Non-Defective Balls: A Math Problem Solved!
Hey guys! Let's dive into a fun math problem about balls – blue ones, green ones, some defective, and some perfectly fine. We're going to figure out just how many balls are without any defects. So, buckle up and let’s get started!
Understanding the Problem
First, let's break down the problem statement. We know there are 644 blue balls. That's our starting point. Now, there are also green balls, but the tricky part is we don't know the exact number right away. We're told there are 520 fewer green balls than blue balls. This means we need to do a little subtraction to figure out how many green balls we have. Once we know the number of blue and green balls, we can move on to the defective ones. There are 32 defective blue balls and 23 defective green balls. Our final goal is to find out how many balls in total are not defective. This involves a few steps, but don't worry, we'll take it one step at a time.
Keywords are important here. Notice how we focus on phrases like “non-defective balls,” “blue balls,” “green balls,” and “defective balls”? These are the clues that help us solve the problem efficiently. Understanding the relationships between these keywords is key to success. Think of it like a detective solving a mystery – every detail counts!
Also, remember that mathematics is all about precision. Make sure you pay close attention to the wording of the problem. “Fewer” means we need to subtract, and identifying these trigger words is crucial. Now that we have a solid understanding of the problem, let’s move on to the next step: calculating the number of green balls.
Calculating the Number of Green Balls
Okay, so we know we have 644 blue balls, and there are 520 fewer green balls. What does that tell us? It means we need to subtract 520 from 644 to find out the exact number of green balls. This is a straightforward subtraction problem, but it's a crucial step in solving the overall question. So, let's get to it!
Grab your pen and paper (or your calculator!), and let's do the math. We're doing 644 minus 520. When we subtract, we start with the ones place: 4 minus 0 is 4. Easy peasy! Next, we move to the tens place: 4 minus 2 is 2. And finally, the hundreds place: 6 minus 5 is 1. So, 644 - 520 = 124.
This means we have 124 green balls. See? That wasn't so bad, was it? Now we know the number of both blue balls (644) and green balls (124). This is a significant step forward, as we now have a complete picture of the total number of balls before we even consider the defects. Remember, careful calculation is key here. A small mistake in this step could throw off our final answer.
Accuracy is super important in math, just like in life! So, always double-check your work. Now that we know how many green balls there are, we can move on to figuring out how many balls are defective. That's the next piece of our puzzle, and we're getting closer to the final solution!
Finding the Total Number of Balls
Now that we know the number of blue balls (644) and the number of green balls (124), let’s calculate the total number of balls. To do this, we simply add the number of blue balls to the number of green balls. This will give us the overall quantity of balls we're dealing with. So, let’s add them up!
We need to add 644 and 124. Again, let’s start with the ones place: 4 plus 4 is 8. Then, the tens place: 4 plus 2 is 6. And finally, the hundreds place: 6 plus 1 is 7. So, 644 + 124 = 768. This tells us that there are a total of 768 balls.
Knowing the total number of balls is essential for figuring out how many are non-defective. Think of it as having the whole pie before you start cutting out slices. We need this total to subtract the number of defective balls later. This step highlights the importance of addition in problem-solving. It might seem basic, but it's a fundamental operation that we use all the time in math.
Pay close attention to the details – it’s what makes the difference between getting the right answer and making a mistake. Now that we know we have 768 balls in total, we can move on to dealing with the defective ones. Ready for the next step? Let's find out how many balls are defective!
Calculating the Total Number of Defective Balls
Alright, we’re making progress! We know the total number of balls (768). Now, we need to figure out how many of those balls are defective. The problem tells us there are 32 defective blue balls and 23 defective green balls. To find the total number of defective balls, we need to add these two numbers together. So, let’s do that!
We’re adding 32 and 23. Starting with the ones place: 2 plus 3 is 5. Then, moving to the tens place: 3 plus 2 is also 5. So, 32 + 23 = 55. This means we have a total of 55 defective balls. This step is another simple addition, but it’s crucial for our final calculation. We need to know this number to subtract it from the total number of balls.
Combining information is a key skill in math and in life. We took the information about defective blue balls and defective green balls and combined it to find the total defective balls. This is what problem-solving is all about! Now that we know the total number of defective balls, we’re just one step away from finding our answer. We’re in the home stretch now.
Finding the Number of Non-Defective Balls
Here we are, guys, at the final step! We know the total number of balls is 768, and we know that 55 of them are defective. So, how do we find out how many are not defective? You guessed it – we subtract the number of defective balls from the total number of balls. This is the final piece of the puzzle, and it's going to give us our answer!
We’re subtracting 55 from 768. This might look a little trickier than our previous calculations, but don’t worry, we can handle it! Let’s start with the ones place: 8 minus 5 is 3. Moving to the tens place: 6 minus 5 is 1. And finally, the hundreds place: 7 minus nothing is 7. So, 768 - 55 = 713.
That means there are 713 non-defective balls. Hooray! We did it! We’ve solved the problem. This final subtraction demonstrates the power of using what we know to find what we don’t know. We started with the total number of balls and the number of defective balls, and we used subtraction to find the number of non-defective balls.
Subtraction is a fundamental operation in math, and this problem shows us how important it is in real-world scenarios. By carefully subtracting the defective balls from the total balls, we’ve arrived at our solution. Now, let's celebrate our success!
Conclusion: The Answer and What We Learned
So, after all our calculations, we've discovered that there are 713 non-defective balls. Great job, everyone! We took a multi-step problem and broke it down into manageable chunks. We started by understanding the problem, then we calculated the number of green balls, found the total number of balls, figured out the total number of defective balls, and finally, we subtracted to find the number of non-defective balls. That's a lot of steps, but we nailed it!
This problem wasn’t just about getting the right answer; it was also about learning how to approach math problems. We used several key mathematical operations: subtraction (to find the number of green balls and non-defective balls) and addition (to find the total number of balls and defective balls). But beyond the math itself, we learned about the importance of reading carefully, breaking down problems, and checking our work.
Problem-solving skills like these aren't just useful in math class; they’re useful in all aspects of life. Whether you’re figuring out how much time you need to get ready in the morning or planning a big project at work, the ability to break down a problem into smaller steps and solve it methodically is invaluable.
I hope you guys had fun solving this problem with me. Remember, math can be challenging, but it’s also rewarding. Keep practicing, keep asking questions, and keep exploring the wonderful world of numbers! Until next time, happy calculating!