$a < b$ and $c$ is a non-zero real number. Which of the following are always true?

I. $a + c < b + c$

II. $ac < bc$ when $c > 0$

III. $\frac{a}{c} < \frac{b}{c}$

IV. $\frac{1}{a} > \frac{1}{b}$ when $0 < a$

Explanation

1. 01

   Adding any number, or multiplying by a positive one, keeps the direction (I and II). For positive numbers, the larger has the smaller reciprocal (IV).

2. 02

   III fails when $c < 0$: $1 < 2$ but $\frac{1}{-1} > \frac{2}{-1}$.