969431 ÷ 11 
We're looking to find how many times 11 goes into 969431.

Let's proceed to step 1:
If we divide 9 by 11, we get 0 and a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 9 after subtracting 0 from 9.
Fetch the next digit (6) from the dividend, attach it to 9 and continue: 96 / 11

Step 2:
When dividing 96 by 11, we get 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 8.0
Subtract 88 from 96 to get 8.
Grab the next digit (9) from the dividend, add it to 8, then carry on: 89 / 11

Moving on to step 3:
The number 11 fits into 89 8 times, leaving a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 88.0
Subtracting 88 from 89 leaves us with 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 11

Going ahead to step 4:
14 divided by 11 is 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 881.0
The remainder is 3 after subtracting 11 from 14.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 11

Advancing to step 5:
11 goes into 33 3 times with a remainder of 0.
Record the quotient 3 as the next digit in the result. 
Result so far: 8813.0
Subtract 33 from 33 to get 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 11

Step 6:
11 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 88130.0
If we subtract 0 from 1, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
11 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 88130.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
11 goes into 100 9 times with a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 88130.09
If we take 99 away from 100, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 9:
11 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 88130.09
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 10:
When dividing 100 by 11, we get 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 88130.0909
Subtract 99 from 100 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 11:
11 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 88130.0909
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 12:
11 goes into 100 9 times with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 88130.090909
If we subtract 99 from 100, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 13:
10 divided by 11 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 88130.090909
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 14:
11 can be fit into 100 9 times, resulting in a remainder of 1.
The next digit of our result is 9. 
Result so far: 88130.09090909
Deduct 99 from 100 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 88130.09090909, and the remainder is 1e-09.