The subtraction method for the matching between the matrix element (ME) and parton shower (PS), that has been developed for combining 0-jet and 1-jet production processes in association with electroweak-boson production in hadron collisions, is extended to multi-jet production. In order to include multi-jet MEs, we have to address the soft-gluon divergence together with the collinear divergence. We introduce an approximation which simultaneously reproduces both divergences in a form suitable for application to our subtraction method. The alteration in the subtraction can be compensated by applying an appropriate correction to corresponding non-radiative events. We demonstrate that $W$ + 0, 1, and 2 jet production processes can be consistently combined using the developed matching method.
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