Calculating 47 + (-23) - 18 A Step-by-Step Solution

Hey guys! Let's break down this math problem together. We've got a series of additions and subtractions with positive and negative numbers, so it's crucial to approach it step-by-step to avoid any confusion. This problem, 47 + (-23) - 18, might seem a bit tricky at first glance, but don't worry, we'll get through it together.

The Basics: Positive and Negative Numbers

Before we dive into the calculation itself, let’s quickly refresh the basics of positive and negative numbers. Positive numbers are greater than zero, while negative numbers are less than zero. When we add a negative number, it’s the same as subtracting a positive number. This is a fundamental concept that will help us solve the problem accurately. Think of it like this: adding a debt is like taking away money you already have.

In our problem, we have 47, which is a positive number, and -23, which is a negative number. The operation 47 + (-23) means we are adding a negative number to a positive one, which, as we just discussed, is the same as subtracting. So, this part of the problem can be rewritten as 47 - 23. Understanding this equivalence is key to simplifying the problem.

Step-by-Step Calculation: 47 + (-23) - 18

Now, let's tackle the problem step-by-step. The first part of the calculation is 47 + (-23). As we established, this is the same as 47 - 23. So, let’s subtract 23 from 47. When we do this, we get 24. This is our intermediate result.

So far, we've simplified the problem to 24 - 18. The next step is to subtract 18 from 24. This is a straightforward subtraction. When we subtract 18 from 24, we get 6. And that, my friends, is our final answer!

To recap, we started with 47 + (-23) - 18. We first simplified 47 + (-23) to 47 - 23, which equals 24. Then, we subtracted 18 from 24, resulting in 6. Therefore, the final answer to the problem is 6. Breaking the problem down into smaller, manageable steps made it much easier to solve.

Common Mistakes and How to Avoid Them

When dealing with problems involving positive and negative numbers, it's easy to make mistakes if we're not careful. One common mistake is confusing addition and subtraction when negative numbers are involved. For example, some people might incorrectly add 23 to 47 instead of subtracting it. To avoid this, always remember that adding a negative number is the same as subtracting a positive number.

Another common mistake is messing up the order of operations. In this problem, we have addition and subtraction, which should be performed from left to right. If we were to subtract 18 from -23 first, we would get a completely different result. To avoid this, always follow the correct order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often remembered by the acronym PEMDAS.

To minimize errors, it's also a good idea to double-check your work. After you've completed the calculation, go back and review each step to make sure you haven't made any mistakes. This simple habit can save you from a lot of frustration. And remember, practice makes perfect! The more you work with positive and negative numbers, the more comfortable you'll become with them.

Real-World Applications of Positive and Negative Numbers

Positive and negative numbers aren't just abstract math concepts; they're used in many real-world situations. Understanding them can help you make better decisions in various aspects of your life. For example, in finance, positive numbers represent income or assets, while negative numbers represent expenses or debts. Knowing how to work with these numbers is crucial for managing your finances effectively.

In science, negative numbers are used to represent temperatures below zero, altitudes below sea level, and electrical charges. In sports, they can represent point differentials or scores in certain situations. The ability to understand and manipulate positive and negative numbers is a valuable skill in many fields.

Even in everyday life, we encounter positive and negative numbers. For instance, if you're tracking your steps with a fitness tracker, you might see a positive number representing the steps you've taken and a negative number representing the steps you need to take to reach your goal. Or, if you're following a recipe, you might need to adjust the amounts of ingredients based on whether you're doubling or halving the recipe, which involves working with positive and negative fractions or decimals.

Conclusion: Mastering Math Step-by-Step

So, there you have it! We've successfully solved the problem 47 + (-23) - 18 by breaking it down into manageable steps. Remember, the key to mastering math is to understand the fundamental concepts and practice regularly. By taking your time, paying attention to detail, and double-checking your work, you can avoid common mistakes and build your confidence in math.

Keep practicing, guys, and you'll become math whizzes in no time! If you have any more math problems you'd like to tackle, feel free to ask. Math can be fun when you approach it with the right attitude and a step-by-step strategy. Remember, every problem is an opportunity to learn something new and sharpen your skills. So, embrace the challenge and keep exploring the fascinating world of mathematics!

