Proportional fair scheduling attains a graceful trade-off between fairness among users and total system throughput. It is simple to implement in single carrier transmission systems, while changes to a prohibitively complex combinatorial problem for multi-carrier transmission systems. This letter addresses a couple of conditions that approximate multi-carrier proportional fair scheduling (MCPF) as carrier-by-carrier proportional fair scheduling (CCPF), which has much lower complexity than MCPF. Numerical results show that the proportional fairness metric of CCPF approaches to that of MCPF for those conditions.