For a projective variety $X$ over $\mathbb{C}$, let us denote by $CH_k(X)$ the Chow group of $k$-cycles of $X$, modulo rational equivalence. Also, let $CH_k(X)_{hom}$ denote $k$-cycles modulo homological equivalence.

I know that $CH_k(X,\mathbb{Q}) = CH_k(X)\otimes \mathbb{Q}$ (follows from flatness of $\mathbb{Q}$ over $\mathbb{Z}$). My question is:

In certain papers they use the notation $CH_k(X,\mathbb{Q})_{hom}$ without the definition; is it also same as $CH_k(X)_{hom}\otimes \mathbb{Q}?$ I just want to be sure without getting into trouble later.

Thanks in advance!