Four digit division

We talked about 3 digit division here:

4 digit division can be done with the same 2 step method as 3 digit division.

Let’s try: 10,000 / 3,235
Mentally, split the 10,000 into 100 | 100 and 3235 into 32 | 35.

1: Focus on the left parts: 100 and the 32. 3 times 32 is 96. 100 - 96 = 4. The remainder of ‘4’ is actually 4 | 00 or 400.
2 So 4 => 400. 3 x 35 = 105. 400-105 = 295.

Add zero => 2950. 2950 < 3235, so next digit is a zero.

Add another zero to 2950 => 29,500. Split into 295 | 00.
1: Left parts of ‘295 | 00’ and ‘32 | 35’ is 295 and 32. Try 9 times. First subtract 9 times 30 and then 9 times 2. 295 - 270 = 25. 25 - 18 = 7 or 7 | 00. Mentally do 295 - 270 first. Then do 25 -18. Small and easy steps.
2. 7 | 00 => 700. We need to subtract 9 times 35 from 700. 9 times 30 is 270 and 9 times 5 is 45. 700 - 270 = 430. 430 - 45 = 385. I do: 430 - 45 => 430 - 30 -15.

Add zero => 3850.
Of course one time. 3850 - 3235 = 615.

Answer so far is 3.091.

Next digit.
Remainder becomes 6150. twice 3235 is too big ,so digit is one and just subtract: 61 | 50 - 32 | 35 = 29|15 = 2915.

Add zero and split into 2 => 291 | 50.
Again, focus only on 291 and the 32. Try 9 times. 291 - 270 = 21. 21 - 18 = 3 or 3 | 50 = 350.
Now focus on 350 and subtract 9 times 35. 350 - 270 = 80. 80 - 45 = 35.
If you realize that 350 = 10 times 35, then subtracting 9 times 35 is easy.

If you see a remainder of 35, we can do 2 digits at the same time:
35 => 3500 and 3500 - 3235 = 165.

We now have 3,0911901.

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