Is it true that $[N*a]=N*[a]$?

Question

Let $[\cdot]$ denote closest integer of a real number. Is it true that $$ [N*a]=N*[a] $$ where $N\in \mathbb{N}$ and $a\in \mathbb{R}$?

Answer 1

Of course not necessary. Let $N=3$ and $a=2.5$, then

$[N\times a]=[3\times 2.5]=[7.5]=7$

$N\times [a]=3\times [2.5]=3\times 2=6$.

Answer 2

No. Let $N=10, a=0.3$. Try it.