Okay, let's dive deeper into why understanding how to simplify problems like 47 + (-23) - 18 is super important. It's not just about getting the right answer; it's about building a solid foundation in math that will help you tackle more complex problems later on. Think of it as mastering the basics so you can build a skyscraper of math knowledge!

Why Rewriting Problems is a Game Changer

When we rewrite a problem, we're essentially making it easier to understand and solve. In this case, we started with 47 + (-23) - 18. The presence of the negative number inside the parentheses might seem a bit confusing at first. But, by rewriting 47 + (-23) as 47 - 23, we've already simplified the problem significantly. This simple change makes the problem less intimidating and easier to process.

Rewriting problems also helps us see the underlying structure and relationships between numbers. It's like decluttering your desk before you start working – it clears the way for clearer thinking. By focusing on the core operations and simplifying the notation, we reduce the chances of making careless errors. This is especially crucial in more complex problems where there are multiple steps and operations involved.

Moreover, rewriting problems can reveal different strategies for solving them. Sometimes, there's more than one way to reach the correct answer. By rewriting the problem, we might spot a shortcut or a more efficient method. This flexibility is a valuable asset in problem-solving. It's like having different tools in your toolbox – you can choose the one that's best suited for the job.

Step-by-Step Rewriting: From Complex to Simple

Let's revisit our problem and see how the rewriting process works step-by-step. We started with 47 + (-23) - 18. The first step was to recognize that adding a negative number is the same as subtracting a positive number. So, we rewrote 47 + (-23) as 47 - 23. This is a fundamental rule in math, and mastering it will save you a lot of headaches.

Next, we performed the subtraction 47 - 23, which gave us 24. Now, our problem looks much simpler: 24 - 18. This is a straightforward subtraction problem that most people can solve easily. The final step is to subtract 18 from 24, which gives us 6. So, the answer is 6.

Notice how rewriting the problem into smaller, more manageable steps made the entire process smoother and less prone to errors. We broke down a seemingly complex problem into a series of simple operations. This is a powerful technique that you can apply to many different types of math problems.

Practice Makes Perfect: Rewriting Strategies

To truly master the art of rewriting problems, you need to practice. The more you do it, the more natural it will become. Start with simple problems and gradually work your way up to more complex ones. The key is to focus on understanding the underlying principles and applying them consistently.

One strategy is to look for opportunities to simplify expressions by combining like terms. For example, if you have a problem like 3x + 2x - x, you can rewrite it as (3 + 2 - 1)x, which simplifies to 4x. This makes the problem much easier to solve.

Another strategy is to use the distributive property to expand expressions. For example, if you have 2(x + 3), you can rewrite it as 2x + 6. This can be helpful when you need to get rid of parentheses or simplify fractions.

Remember, rewriting problems is not just about getting the right answer; it's about developing a deeper understanding of math. It's about learning to see problems from different angles and finding the most efficient way to solve them. So, keep practicing, keep exploring, and keep rewriting!

Real-World Examples: Rewriting in Action

Rewriting problems isn't just a skill for the classroom; it's a valuable tool in many real-world situations. Anytime you need to simplify information or make a complex task more manageable, rewriting can come in handy. Let's look at some examples.

In cooking, recipes often involve fractions and measurements that can be difficult to work with. Rewriting the recipe in terms of simpler measurements or adjusting the quantities to match the number of servings you need is a form of rewriting. For example, if a recipe calls for 3/4 cup of flour and you only want to make half the recipe, you can rewrite the measurement as 3/8 cup.

In finance, budgeting involves tracking income and expenses. Rewriting your expenses into categories (e.g., housing, food, transportation) can help you see where your money is going and identify areas where you can save. This is a form of rewriting that helps you make informed financial decisions.

In project management, breaking down a large project into smaller tasks is a form of rewriting. It makes the project less overwhelming and easier to manage. By rewriting the project into smaller steps, you can create a timeline, assign resources, and track progress more effectively.

Conclusion: The Power of Simplification

In conclusion, understanding how to rewrite problems like 47 + (-23) - 18 is a fundamental skill in math and in life. It's about simplifying complexity, finding clarity, and making tasks more manageable. By mastering the art of rewriting, you'll not only improve your math skills but also enhance your problem-solving abilities in all areas of your life.

