397 ÷ 65 
We want to figure out the number of times 397 can be divided by 65.

Step 1:
65 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 65

On to step 2:
39 divided by 65 is 0 with a remainder of 39.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 39, we end up with 39.
Bring next digit (7) of the dividend behind the 39 and repeat the process: 397 / 65

Step 3:
The number 65 fits into 397 6 times, leaving a remainder of 7.
Use 6 as the next digit of our solution. 
Result so far: 6.0
The remainder is 7 after subtracting 390 from 397.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 4:
If we divide 70 by 65, we get 1 and a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 6.1
Deduct 65 from 70 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 5:
65 can be fit into 50 0 times, resulting in a remainder of 50.
The next digit of our result is 0. 
Result so far: 6.1
The remainder is 50 after subtracting 0 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

On to step 6:
65 can be fit into 500 7 times, resulting in a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 6.107
Deduct 455 from 500 and we're left with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 7:
65 can be fit into 450 6 times, resulting in a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 6.1076
Subtract 390 from 450 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 8:
When dividing 600 by 65, we get 9 with a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 6.10769
If we subtract 585 from 600, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 9:
65 can be fit into 150 2 times, resulting in a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 6.107692
Deduct 130 from 150 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 10:
When dividing 200 by 65, we get 3 with a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 6.1076923
Subtracting 195 from 200 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 11:
If we divide 50 by 65, we get 0 and a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 6.1076923
The remainder is 50 after subtracting 0 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

In conclusion, the division gives 6.1076923 with a balance of 5e-08.