4315378 ÷ 555 
We want to divide 4315378 by 555.

Let's proceed to step 1:
4 divided by 555 is 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 555

Step 2:
When dividing 43 by 555, we get 0 with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 43 leaves us with 43.
Include the next digit (1) from the dividend after 43, then repeat: 431 / 555

On to step 3:
If we divide 431 by 555, we get 0 and a remainder of 431.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 431 after subtracting 0 from 431.
Append the next digit (5) from the dividend to 431 and continue with: 4315 / 555

Let's proceed to step 4:
4315 divided by 555 is 7 with a remainder of 430.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtracting 3885 from 4315 leaves us with 430.
Include the next digit (3) from the dividend after 430, then repeat: 4303 / 555

Step 5:
555 can be fit into 4303 7 times, resulting in a remainder of 418.
The next digit of our result is 7. 
Result so far: 77.0
Subtract 3885 from 4303 to get 418.
Include the next digit (7) from the dividend after 418, then repeat: 4187 / 555

Let's proceed to step 6:
When dividing 4187 by 555, we get 7 with a remainder of 302.
Use 7 as the next digit of our solution. 
Result so far: 777.0
If we take 3885 away from 4187, we end up with 302.
Include the next digit (8) from the dividend after 302, then repeat: 3028 / 555

Step 7:
When dividing 3028 by 555, we get 5 with a remainder of 253.
The next digit of our result is 5. 
Result so far: 7775.0
Deduct 2775 from 3028 and we're left with 253.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2530, and continue the process.

Let's proceed to step 8:
When dividing 2530 by 555, we get 4 with a remainder of 310.
Record the quotient 4 as the next digit in the result. 
Result so far: 7775.4
If we take 2220 away from 2530, we end up with 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3100, and continue the process.

Going ahead to step 9:
If we divide 3100 by 555, we get 5 and a remainder of 325.
Put 5 as the next digit of the answer. 
Result so far: 7775.45
Deduct 2775 from 3100 and we're left with 325.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3250, and continue the process.

Advancing to step 10:
If we divide 3250 by 555, we get 5 and a remainder of 475.
The next digit of our result is 5. 
Result so far: 7775.455
If we take 2775 away from 3250, we end up with 475.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4750, and continue the process.

Our division results in 7775.455 with a remaining 0.0475.