HELP!!!! Please!

Please help me with this problem:


We have a rectangle with sides 199x991 cm. The rectangle is devided into squares with each square side=1 cm (197209 squares all in all). We draw a diagonal. How much squares does the diagonal go through?


Pleaes help me i have been working on this for a week...lol And please try to make it clear so i understand every step wand why you have to do it. THank you!

You should be able at least to get started by working from the solutions to these related exercises:

Basketball Court
Using Relative Primes

Eliz.

thank you but i dont understand this part:

To get a better idea of what's going on, think about how the diagonal
can cross a square. Either it will go through two sides of a tile, or
it will pass through a corner (or two corners, if it's at a 45-degree
angle). Say we had a simpler case, where there are only six tiles,
arranged in a 2 x 3 block:
I know it's not a perfect drawing, but I hope you get the picture
(hah-hah). Notice that when we draw a diagonal, it doesn't go through
any corners except where we started and stopped. If you think about
it, that's because 2 and 3 are *relatively prime*. If two numbers are
relatively prime, it means that their greatest common divisor is 1.
The diagonal passes through 4 squares, because if it doesn't go
through any corners on its way across, then we know it must pass
through a square each time it goes 1 square down, and it must pass
through another square each time it goes 1 square to the right. So it
passes through (2+3)-1 = 4 squares.


i dont really understand what they mean. Can you pelase explain it?

It is pretty clear. If you have graph paper, draw a line thru, say a two by three box. It goes thru three horizontal rows.
It goes thru two veritcal rows.
So it goes thru 2+3-1=4 squares.
Try it with different shapes, some reletively prime, some not. I'm sure the idea will become clear. Since both 199 and 991 are primes they are relatively prime.
BTW. If you don't have graph paper you can print some from
http://www.mathematicshelpcentral.com/graph_paper.htm

Ok thank you and i think im begining to understand. But the quetion is how am i supposed to how many horizontal and vertical lines it goes through? And why do i have to subtract one. Im an idiot. I know that.