Math Problem: Finding The Tens Digit In 3869 + 75 > A
Hey guys! Let's dive into this interesting math problem where we need to figure out something cool. So, the main goal here is to break down a comparison problem and find the place value of a specific digit. Specifically, we're dealing with the inequality 3869 + 75 > A
, and we need to determine the largest possible value for A
and then find the place value of its tens digit. This might sound a bit complicated, but trust me, we'll get through it together step by step.
Understanding the Problem
To kick things off, let’s really understand what the problem is asking us. We've got this expression, 3869 + 75 > A
. What it's saying is that when you add 3869 and 75, the result is going to be bigger than some number we're calling A
. Our mission, should we choose to accept it, is to find the biggest whole number that A
can be without making this statement false. Once we've nailed that down, we're not done! We then need to zoom in on the tens digit of A
and figure out its place value. Place value, remember, is all about what a digit is worth depending on its position in the number (like ones, tens, hundreds, and so on). This part is super important because it’s not just about knowing the digit, but also understanding its value within the whole number.
Breaking Down the Steps
- Calculate the Sum: First things first, we need to figure out what
3869 + 75
actually equals. This will give us a clear number to work with. - Determine the Largest Possible Value for A: Once we have the sum, we need to find the largest whole number that is less than this sum. Remember,
A
has to be smaller than the result of our addition. - Identify the Tens Digit: After we've found the value of
A
, we'll pinpoint the digit that's in the tens place. This is the second digit from the right. - Determine the Place Value: Finally, we'll figure out the place value of the tens digit. This means we'll determine what that digit is actually worth (e.g., if the tens digit is 4, its place value is 40).
Step-by-Step Solution
Okay, let’s roll up our sleeves and solve this problem step by step. We're going to take it nice and slow so everyone can follow along. No math wizardry required, just some good old-fashioned arithmetic and logical thinking!
1. Calculate the Sum
So, the first thing we need to do is add 3869
and 75
. Let’s do this the traditional way, lining up the numbers by their place values and adding column by column.
3869
+ 75
------
Starting with the ones column, we have 9 + 5
, which equals 14. We write down the 4
and carry over the 1
to the tens column.
38⁶9
+ 75
------
4
Moving to the tens column, we now have 1 (carried over) + 6 + 7
, which equals 14. Again, we write down the 4
and carry over the 1
to the hundreds column.
3⁸69
+ 75
------
44
In the hundreds column, we have 1 (carried over) + 8
, which equals 9. We write down the 9
.
3869
+ 75
------
944
Finally, in the thousands column, we simply bring down the 3
since there’s nothing to add to it.
3869
+ 75
------
3944
So, 3869 + 75 = 3944
. Great! We've got our sum. This means our comparison now looks like this: 3944 > A
.
2. Determine the Largest Possible Value for A
Now comes the fun part: figuring out the largest number that A
can be. Remember, A
has to be smaller than 3944. So, what’s the biggest whole number that fits the bill? If you said 3943, you're spot on!
Why 3943? Because it’s the whole number immediately before 3944. If we chose 3944, the comparison wouldn't be true anymore because 3944 is not greater than 3944; it’s equal to it. So, A = 3943
is our answer here.
3. Identify the Tens Digit
Alright, we've found A
, which is 3943. Now, let's zoom in on the tens digit. Remember, the tens digit is the second digit from the right. In 3943, the digits are:
- Thousands: 3
- Hundreds: 9
- Tens: 4
- Ones: 3
So, the tens digit is 4
. Easy peasy!
4. Determine the Place Value
Last but not least, we need to figure out the place value of the tens digit. We know the tens digit is 4
. But what does that 4
mean in the number 3943? Well, it means we have 4 tens. Each ten is worth 10, so 4 tens are worth 4 * 10 = 40
. Therefore, the place value of the tens digit in 3943 is 40. Awesome! We've cracked the code.
Putting It All Together
Let’s quickly recap what we've done. We started with the comparison 3869 + 75 > A
. Our mission was to find the largest number that A
could be and then figure out the place value of its tens digit.
- We calculated the sum:
3869 + 75 = 3944
- We determined the largest possible value for
A
:A = 3943
- We identified the tens digit:
4
- We determined the place value:
40
So, the place value of the tens digit of the largest number that can be written in place of A
is 40. You did it!
Why This Matters
You might be thinking,