4431 ÷ 97 
We're looking to find how many times 97 goes into 4431.

Advancing to step 1:
97 goes into 4 0 times with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 97

On to step 2:
97 can be fit into 44 0 times, resulting in a remainder of 44.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 44 leaves us with 44.
Fetch the next digit (3) from the dividend, attach it to 44 and continue: 443 / 97

Step 3:
When dividing 443 by 97, we get 4 with a remainder of 55.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 388 away from 443, we end up with 55.
Include the next digit (1) from the dividend after 55, then repeat: 551 / 97

Going ahead to step 4:
97 can be fit into 551 5 times, resulting in a remainder of 66.
Put 5 as the next digit of the answer. 
Result so far: 45.0
Subtracting 485 from 551 leaves us with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Going ahead to step 5:
97 goes into 660 6 times with a remainder of 78.
The number 6 becomes the next digit in our result. 
Result so far: 45.6
If we take 582 away from 660, we end up with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Let's proceed to step 6:
97 goes into 780 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 45.68
Deduct 776 from 780 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
The number 97 fits into 40 0 times, leaving a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 45.68
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 8:
400 divided by 97 is 4 with a remainder of 12.
The next digit of our result is 4. 
Result so far: 45.6804
If we take 388 away from 400, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
If we divide 120 by 97, we get 1 and a remainder of 23.
Record the quotient 1 as the next digit in the result. 
Result so far: 45.68041
The remainder is 23 after subtracting 97 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 10:
230 divided by 97 is 2 with a remainder of 36.
The next digit of our result is 2. 
Result so far: 45.680412
Deduct 194 from 230 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 11:
360 divided by 97 is 3 with a remainder of 69.
The next digit of our result is 3. 
Result so far: 45.6804123
Subtract 291 from 360 to get 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Let's proceed to step 12:
The number 97 fits into 690 7 times, leaving a remainder of 11.
Record the quotient 7 as the next digit in the result. 
Result so far: 45.68041237
If we subtract 679 from 690, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

After the division, we end up with 45.68041237 and a remainder of 1.1e-08.