Solving [(-180)+(-220)]+(-144) A Step-by-Step Guide For Everyone

Hey guys! Ever get those math problems that look like a jumbled mess of numbers and parentheses? Don't worry, we've all been there. Today, we're going to break down a problem that might seem a bit intimidating at first glance: [(-180)+(-220)]+(-144). I promise, by the end of this guide, you'll be able to tackle similar problems with confidence. We will solve this mathematical equation step by step, using simple language and clear explanations so everyone can understand. Whether you're a student brushing up on your math skills or just someone who enjoys a good mental workout, you're in the right place. Let's dive in and make math a little less scary, and a lot more fun!

Understanding the Basics: Order of Operations

Before we even touch the numbers, let's quickly revisit a crucial concept: the order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Both acronyms essentially tell us the same thing: the sequence in which we should perform mathematical operations to get the correct answer. This is crucial for ensuring we solve the equation correctly. The order of operations acts as a roadmap for solving mathematical expressions. It dictates which operations should be performed before others, ensuring we arrive at the correct answer. Think of it like following a recipe; you wouldn't bake a cake before mixing the ingredients, right? Similarly, in math, certain operations take precedence.

• Parentheses/Brackets First: Anything inside parentheses or brackets needs to be tackled first. This is like the most important task on our to-do list. When you encounter an expression enclosed in parentheses, your primary focus should be simplifying it before moving on to other operations. Parentheses act as a container, grouping specific parts of an equation that need to be resolved as a single unit. This ensures that the operations within them are prioritized, maintaining the mathematical integrity of the problem. Imagine the parentheses as a fortress; you must conquer what's inside before moving on to the outside world. For example, in our problem [(-180)+(-220)]+(-144), the first thing we'll do is simplify the expression inside the brackets.
• Next Up: Exponents/Orders: If there are any exponents or orders (like squares or cubes), we deal with those next. Exponents represent repeated multiplication, and understanding them is fundamental to more advanced mathematical concepts. They show how many times a number (the base) is multiplied by itself. For instance, 2^3 (2 cubed) means 2 * 2 * 2, which equals 8. Dealing with exponents early in the order of operations helps simplify the expression and sets the stage for subsequent calculations. They essentially amplify the value of a number, so addressing them sooner rather than later ensures accurate results.
• Multiplication and Division: These operations have equal priority, so we perform them from left to right. This is where the left-to-right rule comes into play, ensuring we maintain consistency and avoid ambiguity in our calculations. Multiplication and division are inverse operations, and both involve scaling numbers up or down. Multiplication combines groups of equal sizes, while division splits a quantity into equal parts. Since they are equally important, we address them in the order they appear in the equation, much like reading a sentence from left to right.
• Addition and Subtraction: Finally, we handle addition and subtraction, also from left to right. Like multiplication and division, addition and subtraction are inverse operations with equal priority. Addition combines values, while subtraction finds the difference between them. When faced with a mix of addition and subtraction, we perform the operations sequentially from left to right, ensuring we maintain the correct mathematical flow and arrive at the accurate result.

By remembering and applying PEMDAS/BODMAS, we can ensure that we solve mathematical expressions in the correct order, leading to accurate and consistent results. This is a fundamental principle in mathematics, providing a clear and structured approach to problem-solving.

Step-by-Step Solution: Cracking the Code

Okay, now that we've refreshed our memory on the order of operations, let's tackle the problem: [(-180)+(-220)]+(-144). We're going to break it down into easy-to-follow steps.

Step 1: Focus on the Parentheses/Brackets

According to PEMDAS/BODMAS, we need to deal with what's inside the brackets first. We have (-180)+(-220). Remember, adding a negative number is the same as subtracting. So, this becomes -180 - 220.

Think of it like this: you're already 180 dollars in debt, and then you borrow another 220 dollars. Your total debt is going to be the sum of those two amounts. When adding two negative numbers, we essentially add their absolute values and keep the negative sign. The absolute value of a number is its distance from zero, regardless of direction. So, the absolute value of -180 is 180, and the absolute value of -220 is 220. Adding these together, we get 180 + 220 = 400. Since both numbers were negative, our result is -400.

Therefore, (-180)+(-220) = -400. We've successfully simplified the expression within the brackets. This step is crucial because it reduces the complexity of the problem, making it easier to manage. By addressing the parentheses first, we're following the order of operations and setting the stage for the next steps. It's like clearing the first hurdle in a race, preparing us for the challenges ahead. Make sure you get this first step right, as any error here will propagate through the rest of the solution. Double-check your addition and the negative sign to ensure accuracy. With the brackets resolved, the equation now looks much simpler, and we're ready to move on to the next operation.

Step 2: Rewrite the Equation

Now that we've simplified the expression inside the brackets, we can rewrite the equation. Our original problem was [(-180)+(-220)]+(-144). We found that (-180)+(-220) = -400. So, we can substitute -400 back into the equation, giving us -400 + (-144). Rewriting the equation helps us see the next step more clearly. It's like organizing your workspace before starting a new task. By simplifying the equation, we've reduced the number of operations we need to perform, making the problem less intimidating. This step is all about clarity and setting ourselves up for success.

Step 3: Adding the Remaining Numbers

We're now left with -400 + (-144). Again, adding a negative number is the same as subtracting. This means we can rewrite the expression as -400 - 144. Remember the debt analogy from earlier? Imagine you owe 400 dollars, and then you borrow another 144 dollars. How much do you owe in total? When adding two negative numbers, we add their absolute values and keep the negative sign. The absolute value of -400 is 400, and the absolute value of -144 is 144. Adding these together, we get 400 + 144 = 544. Since both numbers were negative, our final result is -544.

