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© Copyright 1998, Jim Loy
Does long division seem a little mysterious to you? I don't remember being told why it works. Is it a mystery? Or does it make sense?
29)6591
You and I know how to do this division problem. The first digit of the answer would seem to be 2. But, we are going to do it differently. We are going to make a guess at the entire answer. Let's make a guess of 218.
218 29)6591
We are not done yet, as 218 is probably the wrong answer. It was just a guess, after all. Since division is the inverse of multiplication, we need to multiply 218 x 29.
218
29)6591
6322
269
Now, we need to divide 269 by 29. We will make a guess of 8.
8
218
29)6591
6322
269
232
37
It looks like one more will work.
1
8
218
29)6591
6322
269
232
37
29
8
So, we can add these three numbers, 218+8+1=227, which is our answer (with a remainder of 8). That is the same answer that we would get if we divide the normal way.
But, did you see what we did? We just made guesses, multiplied, and subtracted, same as normal long division. Let's do the same division, almost normally.
7
20
200
29)6591
5800
791
580
211
203
8
That is almost normal division. I have added a few zeros, in bold. Do you see that this is not a mystery? It is just like the way we did it above, except that our first guess is 200, instead of 218, because we are leaning toward base 10. The other guesses are different, too.
I could go into more detail. But, that might just cloud the issue. Wasn't it easy to understand?
Note: The remainder means that the division didn't come out even. In grade school, before we learned about fractions, that was good enough. But, we know that the answer is 227 and 8/29. We could go out to several decimal places, if we want.
Also see Modular Arithmetic