Congruent Fractions

Date: 04/03/97 at 18:29:44
From: Clara Rowe
Subject: Congruent Fractions

My teacher gave me an assignment to find out what congruent fractions 
are. I can't find out anywhere. Can you tell me what congruent 
fractions are?

Clara

Date: 04/04/97 at 19:48:16
From: Doctor Mike
Subject: Re: Congruent Fractions

Dear Clara,
  
I think congruent fractions also sometimes go by the name of 
equivalent fractions, meaning they look different but are really 
equal. Here is an example.
  
If you cut a pie straight down the middle, from one edge to the other, 
then you have 2 big pieces that are the same shape. If you take one of 
those 2 pieces you have half of the pie, or the fraction 1/2.   
  
Now think about cutting the pie 2 more times so that you have 6 wedge-
shaped pieces of the same shape.  This is the standard way of cutting 
a round pie for serving.  But now to get half of the pie you have to 
take 3 of the 6 pieces.  When you put this situation in the form of a 
fraction you get 3/6.  This fraction means "3 of the total of 6 equal 
pieces", but you and I both know that what you really have is half of 
a pie.
    
Some fancy restaurants try to make more money by cutting a pie into 
8 equal-size and equal-shape wedge shaped pieces.  In this kind of a 
restaurant, half a pie would be the fraction 4/8 or four eighths.  
  
Anyway, the fractions 1/2, 3/6, and 4/8 all mean half of a pie, and 
they are equivalent fractions.  They look different, but they amount 
to the same thing.  
  
This is making me hungry!  How about you?   I hope this helps.

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/