Therefore, -400 + (-144) = -544. We've successfully performed the addition and arrived at our final answer. This step demonstrates the importance of understanding how negative numbers work in addition and subtraction. By applying the rules correctly, we can confidently navigate these types of calculations and arrive at the accurate result. Always double-check your work, especially when dealing with negative numbers, to ensure you haven't made any sign errors. With this final step completed, we've successfully solved the problem and can confidently state our answer.

The Final Answer: -544

So, after breaking down the problem step by step, we've arrived at the solution: [(-180)+(-220)]+(-144) = -544. Woohoo! You've done it! We started with a seemingly complex expression and, by following the order of operations and carefully working through each step, we've successfully found the answer. This result represents the final outcome of all the mathematical operations we performed. It's the single number that summarizes the entire equation. When presenting your final answer, it's a good practice to double-check your work and ensure you haven't made any errors along the way. You can even use a calculator to verify your solution. The final answer is the culmination of your efforts, and it's important to be confident that it's correct.

Practice Makes Perfect: Tips and Tricks

Now that you've mastered this problem, let's talk about how to keep those math skills sharp. Like any skill, math requires practice. The more you work at it, the more comfortable and confident you'll become. Here are some tips and tricks to help you along the way:

• Practice Regularly: The key to mastering any math concept is consistent practice. Try solving similar problems regularly. Even just 15-20 minutes of practice a day can make a big difference. Consistent practice reinforces the concepts you've learned and helps you develop fluency in solving problems. Think of it like learning a musical instrument; you wouldn't expect to become a virtuoso without regular practice, and math is no different. Regular practice also helps you identify areas where you might need extra help, allowing you to focus your efforts where they're most needed.
• Break Down Complex Problems: As we did in this guide, break down complex problems into smaller, more manageable steps. This makes the problem less intimidating and easier to solve. When faced with a daunting math problem, it's tempting to feel overwhelmed. However, by breaking it down into smaller, more digestible steps, you can tackle each component individually. This approach not only simplifies the problem but also makes it easier to identify and correct any errors along the way. Each step becomes a mini-milestone, providing a sense of accomplishment and motivating you to continue.
• Use Visual Aids: Sometimes, visualizing the problem can help. Draw diagrams or use number lines to understand the concepts better. Visual aids can be particularly helpful when dealing with abstract concepts like negative numbers or fractions. A number line, for example, can make it easier to visualize the addition and subtraction of negative numbers. Diagrams can help you understand the relationships between different quantities in a word problem. By engaging your visual senses, you can create a more concrete understanding of the mathematical concepts involved.
• Don't Be Afraid to Ask for Help: If you're stuck, don't hesitate to ask a teacher, tutor, or friend for help. There's no shame in seeking assistance, and sometimes a fresh perspective can make all the difference. Asking for help is a sign of strength, not weakness. It demonstrates that you're committed to learning and willing to seek out the resources you need. When you encounter a roadblock in your mathematical journey, talking to someone else can often provide clarity and insight. A teacher, tutor, or friend might explain the concept in a different way that resonates with you, or they might point out a simple error that you've overlooked.
• Make it Fun! Math doesn't have to be a chore. Try using online games or puzzles to make learning more enjoyable. There are countless resources available online that can make math learning fun and engaging. Math games and puzzles can help you develop your problem-solving skills in a playful and interactive way. They can also make the learning process less stressful and more enjoyable, which can ultimately lead to greater success. Explore different resources and find what works best for you, whether it's online games, interactive quizzes, or real-world applications of mathematical concepts.

By incorporating these tips into your math practice, you can build a strong foundation and develop a positive attitude towards math. Remember, everyone learns at their own pace, so be patient with yourself and celebrate your progress along the way.

Conclusion: You've Got This!

So, there you have it! We've successfully solved [(-180)+(-220)]+(-144) and explored some valuable tips for mastering math. Remember, math is like a puzzle – it might seem challenging at first, but with the right approach and a little practice, you can solve anything. Keep practicing, stay curious, and don't be afraid to ask for help when you need it. You've got this! We took a step-by-step journey, unraveling the layers of this equation and arriving at the final answer of -544. Along the way, we emphasized the importance of the order of operations, the rules of adding negative numbers, and the value of breaking down complex problems into manageable steps. The process of solving this equation not only enhances our mathematical skills but also cultivates critical thinking and problem-solving abilities that are valuable in various aspects of life.

Math is more than just numbers and equations; it's a powerful tool for understanding the world around us. Whether you're calculating the tip at a restaurant, managing your finances, or designing a building, math is an essential skill. By developing your mathematical abilities, you're empowering yourself to make informed decisions, solve real-world problems, and pursue your goals with confidence. Embrace the challenges that math presents, celebrate your successes, and never stop learning.

So, let's recap our key takeaways: We started by understanding the problem and identifying the operations involved. We then applied the order of operations (PEMDAS/BODMAS) to guide our solution process. We carefully performed each step, paying close attention to the rules of adding and subtracting negative numbers. Finally, we arrived at the correct answer and celebrated our achievement. With the strategies and tips we've discussed, you're well-equipped to tackle similar mathematical challenges in the future. Remember, practice, patience, and a positive attitude are your greatest allies in the world of math. Keep exploring, keep learning, and keep growing your mathematical prowess. You've got this!