7758 ÷ 44 
We want to figure out the number of times 7758 can be divided by 44.

On to step 1:
44 goes into 7 0 times with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Append the next digit (7) from the dividend to 7 and continue with: 77 / 44

Step 2:
When dividing 77 by 44, we get 1 with a remainder of 33.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 44 away from 77, we end up with 33.
Append the next digit (5) from the dividend to 33 and continue with: 335 / 44

Moving on to step 3:
44 can be fit into 335 7 times, resulting in a remainder of 27.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
Subtracting 308 from 335 leaves us with 27.
Fetch the next digit (8) from the dividend, attach it to 27 and continue: 278 / 44

Let's proceed to step 4:
The number 44 fits into 278 6 times, leaving a remainder of 14.
Write down 6 as next digit of the result. 
Result so far: 176.0
Subtract 264 from 278 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 5:
44 can be fit into 140 3 times, resulting in a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 176.3
Deduct 132 from 140 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.

Moving on to step 6:
80 divided by 44 is 1 with a remainder of 36.
Write down 1 as next digit of the result. 
Result so far: 176.31
If we subtract 44 from 80, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 7:
The number 44 fits into 360 8 times, leaving a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 176.318
Subtracting 352 from 360 leaves us 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.

Moving on to step 8:
If we divide 80 by 44, we get 1 and a remainder of 36.
The number 1 becomes the next digit in our result. 
Result so far: 176.3181
Deduct 44 from 80 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 9:
If we divide 360 by 44, we get 8 and a remainder of 8.
The next digit of our result is 8. 
Result so far: 176.31818
Subtracting 352 from 360 leaves us 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.

Step 10:
44 can be fit into 80 1 times, resulting in a remainder of 36.
Record the quotient 1 as the next digit in the result. 
Result so far: 176.318181
Subtract 44 from 80 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 11:
360 divided by 44 is 8 with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 176.3181818
Deduct 352 from 360 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.

Let's proceed to step 12:
80 divided by 44 is 1 with a remainder of 36.
Use 1 as the next digit of our solution. 
Result so far: 176.31818181
The remainder is 36 after subtracting 44 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

The final result is 176.31818181 with a remainder of 3.6e-08.