Solving 100 - (-37) + 13 A Step-by-Step Guide
Hey guys! Ever find yourself scratching your head when you see a math problem with a bunch of pluses and minuses, especially when negative numbers are thrown into the mix? Don't worry, you're not alone! Math can sometimes feel like a puzzle, but once you understand the rules, it becomes a whole lot easier (and even kind of fun!). In this article, we're going to break down a problem that looks trickier than it actually is: 100 - (-37) + 13. We'll go through each step together, so you'll not only get the answer but also understand why it's the answer. So, grab your mental calculators, and let's dive into the world of integer operations!
Understanding the Basics of Integer Operations
Before we jump into the problem itself, let's quickly review some key concepts about integer operations. Integers are simply whole numbers (no fractions or decimals!), and they can be positive, negative, or zero. When we perform operations like addition, subtraction, multiplication, and division with integers, we need to pay close attention to the signs (+ and -). The golden rule to remember is that subtracting a negative number is the same as adding its positive counterpart. This is super important and the key to cracking problems like the one we're tackling today.
Think of it this way: imagine a number line. If you're at 0 and you subtract a positive number, you move to the left (towards the negative side). But if you subtract a negative number, it's like taking away a debt – you're actually moving to the right (towards the positive side)! This concept is crucial for solving our problem, so let's keep it in mind as we move forward. Another important thing to remember is the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us the order in which we should perform operations in a mathematical expression. However, in our case, we only have addition and subtraction, so we'll simply work from left to right. With these basics in mind, we're ready to tackle 100 - (-37) + 13.
Step-by-Step Solution: 100 - (-37) + 13
Okay, let's get down to business! We're going to solve 100 - (-37) + 13 step-by-step, so you can see exactly how it's done. Remember that subtracting a negative is the same as adding a positive, which is the core concept we will be using.
Step 1: Dealing with the Double Negative
The first part of our problem is 100 - (-37). Notice the double negative? This is where our golden rule comes into play! Subtracting a negative number is the same as adding a positive number. So, 100 - (-37) becomes 100 + 37. This is a much simpler operation, right? Now, we just need to add 100 and 37. Think of it as having 100 cookies and getting 37 more – yum!
Step 2: Adding 100 and 37
Adding 100 and 37 is pretty straightforward. We simply add the numbers together: 100 + 37 = 137. So, now we know that 100 - (-37) is equal to 137. We've simplified the first part of our problem, and we're one step closer to the final answer! This step highlights the power of understanding the basic rules of integer operations. By converting the subtraction of a negative to addition, we made the problem much easier to handle.
Step 3: Bringing Down the Remaining Operation
Now that we've solved 100 - (-37), we have 137. But we're not done yet! We still have the + 13 part of the problem to deal with. So, we bring that down, and our problem now looks like this: 137 + 13. We've taken a somewhat complicated expression and broken it down into a simple addition problem. This is a common strategy in math – breaking down complex problems into smaller, more manageable steps.
Step 4: Adding 137 and 13
Finally, we need to add 137 and 13. This is the last step, guys! You can do this in your head, or if you prefer, you can write it out. Adding 137 and 13 gives us 150. And that's it! We've reached the final answer. Give yourselves a pat on the back – you've successfully navigated a problem with integer operations.
Final Answer
So, the answer to 100 - (-37) + 13 is 150. We did it! By breaking down the problem into smaller steps and remembering the rule about subtracting negatives, we were able to solve it without any trouble. Remember, math is like building with blocks – each step builds upon the previous one. Understanding the fundamentals is key to tackling more complex problems.
Why is 100 - (-37) + 13 = 150? A Deeper Dive
Let's take a moment to really understand why 100 - (-37) + 13 equals 150. It's not just about following the steps; it's about grasping the underlying concepts. This deeper understanding will help you tackle similar problems with confidence. We've already touched on the key idea – subtracting a negative number is the same as adding its positive counterpart. But let's explore this a bit further.
