We're dividing 344000 by 9 
Let's see how many times 9 fits into 344000.

Going ahead to step 1:
When dividing 3 by 9, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 9

Moving on to step 2:
9 goes into 34 3 times with a remainder of 7.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 7 after subtracting 27 from 34.
Grab the next digit (4) from the dividend, add it to 7, then carry on: 74 / 9

Step 3:
When dividing 74 by 9, we get 8 with a remainder of 2.
The next digit of our result is 8. 
Result so far: 38.0
If we take 72 away from 74, we end up with 2.
Grab the next digit (0) from the dividend, add it to 2, then carry on: 20 / 9

Going ahead to step 4:
20 divided by 9 is 2 with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 382.0
Subtract 18 from 20 to get 2.
Grab the next digit (0) from the dividend, add it to 2, then carry on: 20 / 9

Advancing to step 5:
9 can be fit into 20 2 times, resulting in a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 3822.0
The remainder is 2 after subtracting 18 from 20.
Append the next digit (0) from the dividend to 2 and continue with: 20 / 9

Going ahead to step 6:
20 divided by 9 is 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 38222.0
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
When dividing 20 by 9, we get 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 38222.2
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
20 divided by 9 is 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 38222.22
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 38222.22, and the remainder is 0.002.