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The geometric-arithmetic mean inequality is undoubtedly the most important one in the area of information aggregation. Recently, some q-rung orthopair fuzzy aggregation operators were proposed based on the Hamacher operations. In this paper, we give a detailed theoretical and practical analysis of the developed Hamacher arithmetic and geometric operators for q-rung orthopair fuzzy values. First, we investigate the monotonicity of these Hamacher aggregation operators on q-rung orthopair fuzzy values with respect to the parameter within Hamacher operations. Then, we discuss the limiting cases of these q-rung orthopair fuzzy Hamacher aggregation operators as the parameter therein approaches to zero or infinity and give a new characterization of the boundedness of these aggregation operators. Subsequently, we establish the geometric-arithmetic mean inequality for q-rung orthopair fuzzy information based on Hamacher operations. Finally, we present a decision making method by use of these aggregation operators and apply it to the problem of enterprise resource planning system selection. [ABSTRACT FROM AUTHOR]