Q&A #1493

Teachers' Lounge Discussion: Dividing fractions

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From: Gail

To: Teacher2Teacher Public Discussion
Date: 2000052411:21:42
Subject: Re: Dividing fractions

I have this in my notes somewhere, but no time to look for it (sorry!)
so I will just do a top of my head response, and hope someone else can
chip in... 
When we divide, we are looking for (some of the time, at least) "how
many groups of ____" there are.  For example, if you are dividing 24
by 5, you are wondering how many groups of 5 there are in 24, right? 
The answer , or quotient, is 4 whole groups, and 4 pieces, or 4/5 left

Suppose you are wondering what 24 divided by 1/2 is.  That problem is
really "how many groups of one half are there in 24"?  well, each
whole is worth two halves, and there are twenty four wholes, so there
are 48 halves.

Suppose that instead of having a whole number, you have a fraction as
the dividend...   3/4, for example.  Then you might wonder what 3/4
divided by1/2 is...    and that is really "how many gorups of 1/2 are
there in 3/4?" Picture it...    a rectangle with three parts shaded
out of four parts...   
What does half of the rectangle look like?  How many halves are there
in that shaded area that 3/4 covers?  There is one entire half, and
then just a part of a half ( half of a half, to be exact...    so the
answer is 1 and 1/2).  

Here is the problem in arithmetic:   3/4 divided by 1/2, which can be
written as a fraction itself, with 3/4 in the numerator, and 1/2 in
the denominator. To simplify that fraction, you can multiply both the
numerator and the denomniator by 2, so you would have 6/4 divided by
2/2, or 3/2 divided by 1, or just 3/2...hope this is a little


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