2210.11 – Fraction Inequality

If $\dfrac{a}{b}<-\dfrac{c}{d}$ where $a, b, c,$ and $d$ are real numbers and $bd \neq 0$ , then:

$a$ must be negative,
$a$ must be positive,
$a$ must be nonzero,
$a$ must be negative or zero, but not positive,
$a$ can be positive, negative, or zero.

Solution

The correct answer is e: $a$ can be positive, negative, or zero. Here are some examples:

$a$ is negative: $\dfrac{-1}{151}<-\dfrac{-1}{2}$
$a$ is zero: $\dfrac{0}{151}<-\dfrac{-1}{2}$
$a$ is positive: $\dfrac{1}{151}<-\dfrac{-1}{2}$