135142 ÷ 15 
We're looking to find how many times 15 goes into 135142.

Going ahead to step 1:
If we divide 1 by 15, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 15

Going ahead to step 2:
15 can be fit into 13 0 times, resulting in a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 13 to get 13.
Bring next digit (5) of the dividend behind the 13 and repeat the process: 135 / 15

Moving on to step 3:
When dividing 135 by 15, we get 9 with a remainder of 0.
Write down 9 as next digit of the result. 
Result so far: 9.0
Deduct 135 from 135 and we're left with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 15

On to step 4:
The number 15 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 90.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 15

Step 5:
When dividing 14 by 15, we get 0 with a remainder of 14.
The next digit of our result is 0. 
Result so far: 900.0
Subtract 0 from 14 to get 14.
Grab the next digit (2) from the dividend, add it to 14, then carry on: 142 / 15

Step 6:
15 goes into 142 9 times with a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 9009.0
Deduct 135 from 142 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.

Step 7:
The number 15 fits into 70 4 times, leaving a remainder of 10.
Record the quotient 4 as the next digit in the result. 
Result so far: 9009.4
Subtracting 60 from 70 leaves us 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.

Let's proceed to step 8:
When dividing 100 by 15, we get 6 with a remainder of 10.
The next digit of our result is 6. 
Result so far: 9009.46
If we subtract 90 from 100, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 9009.466
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 outcome is 9009.466, with a leftover of 0.001.