Find The Number: 364 Plus Sum Of 3-Digit Numbers (1, 3, 4)

Hey guys! Let's dive into a fun math problem today. We're going to figure out a specific number. This number is 364 more than the sum of the smallest and largest three-digit numbers you can make using the digits 1, 3, and 4. Sounds like a bit of a puzzle, right? Don't worry, we'll break it down step by step. This isn't just about getting the right answer; it's about understanding the process. We'll explore how to form the smallest and largest numbers, and then how to put it all together. So, grab your thinking caps, and let's get started! We're going to tackle this problem in a way that's both informative and, dare I say, a little bit fun. Whether you're a math whiz or just trying to brush up on your skills, this is a great exercise in logical thinking and number manipulation. Let's get to it!

Understanding the Problem

Okay, so, the heart of this problem lies in understanding how to manipulate digits to create the smallest and largest possible numbers. The key concept here is place value. Remember, in a three-digit number, the leftmost digit represents the hundreds place, the middle digit represents the tens place, and the rightmost digit represents the ones place. To create the largest number, you'll want to put the biggest digit in the hundreds place, followed by the next biggest in the tens place, and the smallest in the ones place. Conversely, to create the smallest number, you'll do the opposite: put the smallest digit in the hundreds place, followed by the next smallest in the tens place, and the largest in the ones place. Make sense? This is a fundamental concept in number theory, and it's crucial for solving this problem efficiently. We're not just randomly arranging numbers; we're strategically placing them to maximize or minimize the overall value. Once we've mastered this, the rest of the problem will fall into place much more easily. Think of it like building with blocks – you need a solid foundation to build something strong. In this case, our foundation is understanding place value and how it affects the magnitude of a number. So, let's keep this in mind as we move forward and start forming those numbers!

Forming the Smallest and Largest Numbers

Let's put our place value knowledge to work! We have the digits 1, 3, and 4 to play with. First, let's figure out the smallest three-digit number we can create. Remember, we want the smallest digit in the hundreds place, the next smallest in the tens place, and the largest in the ones place. Looking at our digits, the smallest is 1, so that goes in the hundreds place. Next, 3 is smaller than 4, so it goes in the tens place. That leaves 4 for the ones place. So, the smallest number we can form is 134. Now, let's tackle the largest number. We want the biggest digit in the hundreds place, so that's 4. Next, 3 is bigger than 1, so it goes in the tens place. And that leaves 1 for the ones place. Therefore, the largest number we can form is 431. See how strategic placement of the digits made all the difference? It's not just about having the right digits; it's about arranging them in the right order. This is a core skill in mathematics, and it's applicable in many different scenarios. We've successfully identified our two key numbers: 134 and 431. Now, the next step is to find their sum. We're making great progress, guys! Let's keep this momentum going and move on to the next step.

Calculating the Sum

Alright, we've got our smallest number (134) and our largest number (431). The next step is to find their sum. This is where our basic addition skills come into play. We need to add 134 and 431 together. You can do this using the standard addition method, lining up the numbers vertically by place value and adding each column, starting from the ones place. So, 4 + 1 = 5 in the ones place. Then, 3 + 3 = 6 in the tens place. And finally, 1 + 4 = 5 in the hundreds place. This gives us a total of 565. So, the sum of the smallest and largest numbers formed by the digits 1, 3, and 4 is 565. See, that wasn't too tricky, was it? It's just a matter of breaking it down into smaller, manageable steps. We've now successfully completed a significant part of the problem. We know the sum, and we're one step closer to finding our final answer. This step-by-step approach is a valuable problem-solving strategy in all areas of life, not just math. By breaking down complex problems into smaller parts, we can make them much less daunting. Now that we have the sum, let's move on to the final piece of the puzzle!

Adding 364 to the Sum

We're in the home stretch now! We've already found the sum of the smallest and largest numbers (565). The final step is to add 364 to that sum. This will give us the number we're ultimately looking for. Again, we'll use our trusty addition skills. We need to add 565 and 364 together. Just like before, we can line them up vertically by place value and add each column. Starting with the ones place, 5 + 4 = 9. In the tens place, 6 + 6 = 12. We write down the 2 and carry over the 1 to the hundreds place. So, in the hundreds place, we have 5 + 3 + 1 (the carry-over) = 9. This gives us a final total of 929. Therefore, the number that is 364 greater than the sum of the smallest and largest three-digit numbers formed by 1, 3, and 4 is 929. Woohoo! We did it! This was a multi-step problem, but we tackled it successfully by breaking it down into smaller, more manageable parts. This is a powerful technique for approaching any challenging problem. We've not only found the answer but also reinforced our understanding of place value and addition. Pat yourselves on the back, guys!

Final Answer

So, after all that brainpower and number crunching, we've arrived at our final answer. The number that is 364 greater than the sum of the smallest and largest three-digit numbers formed by the digits 1, 3, and 4 is 929. There you have it! We successfully navigated through the problem, breaking it down into clear, logical steps. We started by understanding the importance of place value, then formed the smallest and largest numbers, calculated their sum, and finally, added 364 to that sum. It's like we went on a mathematical adventure together! This wasn't just about finding a number; it was about the journey we took to get there. We reinforced our understanding of key mathematical concepts and honed our problem-solving skills. Remember, the process is just as important as the answer. By understanding the steps involved, you can apply these same strategies to tackle other challenges in math and beyond. I hope you found this explanation helpful and maybe even a little bit fun. Keep practicing, keep exploring, and keep that mathematical curiosity burning! You guys are awesome!