Solving -5 - 10 + 47 A Step-by-Step Mathematical Explanation

Hey guys! Ever stumbled upon a math problem that looks simple but makes you scratch your head? Today, we're diving deep into a seemingly straightforward question: What is the solution to -5 - 10 + 47? This might seem like basic arithmetic, but understanding the underlying principles is crucial for tackling more complex math problems. Let’s break it down step-by-step, ensuring you not only get the answer but also grasp the process. This exploration will not only clarify this particular problem but also enhance your overall mathematical acumen. So, buckle up and let's unravel this numerical puzzle together! Understanding the basics is key to mastering more complex equations, and this problem serves as a perfect stepping stone.

Breaking Down the Problem: -5 - 10 + 47

To effectively solve -5 - 10 + 47, we need to understand the order of operations and how to handle negative numbers. The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), dictates the sequence in which mathematical operations should be performed. In this case, we have subtraction and addition. According to PEMDAS, we perform these operations from left to right. This means we first tackle -5 - 10, and then we add 47 to the result. Dealing with negative numbers can sometimes be tricky, but with a clear understanding of the rules, it becomes much simpler. Visualizing a number line can be incredibly helpful. Imagine starting at -5 and then moving 10 units to the left (because we are subtracting 10). This will give us our first intermediate result. Once we have this, we can then add 47, which means moving 47 units to the right on the number line. By following this methodical approach, we can avoid common pitfalls and arrive at the correct solution. Remember, math is like building blocks; each step is crucial for constructing the final answer. So, let’s get started with the first step: subtracting 10 from -5.

Step 1: Solving -5 - 10

Let's begin by tackling the first part of our equation: -5 - 10. When you subtract a positive number from a negative number, you're essentially moving further into the negative realm. Think of it like owing someone 5 dollars and then owing them another 10 dollars. Your total debt is the sum of these two amounts. In mathematical terms, subtracting 10 from -5 is the same as adding -10 to -5. So, we have -5 + (-10). When adding two negative numbers, you simply add their absolute values and keep the negative sign. The absolute value of -5 is 5, and the absolute value of -10 is 10. Adding these gives us 15. Therefore, -5 + (-10) equals -15. Visualizing this on a number line can provide a clearer understanding. Start at -5 and move 10 units to the left. You will land on -15. This simple step is crucial for solving the entire equation. It sets the stage for the next operation, which is adding 47. By breaking down the problem into smaller, manageable parts, we make it easier to understand and solve. Now that we've found the result of -5 - 10, we can move on to the next step and complete the equation. Remember, each step builds upon the previous one, so understanding each part is key to mastering the whole.

Step 2: Adding 47 to -15

Now that we've solved the first part of our equation and found that -5 - 10 equals -15, we can move on to the next step: adding 47 to -15. This involves adding a positive number to a negative number. Think of it as having a debt of 15 dollars and then receiving 47 dollars. You can use some of that money to pay off your debt, and you'll still have some money left over. To solve this mathematically, we can think of it as 47 - 15. When adding numbers with different signs, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. In this case, the absolute value of -15 is 15, and the absolute value of 47 is 47. So, we subtract 15 from 47. 47 minus 15 is 32. Since 47 is positive and has a larger absolute value than -15, our answer will be positive. Therefore, -15 + 47 equals 32. Again, visualizing this on a number line can be helpful. Start at -15 and move 47 units to the right. You will land on 32. This step completes our equation. We've successfully navigated through the negative numbers and arrived at our final answer. By understanding how to add positive and negative numbers, we can tackle a wide range of mathematical problems. Now that we've completed both steps, let's take a look at the final solution and recap our process.

