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Fraction Diagrams

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Date: 03/13/2002 at 08:53:53
From: Amani Abuhabsah
Subject: Fractions for children

The question that my instructor wanted me to ask students is the
following:

In an adult condominium complex, 2/3 of the men are married to 3/5 of
the women. What fraction of the residents are married?

I multiplied and got 2/5 as the answer. I also thought that because
2/3 of the men are married, 1/3 are not, and because 3/5 of the women
are married, 2/5 are not, so I multiplied that ....

```

```
Date: 03/13/2002 at 12:57:49
From: Doctor Peterson
Subject: Re: Fractions for children

Hi, Amani.

You didn't say how old the students who are expected to do this are;
it's a nice problem that can be solved without much trouble by
algebra, but I'll try a visual method instead.

Here are all the men, 2/3 of whom are married:

+--------------+--------------+--------------+
|              |           married           |
+--------------+--------------+--------------+

Here are all the women, 3/5 of whom are married:

+---------+---------+---------+---------+---------+
|           married           |                   |
+---------+---------+---------+---------+---------+

But the married men are married to the women, so if we assume no
polygamy is allowed, we can match up the married men to the married
women:

+--------------+--------------+--------------+
|              |           married           | men
+--------------+--------------+--------------+
+---------+---------+---------+---------+---------+
women |           married           |                   |
+---------+---------+---------+---------+---------+

Now we can cut my bars into thirds and halves respectively, to find a
common denominator:

+----+----+----+----+----+----+----+----+----+
|              |           married           | men
+----+----+----+----+----+----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
women |           married           |                   |
+----+----+----+----+----+----+----+----+----+----+

However many people are represented by each little chunk, there are 12
chunks of married people out of 9+10 = 19 chunks in all, so 12/19 of
the people are married.

We can do the same thing algebraically. Letting X be the number of
married men and married women, there are 2X married people, 3/2 X men
residents, and 5/3 X women residents, making a ratio of
(2X) / (3/2 X + 5/3 X) = 2/(19/6) = 12/19.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions
Middle School Fractions

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