Distributed average consensus finds extensive applications in multi-agent systems where a group of agents are required to agree upon a common value. Motivated by the need to conserve energy for large-scale multi-agent systems, we propose an infrequent communication scheme that allows the system to reach average consensus at low energy consumption. The proposed scheme divides the original large network into two smaller sub-networks with some overlapping nodes. Agents in the two sub-networks take turns to broadcast and update their local estimates, until reaching consensus. We prove that the proposed scheme guarantees asymptotic convergence when both subnetworks are connected and have overlapping nodes. Simulations corroborate the energy saving capability of the proposed scheme.