Given a hypergraph $H=(V,E)$, the fractional width $w^*(H)$ is $\min \sum_{a\in E}f(a)$ over all non-negative function $f\colon E\rightarrow\mathbb{R}$ such that for any $b\in E$, $\sum_{a\in E}f(a)|a\cap b|\ge 1$.
One claims that when $H$ is $r$-uniform, then $$w^*(H)\ge \nu^*(H)/r,$$ where $\nu^*(H)$ is the fractional matching number of $H$.
I am wondering why this is true. I don't have a clue about how to connect these two parameters together.