Fractional conductance is measured by partitioning a ν=1 edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the ν=1 plateau, respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance e^{2}/3h arising from edge reconstruction. The results reveal a remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing magnetic field.