The Final Solution: 32

After carefully breaking down the problem and following the steps, we've arrived at the final solution: 32. To recap, we started with the equation -5 - 10 + 47. First, we tackled -5 - 10, which gave us -15. Then, we added 47 to -15, resulting in 32. This entire process underscores the importance of following the order of operations and understanding how to work with negative numbers. Math problems, even seemingly simple ones, often require a systematic approach. By breaking them down into smaller, more manageable steps, we can avoid confusion and arrive at the correct answer. Visual aids, like number lines, can also be incredibly helpful in understanding the concepts. They provide a visual representation of the operations and make it easier to grasp the movement between positive and negative numbers. Remember, math is a skill that improves with practice. The more you work through problems and understand the underlying principles, the more confident you'll become. So, don't be discouraged by challenges. Instead, embrace them as opportunities to learn and grow. Now that we've solved this problem, you have a solid understanding of how to approach similar equations. Keep practicing, and you'll become a math whiz in no time!

Why This Matters: Real-World Applications

You might be wondering, “Why does solving -5 - 10 + 47 matter in the real world?” Well, the principles behind this simple equation are applicable to a multitude of everyday situations. Understanding how to work with positive and negative numbers is crucial in various fields, from personal finance to science and engineering. Think about managing your bank account. If you have a starting balance, make a withdrawal, and then receive a deposit, you're essentially performing the same kind of calculations we did in our problem. Negative numbers represent debits or expenses, while positive numbers represent credits or income. Similarly, in science, negative numbers might represent temperatures below zero, while positive numbers represent temperatures above zero. In engineering, these concepts are used in calculating forces, distances, and other physical quantities. The ability to accurately perform these calculations is essential for making sound decisions and solving real-world problems. Moreover, the problem-solving skills you develop by tackling math equations like this one are transferable to other areas of your life. Learning to break down complex problems into smaller, manageable steps is a valuable skill that can be applied in any field. So, while -5 - 10 + 47 might seem like a simple math problem, it's actually a gateway to understanding more complex concepts and developing essential life skills. Keep practicing, and you'll be surprised at how far these foundational skills can take you!

Practice Makes Perfect: Similar Problems to Try

Now that you've mastered the solution to -5 - 10 + 47, it's time to put your skills to the test with some similar problems! Practice is key to solidifying your understanding and building confidence in your mathematical abilities. Try working through these examples on your own, and remember to break them down into smaller steps, just like we did with the original problem. Here are a few equations to get you started:

• -8 - 12 + 60
• -3 + 25 - 15
• -10 - 20 + 55
• 15 - 30 + 40

For each problem, start by tackling the first two numbers, then add or subtract the third number. Pay close attention to the signs (positive and negative) and remember the rules for adding and subtracting integers. Don't be afraid to use a number line to visualize the operations if that helps you. If you get stuck, review the steps we took in solving -5 - 10 + 47. The same principles apply to these problems as well. The more you practice, the more comfortable you'll become with these types of equations. You'll start to recognize patterns and develop a natural intuition for solving them. Remember, math is a journey, not a destination. Each problem you solve is a step forward on that journey. So, grab a pencil and paper, and let's get practicing! With consistent effort, you'll be amazed at how much you can achieve.

Conclusion: Mastering Basic Arithmetic

In conclusion, solving the equation -5 - 10 + 47 is more than just finding the answer (which, as we discovered, is 32). It's about understanding the fundamental principles of arithmetic and developing problem-solving skills that are applicable in various aspects of life. We've walked through the process step-by-step, emphasizing the importance of the order of operations and how to work with negative numbers. We've also highlighted the real-world applications of these skills, from managing finances to understanding scientific concepts. By breaking down complex problems into smaller, more manageable steps, we can make them less daunting and more accessible. Visual aids, such as number lines, can be incredibly helpful in grasping the concepts, especially when dealing with negative numbers. And, of course, practice is essential for mastering any mathematical skill. The more you work through problems, the more confident and proficient you'll become. So, take the time to practice similar equations, and don't be discouraged by challenges. Embrace them as opportunities to learn and grow. Remember, math is a journey, and every problem you solve is a step forward. Keep practicing, keep learning, and you'll be amazed at what you can achieve. So go forth and conquer those numbers!