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### Congruent Fractions

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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
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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/
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Associated Topics:
Elementary Definitions
Elementary Fractions
Middle School Definitions
Middle School Fractions

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