7603 ÷ 44 
Let's see how many times 44 fits into 7603.

Going ahead to step 1:
If we divide 7 by 44, we get 0 and a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 44

Going ahead to step 2:
The number 44 fits into 76 1 times, leaving a remainder of 32.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 44 from 76 and we're left with 32.
Take the next digit (0) from the dividend and append it to 32, then repeat: 320 / 44

Advancing to step 3:
320 divided by 44 is 7 with a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
Subtracting 308 from 320 leaves us with 12.
Fetch the next digit (3) from the dividend, attach it to 12 and continue: 123 / 44

Step 4:
When dividing 123 by 44, we get 2 with a remainder of 35.
Record the quotient 2 as the next digit in the result. 
Result so far: 172.0
If we take 88 away from 123, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 5:
350 divided by 44 is 7 with a remainder of 42.
Put 7 as the next digit of the answer. 
Result so far: 172.7
The remainder is 42 after subtracting 308 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 6:
If we divide 420 by 44, we get 9 and a remainder of 24.
The number 9 becomes the next digit in our result. 
Result so far: 172.79
Subtracting 396 from 420 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 7:
If we divide 240 by 44, we get 5 and a remainder of 20.
The number 5 becomes the next digit in our result. 
Result so far: 172.795
Subtract 220 from 240 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
When dividing 200 by 44, we get 4 with a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 172.7954
Deduct 176 from 200 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 9:
When dividing 240 by 44, we get 5 with a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 172.79545
If we take 220 away from 240, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 10:
44 goes into 200 4 times with a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 172.795454
Deduct 176 from 200 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 11:
The number 44 fits into 240 5 times, leaving a remainder of 20.
Write down 5 as next digit of the result. 
Result so far: 172.7954545
The remainder is 20 after subtracting 220 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 12:
44 can be fit into 200 4 times, resulting in a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 172.79545454
If we subtract 176 from 200, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final result is 172.79545454 with a remainder of 2.4e-08.