509278 ÷ 11 
Let's see how many times 11 fits into 509278.

Let's proceed to step 1:
11 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 11

Step 2:
11 can be fit into 50 4 times, resulting in a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 44 from 50 and we're left with 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 11

Let's proceed to step 3:
11 can be fit into 69 6 times, resulting in a remainder of 3.
The number 6 becomes the next digit in our result. 
Result so far: 46.0
Subtract 66 from 69 to get 3.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 11

Moving on to step 4:
The number 11 fits into 32 2 times, leaving a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 462.0
Subtracting 22 from 32 leaves us with 10.
Grab the next digit (7) from the dividend, add it to 10, then carry on: 107 / 11

Advancing to step 5:
If we divide 107 by 11, we get 9 and a remainder of 8.
Write down 9 as next digit of the result. 
Result so far: 4629.0
The remainder is 8 after subtracting 99 from 107.
Include the next digit (8) from the dividend after 8, then repeat: 88 / 11

Advancing to step 6:
When dividing 88 by 11, we get 8 with a remainder of 0.
Use 8 as the next digit of our solution. 
Result so far: 46298.0
If we subtract 88 from 88, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 7:
The number 11 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 46298.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 8:
0 divided by 11 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 46298.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 46298.0 with a balance of 0.0.