Sum Of Smallest Even And Largest Odd Digit Numbers A Math Problem Solved

October 18, 2025 by Scholario Team 73 views

Understanding the Sum of Smallest Even and Largest Odd Digit Numbers

Hey everyone! Today, let's dive into a fun math problem that involves finding the sum of two special four-digit numbers. We're looking for the smallest four-digit even number with all different digits and the largest four-digit number made up of only odd digits, also with no repeating digits. Sounds like a puzzle, right? Let’s break it down step by step and make sure we understand every detail. Trust me; it’s going to be super interesting!

Finding the Smallest Four-Digit Even Number with Distinct Digits

Okay, so our first task is to identify the smallest four-digit even number where no digit is repeated. When we say "smallest four-digit number," we're thinking about starting with the thousands place. To make the number as small as possible, we want the smallest digit in the thousands place, but remember, we can't use 0 because that would make it a three-digit number. So, what's the next smallest digit? That's right, it's 1! So, our number starts with 1 _ _ _.

Now, let’s move to the hundreds place. We want the smallest digit possible here, and 0 is a great choice. So now we have 10 _ . For the tens place, we need the next smallest digit that hasn't been used yet. We've already used 0 and 1, so the next smallest is 2. Our number now looks like 102.

Finally, we need to figure out the units place. Since the number has to be even, the units digit must be an even number (0, 2, 4, 6, or 8). We've already used 0 and 2, so the next smallest even number is 4. This gives us the number 1024. So, the smallest four-digit even number with distinct digits is 1024. Remember, we focused on making each digit as small as possible while following the rules.

To recap, here’s what we did:

Started with the smallest possible digit for the thousands place (1).
Used 0 for the hundreds place to keep the number small.
Chose the next smallest digit (2) for the tens place.
Selected the smallest available even digit (4) for the units place.

And there you have it! Finding this number was like solving a mini-puzzle, using logic and a bit of number sense. Now, let's move on to the next part of our problem: finding the largest four-digit number with distinct odd digits. This one is going to be just as fun, so stay with me!

Identifying the Largest Four-Digit Number with Distinct Odd Digits

Alright, let’s switch gears and tackle the second part of our problem: finding the largest four-digit number with distinct odd digits. This means we need to create a number using only odd digits (1, 3, 5, 7, and 9), and none of these digits can repeat. To make the number as large as possible, we'll start by thinking about the largest possible digit for each place value, beginning with the thousands place.

For the thousands place, we want the largest odd digit available, which is 9. So our number starts with 9 _ _ _. Now, let’s move to the hundreds place. We still want the largest possible digit, but we can’t use 9 again since all the digits must be different. The next largest odd digit is 7, so our number is now 97 _ _.

Moving on to the tens place, we continue this pattern. We've used 9 and 7, so the next largest odd digit is 5. This makes our number 975_. Finally, for the units place, we need the largest remaining odd digit. We've used 9, 7, and 5, leaving us with 3 and 1. The larger of these is 3, so our number is 9753. Therefore, the largest four-digit number with distinct odd digits is 9753. We’ve successfully found this number by prioritizing the largest digits in the highest place values.

Let's quickly recap how we found this number:

We started with the largest odd digit (9) for the thousands place.
Then, we chose the next largest odd digit (7) for the hundreds place.
We continued this pattern, selecting 5 for the tens place.
Finally, we used the largest remaining odd digit (3) for the units place.

Isn't it cool how we can use these logical steps to solve math problems? Now that we've found both the smallest even number and the largest odd number, we're ready for the final step: adding them together. So, let's head over to the next section where we'll do the addition and get our final answer. You guys are doing awesome, keep up the great work!

Calculating the Sum: Adding the Numbers Together

Okay, we've done the hard work of figuring out the two numbers we need: the smallest four-digit even number with distinct digits (1024) and the largest four-digit number with distinct odd digits (9753). Now comes the satisfying part – adding them together to find the sum. This is where we see all our efforts come together to give us the final answer. Are you guys ready to do some simple arithmetic? Let's jump right in!

We’ll add the numbers column by column, starting from the rightmost column (the units place) and moving to the left. This is the standard way we usually add numbers, and it helps us keep everything organized and accurate.

First, let's add the digits in the units place: 4 + 3 = 7. So, the units digit of our sum is 7.

Next, we move to the tens place: 2 + 5 = 7. The tens digit of our sum is also 7.

Now, let's add the digits in the hundreds place: 0 + 7 = 7. So, the hundreds digit of our sum is 7.

Finally, we add the digits in the thousands place: 1 + 9 = 10. This gives us 10 in the thousands place, which means our sum has five digits. We write down 0 in the thousands place and carry over the 1 to the ten-thousands place.

Putting it all together, we have 10777. So, the sum of 1024 and 9753 is 10777. We've successfully added the two numbers and found our final answer!

Here’s a quick recap of the addition process:

Units place: 4 + 3 = 7
Tens place: 2 + 5 = 7
Hundreds place: 0 + 7 = 7
Thousands place: 1 + 9 = 10
The total sum: 10777

Woo-hoo! We made it! We found the two numbers and calculated their sum. This was a fantastic exercise in using logic, understanding place value, and performing addition. Give yourselves a pat on the back, guys, because you've tackled a pretty cool math problem. Now, let's wrap up with a final summary of our solution and see what we've learned.

Final Answer and Key Takeaways

Alright, guys, we’ve reached the end of our mathematical journey, and what a journey it has been! We started with a tricky question, broke it down into manageable parts, and solved it step by step. Now, let's recap our findings and highlight the key things we learned along the way. This will help solidify our understanding and make sure we can tackle similar problems in the future.

So, to remind ourselves, the original question was: What is the sum of the smallest four-digit even number with distinct digits and the largest four-digit number with distinct digits, each of which is an odd number? We found that:

The smallest four-digit even number with distinct digits is 1024.
The largest four-digit number with distinct odd digits is 9753.
The sum of these two numbers is 10777.

Therefore, our final answer to the problem is 10777. Awesome job, everyone!

But more than just getting the right answer, it’s important to understand the process we used. Here are some key takeaways from this problem:

Break It Down: Complex problems become much easier when you break them down into smaller, more manageable parts. We tackled this problem by first finding each number separately and then adding them.
Understand Place Value: Place value is crucial in determining the size of a number. Knowing that the thousands place has more weight than the hundreds place helped us find the smallest and largest numbers efficiently.
Use Logic: We used logical reasoning to find the digits for each number. For example, to find the smallest even number, we started with the smallest possible digits while ensuring the number remained even.
Check Your Work: Always double-check your calculations to avoid mistakes. A small error in one step can lead to a wrong final answer.
Practice Makes Perfect: The more you practice problems like this, the better you'll become at problem-solving. Math is like a muscle – the more you use it, the stronger it gets!

In conclusion, this problem wasn't just about adding numbers; it was about thinking critically, using logic, and applying our knowledge of place value. You guys did an amazing job walking through each step with me. I hope you had fun and learned something new. Keep practicing and challenging yourselves with math problems, and you’ll become math superstars in no time! Thanks for joining me, and I’ll see you in the next fun math adventure!