The ratio of the B-s(0) and B-0 fragmentation fractions, f(s)/f(d), in proton-proton collisions at the LHC, is obtained as a function of B-meson transverse momentum and collision center-of-mass energy from the combined analysis of different B-decay channels measured by the LHCb experiment. The results are described by a linear function of the meson transverse momentum or with a function inspired by Tsallis statistics. Precise measurements of the branching fractions of the B-s(0) -> J/psi phi and B-s(0)-> D-s(-)pi(+) decays are performed, reducing their uncertainty by about a factor of 2 with respect to previous world averages. Numerous B-s(0) decay branching fractions, measured at the LHCb experiment, are also updated using the new values of f(s)/f(d) and branching fractions of normalization channels. These results reduce a major source of systematic uncertainty in several searches for new physics performed through measurements of B-s(0) branching fractions.