1. On the island, $2 / 3$ of all men are married and $3 / 5$ of all women are married. What fraction of the island's population is married
1. Let the number of married couples on the island be $N$ (i.e., $N$ women are married, and $N$ men are married). According to the problem, $N$ married women constitute $3 / 5$ of all women on the island, so there are $5 N / 3$ women on the island. Similarly, married men constitute $2 / 3$ of all men on the island, so there are $3 N / 2$ men on the island.

Therefore, the total number of residents on the island is $\frac{5}{3} N + \frac{3}{2} N = \frac{19}{6} N$, and $2 N$ residents are married. Thus, the desired fraction is

$$
\frac{2 N}{19 N / 6} = \frac{12}{19}
$$