Answer
$-a$ is a odd number, because $a$ can be write as $2k+1$, substituting in the expression $-a$, we obtain that $-a = 2(-k - 1) + 1$, that is a odd number.
Work Step by Step
Let $a$ be a odd integer. $a$ can be write as:
$a = 2 k + 1$
(with $k$ being one integer number)
$k \in \mathbb{Z}$
Now, let's see what happens with $-a$:
$\begin{split}
-a & = -(2k + 1) \\
& = -2k -1 \\
& = -2k -2 + 1 \\
& = 2(-k - 1) + 1 \\
\end{split}$
Since $-k - 1$ is an integer, then $2(-k - 1) + 1$ is an odd number, by the definition of odd numbers.
