State true/false:

The rational numbers, $\frac{1}{-2}+\frac{-5}{4}$ exhibit the closure property.

The given statement is true.

The closure property for rational numbers states that when two rational numbers are combined using the operations of addition, subtraction, multiplication, and division (provided the denominator is not zero), the result is also a rational number.

Given, $\frac{1}{-2}+\frac{-5}{4}$

LCM of 2 and 4 is 4.

$-\frac{1}{2}+\frac{-5}{4}=\frac{(-1)\times 2+(-5)}{4}=\frac{-2-5}{4}=\frac{-7}{4}$

In the expression $\frac{1}{-2}+\frac{-5}{4}$, both $-\frac{1}{2}$ and $-\frac{5}{4}$ are rational numbers, and the result of their addition, $-\frac{7}{4}$ is also a rational number. 

So, the given expression exhibits the closure property.