Long division(with and without polynomials)

[Byrgg]

I had to relearn long division recently, because I just started division with polynomials in my math class. I realized that I didn't quite understand the whole process of long division. I can follow the steps that the teacher sets out, I just don't really understand the steps, why you use this specific method. I'm not debatingit or anything, I'm just wondering about the reasoning behind the steps, I guess another way to describe what I'm looking for would be how someone would come up with the idea of long division, and understand why you take all of the steps. This is probably really simple, but I just don't really understand it. He's an example to aid this explanation: 210/7.

I used a fairly simple example just so that I can get the important points. If someone could explain the process of long dividing this, as well as the reasoning, I'd be greatful. Note, I know how to long divide it, I just understand the method.

I'll get to the harder polynomial confusion after this has been sorted out. Thanks in advance.

 

[matt grime]

what does 210 over 7 mean? we trying to find numbes q and r so that 210 = 7*q + r. 210 has three figures so we start by seeing if we can write 210 as 700*s + something positive. cose then we could write

210 =7*100*s + something

and work on the something recursively.

Of course 210 is less than 700 so we can't do this. The next nicest big multiple of 7 is 70, so what happens if we try to write 210 as 70*3 +0 so we stop.Try working through a more difficult example to see what's going on

 

[Byrgg]

Ok, a more difficult example, let's say 567/8.