A frequency beam splitter (FBS) with the split ratio of 0.5, i.e., 50/50 FBS, can be used as the frequency-mode Hadamard gate for frequency-encoded photonic qubits. A FBS with the split ratio of 1 is exactly the coherent frequency converter (CFC) for frequency up or down conversion of photons. Previous works revealed that all kinds of 50/50 FBS and CFC operating at the single-photon level had overall efficiency or output-to-input ratio around 50% or less. In this work, our 50/50 FBS and CFC are made with the four-wave mixing (FWM) process based on the double- electromagnetically induced transparency (EIT) scheme. We achieved an overall efficiency of in the 50/50 FBS and that of in the CFC using coherent-state single photons, both of which are the best up-to-date records. Furthermore, we utilize the scheme of Hong-Ou-Mandel interference (HOMI) to measure the fidelity or degree of coherence of the FBS. The fidelity indicated by the HOMI's measurement of the 50/50 FBS is . This high fidelity demonstrates the low noise of the frequency conversion in the EIT-based FWM process. Such low-loss high-fidelity FBS with the tunable split ratio can lead to useful operations or devices in long-distance quantum communication.