Measurements of differential cross sections are presented for the production of a Z boson and at least one hadronic jet in proton-proton collisions at root s = 7 TeV, recorded by the CMS detector, using a data sample corresponding to an integrated luminosity of 4.9 fb(-1). The jet multiplicity distribution is measured for up to six jets. The differential cross sections are measured as a function of jet transverse momentum and pseudorapidity for the four highest transverse momentum jets. The distribution of the scalar sum of jet transverse momenta is also measured as a function of the jet multiplicity. The measurements are compared with theoretical predictions at leading and next-to-leading order in perturbative QCD.Austrian Federal Ministry of Science, Research and EconomyAustrian Science FundBelgian Fonds de la Recherche ScientifiqueFonds voor Wetenschappelijk OnderzoekConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Bulgarian Ministry of Education and ScienceCERNChinese Academy of SciencesMinistry of Science and TechnologyNational Natural ScienceFoundationofChinaColombian FundingAgency (COLCIENCIAS)Croatian Ministry of Science, Education, and SportCroatian Science FoundationResearch Promotion Foundation, CyprusMinistry of Education and Research, EstoniaEstonian Research Council, EstoniaEuropean Regional Development Fund, EstoniaAcademy of FinlandFinnish Ministry of Education and CultureHelsinki Institute of PhysicsInstitut National de Physique Nucleaire et de Physique des Particules / CNRS, FranceCommissariat a l'Energie Atomique et aux Energies Alternatives / CEA, FranceBundesministerium fur Bildung und Forschung, GermanyDeutsche Forschungsgemeinschaft, GermanyHelmholtz-Gemeinschaft Deutscher Forschungs zentren, GermanyGeneral Secretariat for Research and Technology, GreeceNational Scientific Research Foundation, HungaryNational Innovation Office, HungaryDepartment of Atomic Energy, IndiaDepartment of Science and Technology, IndiaInstitute for Studies in Theoretical Physics and Mathematics, IranScience Foundation, IrelandIstituto Nazionale di Fisica Nucleare, ItalyKorean Ministry of Education, Science and Technology, Republic of KoreaWorld Class University program of NRF, Republic of KoreaLithuanian Academy of SciencesMinistry of Education, and University of Malaya (Malaysia)Mexican Funding Agency (CINVESTAV)Mexican Funding Agency (CONACYT)Mexican Funding Agency (SEP)Mexican Funding Agency (UASLP-FAI)Ministry of Business, Innovation and Employment, New ZealandPakistan Atomic Energy CommissionMinistry of Science and Higher Education, PolandNational Science Centre, PolandFundacao para a Cienciaea Tecnologia, PortugalJINR, DubnaMinistry of Education and Science of the Russian FederationFederal Agency of Atomic Energy of the Russian FederationRussian Academy of SciencesRussian Foundation for Basic ResearchMinistry of Education, Science and Technological Development of SerbiaSecretaria de Estado de Investigacion, Desarrollo e Innovacion and Programa Consolider-Ingenio, SpainSwiss Funding Agency (ETH Board)Swiss Funding Agency (ETH Zurich)Swiss Funding Agency (PSI)Swiss Funding Agency (SNF)Swiss Funding Agency (UniZH)Swiss Funding Agency (Canton Zurich)Swiss Funding Agency (SER)Ministry of Science and Technology, TaipeiThailand Center of Excellence in PhysicsInstitute for the Promotion of Teaching Science andTechnologyofThailandSpecialTaskForceforActivating ResearchNational Science and Technology Development Agency of ThailandScientific and Technical Research Council of TurkeyTurkish Atomic Energy AuthorityNational Academy of Sciences of Ukraine, UkraineState Fund for Fundamental Researches, UkraineScience and Technology Facilities Council, United KingdomU.S. Department of EnergyU.S. National Science FoundationMarie Curie programEuropean Research CouncilEPLANET (European Union)Leventis FoundationA. 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