We develop the foundations for confirming monotonicity of a multi-term reciprocal function approximation. We introduce the concept of operand recoding to improve the accuracy of multipartite approximation. The results are applied to provide a proposed four-partite reciprocal implementation with total table size ∼27 Kbytes, that yields an IEEE standard, single precision sized format (24 bit) reciprocal instruction, that is a one-ulp monotonic reciprocal.