if a 100 by 104 rectangle is divided into unit squares, a diagonal line will pass through how many unit squares?

3 by 3 square diagonal passes through 3 squares. 3 by 6 diagonal passes through 6 squares. the answer is not 104.

well, this is an interesting question. trying to find a pattern is the right way to go. i first reduced your rectangle to a rectangle that has dimensions of 25 by 26, since the diagonal of the full rectangle will also pass through the corner of this rectangle....this will happen 4 times for your full diagonal. it's kind of like slope....you did a 3 by 6 rectangle already. a slope of 3/6 is the same as the slope 1/2.....3 times, if you know what i mean.
 
i then drew rectangles with dimensions which have no common factors. like a rectangle of 2 by 3 or 3 by 7. this is what i found.
 
dimensions                number of squares diagonal passes through
2 by 3                                            4
2 by 5                                            6
3 by 4                                            6
4 by 7                                           10
5 by 9                                           13
3 by 7                                            9
 
i'm pretty convinced that you add the 2 dimensions and then subtract 1when the dimensions are reduced like i did.
so, i think your answer should be 25 + 26 - 1 which is 50. then multiply that by 4 to get 200.
 
hope this helped.....and i think it's correct!!!!