Multiplying Fractions

Date: 01/20/97 at 10:31:59
From: Jen
Subject: Multiplication

Since we have defined multiplication as repeated addition, how is 
it possible that when you multiply two fractions, the product is 
smaller than either of the fractions?  

Date: 01/20/97 at 13:34:58
From: Doctor Ken
Subject: Re: Multiplication

Hi there -

Perhaps a more useful way to think of multiplication is to use the 
words "groups of."  For instance, when you have 4 x 5, think of it as 
"4 groups of 5".  We can write that out as 5 + 5 + 5 + 5, and add it 
up to get 20.  If we have 1/2 x 2, then we think of it as "half a 
group of twos", so our total is 1.  If we have 1/3 x 1/4, then that's 
one-third of a group of 1/4ths, and maybe this will make more sense to 
you.  One-third of a positive number is always smaller than the 
original number was.  That's one way to make sense of the equation 
1/3 x 1/4  =  1/12.

-Doctor Ken,  The Math Forum
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