>>13552750Long division uses 2 properties of numbers.
If you do 12 / 3 you get 4 right?
If you do 120 / 3 you get 40.
If you do 1200 / 3 you get 400.
What about 12000 / 3? 4000.
Property #1: You can just ignore the 0s at the end when doing the division and then add them back after
Note: If you get fractional answers, instead of adding 0, adjust the decimal.
For example, 5 / 4 is 1.25, so 50 / 4 is 12.5, and 500 / 4 is 125.
What is 2468 / 2?
You can just divide each digit by itself right?
That because 2468 / 2 = (2000 + 400 + 60 + 8) / 2 = 2000 / 2 + 400 / 2 + 60 / 2 + 8 / 2 = 1000 + 200 + 30 + 4 = 1234
Property #2: The division of a sum is just the sum of the divisions. (i.e. division is distributive)
OK so how does long division work, let's say I want to do 3225 / 25.
I can't do it all at once, so I'll just do a few digits at a time (I can do that because of property #2).
3 by itself is not big enough to be divided by 25.
32 is big enough. 25 can only go once into 32. So I'm going to take out 2500 out of 3225.
3225 / 25 = 2500 / 25 + 725 / 25 = 100 + 725 / 25
OK, now I have to do 725 / 25. Again, I'm going to take just enough digits until I get 25 or more, in this case, I take 72.
25 goes 2 times in 72. So I'm going to take out 500 out of 725.
100 + 725 / 25 = 100 + 500 / 25 + 125 / 25 = 100 + 20 + 125 / 25
Almost done, now I have to do 125/25. I need to take just enough digits until I get 25 or more. 1 is not enough, 12 is not enough, I need to take everything 125. Not shortcut for this one, I can do this one in my head 125 / 25 = 9.
So we have:
3225 / 25 = 2500 / 25 + 500 / 25 + 125 / 25 = 100 + 20 + 9 = 129.
Long division is just that, but with notational shortcuts.
For example, instead of writing 3225 / 25 = 2500 / 25 + 725 / 25 = 100 + 725 / 25
You just put the 1 at the hundreds position on top and carry down the 725 bellow.
