The fractional quantum Hall effect (FQHE) has been observed in ultraclean suspended graphene, revealing strongly correlated electron states under magnetic fields. In two-dimensional (2D) electron systems, strong magnetic fields dominate Coulomb interactions, leading to novel states like FQH liquids. These liquids involve complex composite quasiparticles, with Hall conductivity quantized as rational fractions of the conductance quantum. Graphene, with its massless chiral fermions, has shown unusual IQH effects, but its correlated electron phenomena were previously weak due to disorder. Here, the FQHE is observed in ultraclean suspended graphene, showing a tunable energy gap at low carrier density. The IQH effect in graphene exhibits unique filling factors due to its four-fold spin and valley degeneracy and Berry phase. At high magnetic fields, additional IQH states emerge, suggesting electron-electron interactions lift degeneracy. The FQHE in graphene, predicted to occur due to strong interactions, has been observed in suspended graphene with high mobility. The FQHE is identified as a v=1/3 state, with conductance values consistent with this state. The insulating state at low density is observed, with a tunable energy gap. The FQHE in graphene is robust, attributed to enhanced electron interactions due to reduced dielectric screening. These findings suggest graphene could be a platform for exotic quantum devices, such as topologically protected quantum computing.The fractional quantum Hall effect (FQHE) has been observed in ultraclean suspended graphene, revealing strongly correlated electron states under magnetic fields. In two-dimensional (2D) electron systems, strong magnetic fields dominate Coulomb interactions, leading to novel states like FQH liquids. These liquids involve complex composite quasiparticles, with Hall conductivity quantized as rational fractions of the conductance quantum. Graphene, with its massless chiral fermions, has shown unusual IQH effects, but its correlated electron phenomena were previously weak due to disorder. Here, the FQHE is observed in ultraclean suspended graphene, showing a tunable energy gap at low carrier density. The IQH effect in graphene exhibits unique filling factors due to its four-fold spin and valley degeneracy and Berry phase. At high magnetic fields, additional IQH states emerge, suggesting electron-electron interactions lift degeneracy. The FQHE in graphene, predicted to occur due to strong interactions, has been observed in suspended graphene with high mobility. The FQHE is identified as a v=1/3 state, with conductance values consistent with this state. The insulating state at low density is observed, with a tunable energy gap. The FQHE in graphene is robust, attributed to enhanced electron interactions due to reduced dielectric screening. These findings suggest graphene could be a platform for exotic quantum devices, such as topologically protected quantum computing.