, you'll arrive at the correct destination. Ignoring this order can lead to all sorts of wrong answers, so it's super important to remember PEMDAS/BODMAS! It helps us to break down complex problems into smaller, manageable steps. This will make it easier to solve the problem and you will be more confident. Remember, understanding the underlying principles is key to mastering these concepts. So let's use the PEMDAS rules to make sure our work is correct.

Step-by-Step Solution

Let's get down to the actual calculation. We'll go through it step by step, so you can see exactly how it's done. Don't worry if it seems like a lot at first; each step is manageable. We will break the problem down into smaller chunks, making it easier to solve. We'll start with the division and multiplication parts of the equation, working from left to right.

Step 1: Division and Multiplication (Left to Right)

First, let's look at the division and multiplication parts of the equation. We’ll go from left to right, like reading a book. Here's what we have:

• $45 ÷ (-9) = -5$
• $-5 × 24 = -120$
• $81 ÷ 9 = 9$
• $-6 ÷ (-2) = 3$

So, after these calculations, the equation becomes: $-120 - 9 - 24 + 12 + 3$. See? We're already making progress by simplifying the expression. It's like peeling an onion; each layer we remove brings us closer to the core. We're effectively reducing the complexity of the equation, making it easier to handle. Now, we are ready to move on the next step!

Step 2: Addition and Subtraction (Left to Right)

Now, let's handle the addition and subtraction. We'll continue to move from left to right. Here's what we have:

• $-120 - 9 = -129$
• $-129 - 24 = -153$
• $-153 + 12 = -141$
• $-141 + 3 = -138$

So, after all the calculations, we end up with the answer: $-138$. See how we've systematically worked through the problem? It’s all about taking it one step at a time and following the order of operations. Doing this method will help you to solve any equation. It doesn't matter how complicated it seems at first; just break it down, follow the rules, and you'll get there. By following these steps, you can confidently solve any similar math problem that comes your way. Always double-check your work, and don't hesitate to practice with more examples. The more you practice, the easier it becomes.

Final Answer and Explanation

So, the final answer to the equation $45 ÷ (-9) × 24 - 81 ÷ 9 - 24 + 12 - 6 ÷ (-2)$ is $-138$. Great job, guys! We've successfully navigated through the equation using the order of operations. By following the steps outlined above, we've arrived at the correct solution. Remember, the key to solving such problems lies in understanding and applying the rules of PEMDAS/BODMAS. The problem might have seemed complex at first, but by breaking it down into smaller steps, we've simplified the process and made it manageable. Now you can use this approach to tackle similar math problems with confidence. Keep practicing, and you'll become a pro in no time! Always take your time, double-check your calculations, and you'll be well on your way to mastering mathematical equations. Remember, with practice and understanding, anything is possible!

Tips for Success

To really nail these kinds of problems, here are a few tips:

• Practice, practice, practice! The more you solve these types of equations, the more familiar you'll become with the order of operations and the quicker you'll be at solving them. Do a variety of problems to become comfortable with different types of numbers and operations.
• Write it out. Don't try to do everything in your head. Write down each step clearly. This helps you avoid mistakes and makes it easier to spot any errors if you need to go back and check your work. Writing things down helps you stay organized and reduces the chances of making a mistake. It also makes it easier to retrace your steps if you get stuck.
• Double-check your work. After you've solved the problem, go back and check each step. Make sure you haven't missed any signs or made any calculation errors. This helps to catch any mistakes before you get the final answer. Double-checking can save you from a lot of unnecessary frustration and help you build confidence in your abilities.
• Use a calculator for the arithmetic. While you want to understand the process, there's no harm in using a calculator for the actual calculations. This will speed things up and reduce the chance of making a simple arithmetic error, allowing you to focus on the order of operations.
• Break it down. Don't try to solve the entire problem in one go. Break it down into smaller, manageable steps, as we've done here. This makes the problem less daunting and easier to solve. Breaking down a complex problem into smaller parts makes the problem more manageable and easier to understand. This is a very valuable skill not only in math but in life in general.
• Understand the signs. Pay very close attention to the signs (+ and -). One small mistake with a sign can change your answer completely.
• Learn from mistakes. If you make a mistake, don't get discouraged. Instead, try to understand where you went wrong. This is a great way to improve your skills. Use mistakes as learning opportunities. Analyze where you went wrong and how to avoid the same mistake in the future.

Conclusion: You Got This!

So, there you have it! We've tackled a math problem together, step by step. We hope this guide has helped you understand how to approach and solve this type of equation. Remember, math is like any other skill; it takes practice and patience. But with the right approach and a little bit of effort, you can master it. Keep practicing, keep learning, and don’t be afraid to ask for help when you need it. Math is a fundamental skill, and mastering it will benefit you in many areas of life. We are confident that you now have a solid understanding of how to solve this type of equation. Keep up the great work, and you'll be amazed at how much you can achieve. We hope that this article has been helpful and has empowered you to tackle similar problems with confidence. Thanks for joining us on this math adventure, and remember, keep practicing and never give up on the fun of solving math problems!