Dividing Fractions

Date: 18 Mar 1995 23:31:33 -0500
From: Janet Lowe
Subject: Question on fractions

Dear Dr. Math,

My class would like a explanation on why you invert and 
multiply when dividing fractions.

Thanks!

5TH Graders at Kohl Elementary
Janet Lowe 
Boulder Valley Public Schools

Date: 20 Mar 1995 11:16:46 -0500
From: Dr. Sydney
Subject: Re: Question on fractions

Hello!

We are glad you wrote to us with your question.  You asked 
why you invert and multiply when dividing fractions, but, 
actually whether you realize it or not, you also invert and 
multiply when you are dividing whole numbers.  For 
instance, if you were to divide 2 by 3, you would write 2/3, 
right?  Well, that really is the same thing as multiplying 2 
by 1/3 (the inverse of 3), because 2 times 1/3 is 2/3.  Do 
you see?

So, you might ask, why do you invert and multiply when 
dividing numbers.  This is because when you are dividing 2 
numbers, you can always write the fraction as a product of 
two numbers, the numerator times the inverse of the 
denominator.  Take a fraction like 3/4.  We can write 3/4 
as 3 times 1/4, right?  And, 1/4 is the inverse of 4.  So, it 
makes sense to invert and multiply.  

I hope this helps clear any confusion!  Please write back if 
you have any more questions at all. 

--Sydney, "Dr. Math"