>I would like to be able to come up with a concrete 'materials' >model of what is occurring. (I don't have one presently) > > >1/4 is 5/12 of 3/5. I pulled this from Ted's post and tried to >demonstrate this with tiles, but I was not able to it. Can you help me?
Well here is one way to represent this concretely.
Start with a strip of paper 20 cm long, ruled every 1 cm, as follows... ________ | | | | | | etc, (this diagram shows the first 2 cm of the strip) | | | ________
Colour in 1/4 of the strip, starting at the left. You will colour in 5 of the rectangles.
Cut off 3/5 of the strip, from the left, ie, 12 of the rectangles. Of those 12 rectangles, 5 are coloured in.
So 1/4 (of the whole strip) is 5/12 of 3/5 (of the whole strip).
BTW, I appreciated how Ted put these problems into a context. If my goal is to mark 3/5 of my exam papers today, and I've already marked 1/4 of them, why, I'm 5/12 of the way there!
Rex Boggs | High above the hushed crowd, firstname.lastname@example.org | Rex tried to remain focused. | Still, he couldn't shake one Glenmore High School | nagging thought: He was an Rockhampton, Quensland | old dog and this was a new Australia | trick - Gary Larson