75109 ÷ 78 
Our goal is to divide 75109 by 78.

Moving on to step 1:
7 divided by 78 is 0 with a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Grab the next digit (5) from the dividend, add it to 7, then carry on: 75 / 78

Going ahead to step 2:
75 divided by 78 is 0 with a remainder of 75.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 75 and we're left with 75.
Take the next digit (1) from the dividend and append it to 75, then repeat: 751 / 78

Advancing to step 3:
If we divide 751 by 78, we get 9 and a remainder of 49.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we subtract 702 from 751, we get 49.
Grab the next digit (0) from the dividend, add it to 49, then carry on: 490 / 78

Advancing to step 4:
The number 78 fits into 490 6 times, leaving a remainder of 22.
The number 6 becomes the next digit in our result. 
Result so far: 96.0
If we subtract 468 from 490, we get 22.
Include the next digit (9) from the dividend after 22, then repeat: 229 / 78

Advancing to step 5:
When dividing 229 by 78, we get 2 with a remainder of 73.
Use 2 as the next digit of our solution. 
Result so far: 962.0
If we take 156 away from 229, we end up with 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Moving on to step 6:
The number 78 fits into 730 9 times, leaving a remainder of 28.
Put 9 as the next digit of the answer. 
Result so far: 962.9
Subtracting 702 from 730 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 7:
78 goes into 280 3 times with a remainder of 46.
The next digit of our result is 3. 
Result so far: 962.93
Subtract 234 from 280 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 8:
When dividing 460 by 78, we get 5 with a remainder of 70.
Put 5 as the next digit of the answer. 
Result so far: 962.935
If we subtract 390 from 460, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 9:
78 can be fit into 700 8 times, resulting in a remainder of 76.
Put 8 as the next digit of the answer. 
Result so far: 962.9358
Deduct 624 from 700 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 10:
If we divide 760 by 78, we get 9 and a remainder of 58.
The next digit of our result is 9. 
Result so far: 962.93589
Deduct 702 from 760 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 11:
If we divide 580 by 78, we get 7 and a remainder of 34.
Use 7 as the next digit of our solution. 
Result so far: 962.935897
The remainder is 34 after subtracting 546 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 12:
If we divide 340 by 78, we get 4 and a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 962.9358974
If we take 312 away from 340, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 13:
78 can be fit into 280 3 times, resulting in a remainder of 46.
Record the quotient 3 as the next digit in the result. 
Result so far: 962.93589743
Subtracting 234 from 280 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

The quotient of the division is 962.93589743, and the remainder is 4.6e-08.