3475 divided by 15 
We're looking to find how many times 15 goes into 3475.

Let's proceed to step 1:
If we divide 3 by 15, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 15

Advancing to step 2:
15 goes into 34 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 30 away from 34, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 15

Let's proceed to step 3:
15 can be fit into 47 3 times, resulting in a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 23.0
If we take 45 away from 47, we end up with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 15

On to step 4:
15 goes into 25 1 times with a remainder of 10.
The next digit of our result is 1. 
Result so far: 231.0
The remainder is 10 after subtracting 15 from 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 5:
If we divide 100 by 15, we get 6 and a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 231.6
Deduct 90 from 100 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.

Going ahead to step 6:
100 divided by 15 is 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 231.66
Deduct 90 from 100 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.

The final result is 231.66 with a remainder of 0.01.