20. On a remote desert island a team of anthropologists finds that 2/3 of the adult females are married to 1/2 of the adult males. Assuming that all marriages are monogamous and heterosexual, what fraction of the adults on the island are married?

 

A picture is helpful in dealling with this problem. We want to match up 2/3 of the females with 1/2 of the men

 

 

The shaded regions represent the married adults, and the unshaded regions represent the unmarried adults. If we express the 1/2 of the men as 2/4 of the men, then the regions for the men and the women matcvh up, and we see that there are a total of 4 shaded regions out of 7 total regions. As a result, 4/7 of the adults are married.

 

This is a problem where you would want to find common numerators and add the tops and bottoms.