ATAR Notes: Forum

VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: Martoman on April 07, 2010, 09:48:44 pm

Title: division problem verification
Post by: Martoman on April 07, 2010, 09:48:44 pm: http://img146.imageshack.us/i/divisionv.png/

That picture is taken from a book. Am i going completely nuts, or when they assign values to r like r = 0,1,2 THEY COMPLETELY ignore the r term next to the 8? Or am I missing something.
Title: Re: division problem verification
Post by: TrueTears on April 07, 2010, 09:51:53 pm: Quote from: Martoman on April 07, 2010, 09:48:44 pm
http://img146.imageshack.us/i/divisionv.png/

That picture is taken from a book. Am i going completely nuts, or when they assign values to r like r = 0,1,2 THEY COMPLETELY ignore the r term next to the 8? Or am I missing something.
heh i see you're reading gareth, nice :P

anyways it's because the coefficient of q is 4, thus r must always be smaller than 4, so we have the values 0 , 1, 2, 3
Title: Re: division problem verification
Post by: Martoman on April 07, 2010, 10:01:58 pm: No no, i get that, but its the fact that say r = 0, doesn't that mean n = $4(4q^2 + 2q(0)) + 0$

So n = $16q^2$
Title: Re: division problem verification
Post by: kamil9876 on April 07, 2010, 10:14:51 pm: yes, if $r=0$ , then the number is equal to $16q^2$ for some integer $q$ .

It makes sense, $r=0$ means that a is a multiple of $4$ , hence $a=4q$ for some integer $q$ , and therefore $n=a^2=16q^2$

Modular arithmetic deals with this kind of stuff really easily.
Title: Re: division problem verification
Post by: Martoman on April 07, 2010, 10:18:12 pm: Quote from: kamil9876 on April 07, 2010, 10:14:51 pm
yes, if $r=0$ , then the number is equal to $16q^2$ for some integer $q$ .

It makes sense, $r=0$ means that a is a multiple of $4$ , hence $a=4q$ for some integer $q$ , and therefore $n=a^2=16q^2$

Modular arithmetic deals with this kind of stuff really easily.

SO WHY DOES THE BOOK KEEP THE R THERE???
I am officially losing it.
Title: Re: division problem verification
Post by: kamil9876 on April 07, 2010, 10:22:02 pm: Well yes, they could just as well have subbed it in and it you woudl still get the same information: its a multiple of 4.

Anything of the form 4(some integer) + 0 is a multiple of 4.

I guess they just didn't clean up the "some integer" part, but that's ok because you only need to know that it is an integer, and it is indeed.
Title: Re: division problem verification
Post by: Martoman on April 07, 2010, 10:27:29 pm: ... thank you for clearing up my insanity.
Title: Re: division problem verification
Post by: TrueTears on April 07, 2010, 10:29:29 pm: btw a tip, don't read too much into detail into the workings in gareth, try it urself, they're not always clear on the working :P
Title: Re: division problem verification
Post by: Blakhitman on April 08, 2010, 01:17:44 am: And you're 14 years old?

I didn't even know what a pro numeral was then...
Title: Re: division problem verification
Post by: Martoman on April 08, 2010, 01:52:34 am: mmmm i bet you didn't do methods when you were 13 either.