Fractional permissions enable sophisticated management of resource accesses in both sequential and concurrent programs. Entailment checkers for formulae that contain fractional permissions must be able to reason about said permissions to verify the entailments. We show how entailment checkers for separation logic with fractional permissions can extract equation systems over fractional shares. We develop a set decision procedures over equations drawn from the sophisticated boolean binary tree fractional permission model developed by Dockins
. We prove that our procedures are sound and complete and discuss their computational complexity. We explain our implementation and provide benchmarks to help understand its performance in practice. We detail how our implementation has been integrated into the HIP/SLEEK verification toolset. We have machine-checked proofs in Coq.