This paper presents a systematic approach to achieving fairness in binary classification, focusing on two well-known quantitative definitions of fairness: demographic parity (DP) and equalized odds (EO). The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. The approach is general and can handle a wide range of fairness definitions, including those formalized via linear inequalities on conditional moments. The paper introduces two reductions that work for any representation of the cost-sensitive classifier and compares favorably to prior baselines on various datasets, overcoming some of their disadvantages. The experimental results demonstrate the utility of the general-purpose approach for combining machine learning methods and quantitative fairness definitions.This paper presents a systematic approach to achieving fairness in binary classification, focusing on two well-known quantitative definitions of fairness: demographic parity (DP) and equalized odds (EO). The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. The approach is general and can handle a wide range of fairness definitions, including those formalized via linear inequalities on conditional moments. The paper introduces two reductions that work for any representation of the cost-sensitive classifier and compares favorably to prior baselines on various datasets, overcoming some of their disadvantages. The experimental results demonstrate the utility of the general-purpose approach for combining machine learning methods and quantitative fairness definitions.