127 ÷ 16 
Let's see how many times 16 fits into 127.

Going ahead to step 1:
When dividing 1 by 16, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 16

Going ahead to step 2:
If we divide 12 by 16, we get 0 and a remainder of 12.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 12 and we're left with 12.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 16

On to step 3:
16 goes into 127 7 times with a remainder of 15.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
The remainder is 15 after subtracting 112 from 127.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 4:
When dividing 150 by 16, we get 9 with a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 7.9
Subtract 144 from 150 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 5:
16 goes into 60 3 times with a remainder of 12.
The next digit of our result is 3. 
Result so far: 7.93
Subtract 48 from 60 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 6:
16 can be fit into 120 7 times, resulting in a remainder of 8.
The next digit of our result is 7. 
Result so far: 7.937
Deduct 112 from 120 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 7:
80 divided by 16 is 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 7.9375
The remainder is 0 after subtracting 80 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
16 goes into 0 0 times with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 7.9375
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
16 can be fit into 0 0 times, resulting in a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 7.9375
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 7.9375 with a balance of 0.0.