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Andrus, an All-Star last season after being runner-up for AL rookie of the year in 2009, got a $452,180 contract for this season.
The Rangers also reached deals Saturday with utility infielder Andres Blanco ($520,000), outfielder Craig Gentry ($416,000) and right-handers Omar Beltre ($415,000), Eric Hurley ($415,000) and Alexi Ogando ($430,150).
Right-hander Pedro Strop is the only player on the team's 40-man roster who has not yet signed a 2011 contract. The Rangers play their spring training opener Sunday.