The Magic of Subtracting Negatives
Think of a number line again. When you subtract a positive number, you move to the left. For example, 100 - 37 means starting at 100 and moving 37 units to the left. But when you subtract a negative number, it's like reversing that direction. Subtracting -37 is like moving 37 units to the right. This might seem counterintuitive at first, but it's a fundamental rule of math. You can also think of it in terms of debt. If you have a debt of $37 (-37), and someone takes that debt away (subtracts -37), it's like you've gained $37. This is why 100 - (-37) is the same as 100 + 37.
The Importance of Order of Operations
While our problem only involved addition and subtraction, it's worth reiterating the importance of the order of operations (PEMDAS/BODMAS) in general. If we had multiplication or division in the mix, we would need to perform those operations before addition and subtraction. In our case, since we only had addition and subtraction, we worked from left to right, which is the standard procedure. Understanding and applying the correct order of operations is crucial for getting the right answer in more complex mathematical expressions. It ensures that everyone arrives at the same solution, no matter who is solving the problem.
Applying the Concept to Real-World Scenarios
Math isn't just about numbers on a page; it's a tool for understanding the world around us. Integer operations, in particular, have many real-world applications. Think about temperature changes: if the temperature drops by -10 degrees (meaning it gets 10 degrees colder), it's the same as saying the temperature decreased by 10 degrees. Or consider finances: a negative balance in your bank account is a debt, and subtracting a negative balance (paying off some of the debt) increases your overall balance. By understanding the concepts behind integer operations, you can apply them to a wide range of situations.
Practice Makes Perfect: More Problems to Try
Now that you've mastered 100 - (-37) + 13, it's time to put your skills to the test! The best way to solidify your understanding of integer operations is to practice, practice, practice. Here are a few more problems for you to try. Don't be afraid to make mistakes – that's how we learn! Remember to break down each problem into steps and apply the golden rule: subtracting a negative is the same as adding a positive.
Example Problems
- 50 - (-25) + 10 = ?
- -20 + (-15) - (-30) = ?
- 75 - (-40) - 20 = ?
- -100 + 50 - (-25) = ?
- 200 - (-100) + (-50) = ?
Tips for Solving
- Rewrite the problem: The first thing you should do is rewrite the problem, changing any subtractions of negative numbers into additions. This will make the problem much easier to visualize and solve.
- Work from left to right: Once you've simplified the problem, perform the operations from left to right. This will ensure that you follow the correct order of operations.
- Use a number line: If you're still struggling with the concept of subtracting negatives, try using a number line. Visualizing the problem can make it easier to understand.
- Check your work: Once you've found an answer, take a moment to check your work. You can do this by plugging the answer back into the original equation or by using a calculator.
By working through these practice problems, you'll build confidence in your ability to solve integer operation problems. Remember, math is a skill that improves with practice, just like playing a musical instrument or a sport. The more you practice, the better you'll become!
Conclusion: You've Conquered Integer Operations!
Awesome job, guys! You've successfully tackled the problem 100 - (-37) + 13 and learned some important concepts about integer operations along the way. We started by understanding the basics, then broke down the problem step-by-step, and finally explored the underlying principles behind our solution. Remember, the key takeaway is that subtracting a negative number is the same as adding a positive number. This simple rule can unlock a whole world of mathematical possibilities!
Keep Exploring the World of Math
Math is a fascinating and powerful tool, and we've only scratched the surface here. There's so much more to learn and explore! Whether you're interested in algebra, geometry, calculus, or any other branch of math, the skills you've learned today will serve you well. So, keep practicing, keep asking questions, and most importantly, keep having fun with math!
Share Your Knowledge
Now that you've mastered integer operations, why not share your knowledge with others? Help a friend who's struggling with math, or explain the concept to a family member. Teaching others is a great way to reinforce your own understanding and make a positive impact on those around you. Math is a universal language, and the more people who understand it, the better!
Final Thoughts
We hope this article has helped you gain a better understanding of integer operations and how to solve problems like 100 - (-37) + 13. Remember, math is a journey, not a destination. There will be challenges along the way, but with persistence and a positive attitude, you can conquer anything! So, keep exploring, keep learning, and never stop believing in your mathematical abilities. You've got this!
