1. Given real numbers $a$, $b$, $c$ satisfy $(a+b)(b+c)(c+a)=0$ and $abc<0$. Then the value of the algebraic expression $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}$ is
$=.1 .1$.
From $(a+b)(b+c)(c+a)=0$, we know that at least two of $a, b, c$ are opposite numbers. Also, since $abc<0$, it follows that among $a, b, c$, there must be two positive and one negative.
Thus, the value of $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}$ is 1.