Fraction DiagramsDate: 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 .... Can you help me get the answer please? Thanks a lot. 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/ |
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