We divide 37742 by 88
We want to figure out the number of times 37742 can be divided by 88.

Going ahead to step 1:
When dividing 3 by 88, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 88

Moving on to step 2:
88 can be fit into 37 0 times, resulting in a remainder of 37.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Fetch the next digit (7) from the dividend, attach it to 37 and continue: 377 / 88

Step 3:
When dividing 377 by 88, we get 4 with a remainder of 25.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 352 away from 377, we end up with 25.
Bring next digit (4) of the dividend behind the 25 and repeat the process: 254 / 88

Let's proceed to step 4:
When dividing 254 by 88, we get 2 with a remainder of 78.
Use 2 as the next digit of our solution. 
Result so far: 42.0
Subtracting 176 from 254 leaves us with 78.
Bring next digit (2) of the dividend behind the 78 and repeat the process: 782 / 88

Going ahead to step 5:
88 goes into 782 8 times with a remainder of 78.
Use 8 as the next digit of our solution. 
Result so far: 428.0
The remainder is 78 after subtracting 704 from 782.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Going ahead to step 6:
88 can be fit into 780 8 times, resulting in a remainder of 76.
The number 8 becomes the next digit in our result. 
Result so far: 428.8
The remainder is 76 after subtracting 704 from 780.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Let's proceed to step 7:
When dividing 760 by 88, we get 8 with a remainder of 56.
Put 8 as the next digit of the answer. 
Result so far: 428.88
Deduct 704 from 760 and we're left with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

In conclusion, the division gives 428.88 with a balance of 0.056.