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In a certain condominium community, 2/3 of all the women are married (to men) and 3/5 of all the men are married (to women). What fraction of the entire condominium community is married?

The fraction of married women (M) to unmarried women (U) and the fraction of married men (M) to unmarried men (U) can be visualized as follows.



We know that the number of women who are married equals the number of men who are married. So the women’s M region and the men’s M region must be the same size. By using the same units in both the women’s diagram and the men’s diagram, we see that the two M regions are six units long each. This represents a total of 12 units out of a total possible of 19 units (9 from the women plus 10 from the men). So 12/19 of the condominium community is married.