We're dividing 961975 by 9 
Our goal is to divide 961975 by 9.

Moving on to step 1:
9 goes into 9 1 times with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 9 from 9 to get 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 9

On to step 2:
The number 9 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we subtract 0 from 6, we get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 9

Let's proceed to step 3:
61 divided by 9 is 6 with a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 106.0
The remainder is 7 after subtracting 54 from 61.
Bring next digit (9) of the dividend behind the 7 and repeat the process: 79 / 9

Moving on to step 4:
If we divide 79 by 9, we get 8 and a remainder of 7.
The number 8 becomes the next digit in our result. 
Result so far: 1068.0
The remainder is 7 after subtracting 72 from 79.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Moving on to step 5:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 10688.0
If we subtract 72 from 77, we get 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 9

Advancing to step 6:
9 can be fit into 55 6 times, resulting in a remainder of 1.
The next digit of our result is 6. 
Result so far: 106886.0
The remainder is 1 after subtracting 54 from 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
When dividing 10 by 9, we get 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 106886.1
If we subtract 9 from 10, 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.

Moving on to step 8:
10 divided by 9 is 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 106886.11
Deduct 9 from 10 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 106886.11, and the remainder is 0.001.