111762 ÷ 97 
We're looking to find how many times 97 goes into 111762.

On to step 1:
1 divided by 97 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 97

Going ahead to step 2:
97 can be fit into 11 0 times, resulting in a remainder of 11.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 11 leaves us with 11.
Include the next digit (1) from the dividend after 11, then repeat: 111 / 97

On to step 3:
The number 97 fits into 111 1 times, leaving a remainder of 14.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 97 away from 111, we end up with 14.
Bring next digit (7) of the dividend behind the 14 and repeat the process: 147 / 97

Let's proceed to step 4:
97 can be fit into 147 1 times, resulting in a remainder of 50.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we subtract 97 from 147, we get 50.
Take the next digit (6) from the dividend and append it to 50, then repeat: 506 / 97

Going ahead to step 5:
506 divided by 97 is 5 with a remainder of 21.
The next digit of our result is 5. 
Result so far: 115.0
Subtracting 485 from 506 leaves us with 21.
Bring next digit (2) of the dividend behind the 21 and repeat the process: 212 / 97

Step 6:
97 can be fit into 212 2 times, resulting in a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 1152.0
If we take 194 away from 212, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 7:
The number 97 fits into 180 1 times, leaving a remainder of 83.
The next digit of our result is 1. 
Result so far: 1152.1
The remainder is 83 after subtracting 97 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Let's proceed to step 8:
When dividing 830 by 97, we get 8 with a remainder of 54.
The next digit of our result is 8. 
Result so far: 1152.18
Deduct 776 from 830 and we're left with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 9:
When dividing 540 by 97, we get 5 with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 1152.185
Subtracting 485 from 540 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Advancing to step 10:
If we divide 550 by 97, we get 5 and a remainder of 65.
Use 5 as the next digit of our solution. 
Result so far: 1152.1855
The remainder is 65 after subtracting 485 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The final result is 1152.1855 with a remainder of 0.00065.