We look at the division of 61540 by 9 
Our goal is to divide 61540 by 9.

Moving on to step 1:
The number 9 fits into 6 0 times, leaving a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (1) from the dividend and append it to 6, then repeat: 61 / 9

On to step 2:
If we divide 61 by 9, we get 6 and a remainder of 7.
Write down 6 as next digit of the result. 
Result so far: 6.0
Deduct 54 from 61 and we're left with 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 9

On to step 3:
9 goes into 75 8 times with a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 68.0
The remainder is 3 after subtracting 72 from 75.
Grab the next digit (4) from the dividend, add it to 3, then carry on: 34 / 9

Let's proceed to step 4:
9 can be fit into 34 3 times, resulting in a remainder of 7.
The next digit of our result is 3. 
Result so far: 683.0
If we subtract 27 from 34, we get 7.
Take the next digit (0) from the dividend and append it to 7, then repeat: 70 / 9

Going ahead to step 5:
9 goes into 70 7 times with a remainder of 7.
Put 7 as the next digit of the answer. 
Result so far: 6837.0
Deduct 63 from 70 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 6:
9 goes into 70 7 times with a remainder of 7.
The next digit of our result is 7. 
Result so far: 6837.7
Subtract 63 from 70 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
When dividing 70 by 9, we get 7 with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 6837.77
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The final result is 6837.77 with a remainder of 0.007.