We're dividing 369674 by 45 
We want to figure out the number of times 369674 can be divided by 45.

Advancing to step 1:
When dividing 3 by 45, we get 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 45

Moving on to step 2:
When dividing 36 by 45, we get 0 with a remainder of 36.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 36 after subtracting 0 from 36.
Bring next digit (9) of the dividend behind the 36 and repeat the process: 369 / 45

On to step 3:
When dividing 369 by 45, we get 8 with a remainder of 9.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtracting 360 from 369 leaves us with 9.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 45

On to step 4:
When dividing 96 by 45, we get 2 with a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 82.0
Deduct 90 from 96 and we're left with 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 45

Moving on to step 5:
The number 45 fits into 67 1 times, leaving a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 821.0
If we subtract 45 from 67, we get 22.
Append the next digit (4) from the dividend to 22 and continue with: 224 / 45

On to step 6:
224 divided by 45 is 4 with a remainder of 44.
The next digit of our result is 4. 
Result so far: 8214.0
If we take 180 away from 224, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 7:
45 can be fit into 440 9 times, resulting in a remainder of 35.
Put 9 as the next digit of the answer. 
Result so far: 8214.9
If we take 405 away from 440, 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.

On to step 8:
If we divide 350 by 45, we get 7 and a remainder of 35.
Write down 7 as next digit of the result. 
Result so far: 8214.97
Subtract 315 from 350 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 9:
350 divided by 45 is 7 with a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 8214.977
Subtract 315 from 350 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Our division results in 8214.977 with a remaining 0.0035.