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In the standard approach, predictions of perturbative Quantum Chromodynamicsfor ratios of cross sections are computed as the ratio of fixed-orderpredictions for the numerator and the denominator. Beyond the lowest order inthe perturbative expansion, the result does, however, not correspond to afixed-order prediction for the ratio. This article describes how exactfixed-order results for ratios of arbitrary cross sections can be obtained. Thegeneral method for computations in any order of the perturbative expansion isderived, and results for next-to-leading order and next-to-next-to-leadingorder calculations are given. The approach is applied to theory predictions forvarious multi-jet cross section ratios measured at hadron colliders. The twomethods are compared with each other and with the experimental data.Recommendations are made how to obtain improved theory predictions with morerealistic uncertainty estimates.

Perturbative QCD predictions in fixed order for cross section ratios