Solving Math: -125 - 100 : 2 + (-3 - (-10) × 4) Explained
Guys, let's dive into a mathematical adventure! We're going to solve the expression -125 - 100 : 2 + (-3 - (-10) × 4). This might seem a bit daunting at first, but trust me, with the right approach and a little bit of patience, we'll crack it! This is a great way to brush up on your arithmetic skills and understand the order of operations. Let's break it down step by step, making sure we don't miss any important details. We'll explain everything in a way that's easy to understand, so even if you're not a math whiz, you'll be able to follow along. Ready to get started? Let's go!
Understanding the Order of Operations (PEMDAS/BODMAS)
Before we jump in, it's super important to understand the order of operations. You might have heard of PEMDAS or BODMAS. Both are essentially the same, just with different names for the first step. PEMDAS stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is similar, with Brackets, Orders (powers/indices), Division and Multiplication, and Addition and Subtraction. These rules are crucial because they tell us the order in which we need to perform calculations to get the correct answer. Without following this order, you'll likely end up with a wrong answer, and nobody wants that, right? So, let's remember PEMDAS/BODMAS as our guide. It's like a roadmap for our mathematical journey. First, we deal with what's inside the parentheses or brackets. Then we handle any exponents or orders. After that, we tackle multiplication and division from left to right, and finally, we take care of addition and subtraction from left to right. Got it? Great! Now, let's apply this to our problem.
Parentheses/Brackets First
Our expression is -125 - 100 : 2 + (-3 - (-10) × 4). According to PEMDAS/BODMAS, we start with the parentheses. We have the expression (-3 - (-10) × 4) inside the parentheses. Inside this, we see multiplication, so we'll handle that first. Remember, multiplication and division come before addition and subtraction. So, (-10) × 4 = -40. Now our expression inside the parentheses becomes (-3 - (-40)). Double negatives become positive, so -3 - (-40) is the same as -3 + 40, which equals 37. Now, we've simplified the expression inside the parentheses to just 37.
Back to the Main Expression
Now our main expression has become -125 - 100 : 2 + 37. We've dealt with the parentheses, so the next step is to look for any exponents or orders, but we don't have any in this problem. So, we move on to the next step which is division and multiplication. Here, we have 100 : 2. This means 100 divided by 2, which is 50. Our expression is now -125 - 50 + 37. We're getting closer!
Addition and Subtraction
Finally, we move on to addition and subtraction from left to right. First, we have -125 - 50. This is like owing someone 125 and then owing them another 50. So, it becomes -175. Our expression is now -175 + 37. This means we have -175 and add 37. So, -175 + 37 = -138. And there you have it, folks! We've solved the expression! The answer is -138. Wasn't that fun? By following the order of operations step-by-step, we've successfully tackled this math problem. Remember to practice, and you'll get better at it every time. Math can be like a puzzle, and solving it is incredibly rewarding. Keep up the great work!
Step-by-Step Solution
Let's recap the solution step-by-step to make sure everything is crystal clear.
- Original Expression: -125 - 100 : 2 + (-3 - (-10) × 4)
- Parentheses/Brackets: (-10) × 4 = -40
- Inside Parentheses: -3 - (-40) = -3 + 40 = 37
- Modified Expression: -125 - 100 : 2 + 37
- Division: 100 : 2 = 50
- Modified Expression: -125 - 50 + 37
- Subtraction: -125 - 50 = -175
- Addition: -175 + 37 = -138
- Final Answer: -138
See? That's all it takes. By breaking down the problem into smaller, manageable steps, we make it much easier to solve. This approach is useful not just for math problems, but also for many other challenges in life. The key is to analyze the problem, make a plan, and then execute the plan step-by-step. This systematic approach helps us avoid mistakes and arrive at the correct solution. Also, remember that practice makes perfect. The more you practice, the more confident you'll become in tackling these types of problems. Don't be afraid to make mistakes, because mistakes are learning opportunities. Each time you make a mistake, you learn something new, which helps you improve your skills. So, keep practicing, keep learning, and you'll master these concepts in no time. Always double-check your work, because that's a great way to ensure you haven't missed anything. Also, it's okay to ask for help if you're stuck. Math is much more fun when you solve it together.
Tips for Solving Mathematical Expressions
Here are some useful tips to help you solve mathematical expressions more easily and accurately. Remember, these tips are like secret weapons in your math arsenal! Firstly, always remember and apply the order of operations (PEMDAS/BODMAS). This is the golden rule for solving any mathematical expression, as it provides the correct sequence of calculations. Make sure you don't skip any steps. Write down each step clearly to avoid confusion and mistakes. Secondly, break down the problem into smaller parts. Large expressions can seem overwhelming, so break them down into simpler, manageable steps. This helps you focus on one part at a time, making the process less daunting. Thirdly, use parentheses to clarify the order. If you're unsure about the order of operations, use parentheses to explicitly state the sequence of calculations. This can help avoid confusion and make your intentions clear. Next, double-check your work. After you've solved an expression, go back and review your calculations to catch any errors. It's easy to make a mistake, so a quick review can save you from a wrong answer. Also, practice regularly. The more you practice solving expressions, the more comfortable and proficient you'll become. Try working through different types of problems to familiarize yourself with various mathematical concepts. Finally, seek help when you need it. If you get stuck, don't hesitate to ask for help from a teacher, classmate, or online resource. Sometimes, a fresh perspective can clarify things and help you understand the problem better. Remember, learning math is a journey, not a race. Embrace the process, stay curious, and keep practicing, and you'll be amazed at how far you can go. Never give up! You got this!
Common Mistakes and How to Avoid Them
Let's talk about some common mistakes people make when solving math problems, and how we can avoid them. This is like having a shield against the most frequent pitfalls. One of the most common mistakes is not following the order of operations. This leads to incorrect answers, so always remember PEMDAS/BODMAS! Make sure to solve in the correct order. Second, careless errors in calculations. This is when you make mistakes in simple calculations like adding, subtracting, multiplying, or dividing. To avoid this, always double-check your work, and use a calculator if you are allowed to, especially for long calculations. Always take your time, and write down each step. Third, misunderstanding the meaning of parentheses. Parentheses can be tricky, so be sure to understand what's inside of them. Sometimes people skip the parentheses, or they calculate the contents of the parentheses incorrectly. Remember, parentheses should always be solved first. Fourth, incorrectly handling negative numbers. Many people struggle with adding and subtracting negative numbers. Remember that subtracting a negative number is the same as adding a positive number. Fifth, forgetting to distribute. If you're dealing with expressions that involve distribution, don't forget to distribute correctly to each term inside the parentheses. Finally, not showing your work. It's easy to make mistakes if you try to do everything in your head. Write down each step clearly to help you spot mistakes and understand your process. By being aware of these common mistakes and taking the time to avoid them, you can improve your accuracy and confidence when solving mathematical expressions. Always be meticulous and patient when you're working on a math problem. Every little detail counts.