  The ratio of the strange quark momentum fraction $\langle
x\rangle_{s+\bar{s}}$ to that of light quark $u$ or $d$ in disconnected
insertions (DI) is calculated on the lattice with overlap fermions on four
domain wall fermion ensembles. These ensembles cover three lattice spacings,
three volumes and several pion masses including the physical one, from which a
global fitting is carried out. A complete nonperturbative renormalization and
the mixing between the quark and glue operators are taken into account. We find
the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}}
({\rm DI})=0.795(79)(77)$ at $\mu = 2$ GeV in the $\overline{{\rm MS}}$ scheme.
This ratio can be used as a constraint to better determine the strange parton
distribution especially in the small $x$ region in the global fittings of PDFs
when the connected and disconnected sea are fitted and evolved separately,
demonstrating a new way that connects lattice calculations with global
analyses.