Keep rewriting, guys, and you'll be amazed at how much easier things become! Remember, every problem is an opportunity to practice your rewriting skills and unlock new solutions. So, embrace the challenge and keep simplifying your world, one step at a time.

Alright, let’s zoom in on the final answer: 6. It’s not just a number; it’s the culmination of our step-by-step journey through the problem 47 + (-23) - 18. Understanding why 6 is the correct answer involves revisiting our process and solidifying the concepts we’ve covered. So, let's break it down one last time to make sure we've nailed it!

The Significance of the Solution

In math, the solution to a problem isn't just a random number; it's the precise value that satisfies the given conditions. In our case, the conditions are the series of operations: 47 + (-23) - 18. The number 6 is the only value that results from performing these operations in the correct order. It's like a puzzle piece that perfectly fits into the equation.

Understanding the significance of the solution helps us appreciate the logic and precision of mathematics. It's not about guessing or memorizing; it's about applying rules and principles to arrive at a definitive answer. The number 6 represents the final destination of our calculation, the point where all the pieces come together.

Moreover, the solution 6 is a testament to our ability to simplify and solve problems. We started with a problem that might have seemed a bit daunting at first, but by breaking it down into smaller steps, we were able to conquer it. The number 6 is a symbol of our problem-solving prowess, a reminder that we can tackle challenges if we approach them methodically.

Reviewing the Steps: From Start to Finish

To fully grasp why 6 is the solution, let's quickly review the steps we took to get there. First, we started with the problem 47 + (-23) - 18. The presence of the negative number inside the parentheses prompted us to rewrite the problem. We recognized that adding a negative number is the same as subtracting a positive number, so we rewrote 47 + (-23) as 47 - 23.

Next, we performed the subtraction 47 - 23, which gave us 24. This simplified our problem to 24 - 18. This is a crucial step because it reduces the complexity of the problem and makes it easier to solve. It's like clearing away the clutter so you can see the path clearly.

Finally, we subtracted 18 from 24, which resulted in 6. And there you have it: the solution to the problem. Each step in the process was essential in arriving at the correct answer. If we had skipped a step or made a mistake along the way, we would have ended up with a different result.

Alternative Approaches: Verifying the Answer

In math, it's always a good idea to verify your answer using alternative approaches. This not only confirms that your solution is correct but also deepens your understanding of the problem. So, let's explore some alternative ways to verify that 6 is indeed the correct solution to 47 + (-23) - 18.

One approach is to use a calculator. Simply enter the expression 47 + (-23) - 18 into a calculator, and it will display the answer: 6. This is a quick and easy way to check your work, especially if you're dealing with more complex calculations.

Another approach is to use a number line. Imagine a number line with 47 marked on it. Adding -23 means moving 23 units to the left, which brings us to 24. Then, subtracting 18 means moving 18 units further to the left, which lands us at 6. This visual representation can be helpful for understanding the operations and verifying the answer.

Common Misconceptions: Avoiding the Pitfalls

Before we wrap up, let's address some common misconceptions that can lead to incorrect answers in problems like this. One common mistake is confusing addition and subtraction when dealing with negative numbers. Remember, adding a negative number is the same as subtracting a positive number, and vice versa.

Another mistake is not following the correct order of operations. In this problem, we have addition and subtraction, which should be performed from left to right. If we were to subtract 18 from -23 first, we would get a completely different result. So, always follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

To avoid these pitfalls, it's essential to practice regularly and pay close attention to the details of the problem. Double-check your work, use alternative approaches to verify your answer, and don't hesitate to ask for help if you're stuck.

Conclusion: The Beauty of Mathematical Precision

So, there you have it! We've explored the problem 47 + (-23) - 18 from every angle and confirmed that 6 is indeed the correct solution. We've reviewed the steps, verified the answer using alternative approaches, and addressed common misconceptions. By understanding the process and the reasoning behind it, we've not only solved the problem but also deepened our understanding of mathematics.

Keep exploring, guys, and you'll discover the beauty of mathematical precision! Remember, every problem is an opportunity to learn something new and sharpen your skills. So, embrace the challenge and keep striving for accuracy and understanding. The number 6 is not just an answer; it's a symbol of our mathematical journey, a testament to our ability to reason, solve, and conquer.