7738 divided by 48 
We want to figure out the number of times 7738 can be divided by 48.

Advancing to step 1:
When dividing 7 by 48, we get 0 with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 48

Advancing to step 2:
When dividing 77 by 48, we get 1 with a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 48 from 77, we get 29.
Take the next digit (3) from the dividend and append it to 29, then repeat: 293 / 48

Moving on to step 3:
48 can be fit into 293 6 times, resulting in a remainder of 5.
The next digit of our result is 6. 
Result so far: 16.0
Subtracting 288 from 293 leaves us with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 48

Moving on to step 4:
If we divide 58 by 48, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 161.0
If we subtract 48 from 58, 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.

Going ahead to step 5:
48 goes into 100 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 161.2
Subtract 96 from 100 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 6:
The number 48 fits into 40 0 times, leaving a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 161.2
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 7:
400 divided by 48 is 8 with a remainder of 16.
Put 8 as the next digit of the answer. 
Result so far: 161.208
Subtracting 384 from 400 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 8:
48 goes into 160 3 times with a remainder of 16.
Use 3 as the next digit of our solution. 
Result so far: 161.2083
Subtract 144 from 160 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 9:
160 divided by 48 is 3 with a remainder of 16.
The next digit of our result is 3. 
Result so far: 161.20833
Subtracting 144 from 160 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final result is 161.20833 with a remainder of 1.6e-05.