Date: Aug 10, 1995 12:14 PM
Author: David Van Slyke
Subject: Re: nctm-l-digest V1 #119


> From: rex@bertha.cqu.edu.au (Rex Boggs)
> Date: Wed, 9 Aug 1995 19:48:40 +1000
> Subject: re: el fractions etc


[snip!]

> But what question can you pose where the necessary operation is
> dividing, say, 1/4 by 3/5? I used to think there weren't any such
> questions, until I read a good response last year (somewhere on the Net..)
>
> Think of division of fractions another way -
> first think of 3 divide 6 = 1/2 as meaning that 3 is 1/2 of 6. Also,
> 1/4 divide 2 = 1/8 means that 1/4 is 1/8 of 2, So 1/4 divide 3/5
> becomes ' 1/4 is what part of 3/5?' and the answer is that 1/4 is
> 5/12 of 3/5.
>
> I haven't come across anything better than that.


How about the following:

How many quarter-pound bags of rice would you need to buy in
order to have 5 1/2 pounds of rice?


(For a very thought provoking article on this subject, I recommend "The
Mathematical Understandings that Prospective Teachers Bring to Teacher
Education", by Deborah Loewenberg Ball, The Elementary School Journal,
Vol 90, No 4, Pg 449-466)

-DVS