Q&A #16329

Division of Fractions

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From: Gail (for Teacher2Teacher Service)
Date: Nov 30, 2005 at 18:21:25
Subject: Re: Division of Fractions

Dear Angelina,

This is just what my 6th grade students are working on right now.

Think about it this way...   You have 1 3/4 of something, maybe a cake, or a 
container of some juice...   and you have to share it with others.  Suppose 
the servings will be the size of "1/2" -- in this case, one half of whatever 
the whole thing is that you are serving.  You are trying to find out how 
many servings you can get from that cake, or the juice.

I tell my students to look at the problem this way:  how many 1/2s can you 
get from 1 3/4?   You can estimate it by thinking about how many halves you 
can get from 2...   since there are 2 halves in 1, there must be 4 halves in 
2.  That is a good estimate for you to start with.

So, when you actually find the exact answer, you are still looking for how 
many halves are in the amount 1 3/4.  You know there are 2 in the whole 1, 
and another  half in the 3/4.  there is a little piece left over, isn't 
there?  That is the tough part -- trying to figure out how much that piece 
is worth.  If you compare it to the 1/2 you are dividing by, you will notice 
that the little piece is half the size of the 1/2.  That is good to notice.  
You will use that information in your answer.  There are 3 "halves" and 1/2 
of a half in 1 3/4.

Then, to do the problem with numbers, just change the 1 3/4 into an improper 
fraction, 7/4.  Instead of dividing, just multiply by the reciprocal of 1/2, 
which is 2/1.

7/4 x 2/1 = 14/4   or 7/2    or 3 1/2.   You can get 3 1/2 servings of cake, 
or juice, from 1 3/4, if the servings are 1/2 in size.

Hope this helps...  

 -Gail, for the T2T service

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