First,make sure you order the correct diameter tires. There are two 16" wheel sizes,349 and 305,and they cannot be interchanged. Given that your bike came with 1.75" tires,I'm about 99% certain you're running 305's,but check the sidewall markings to make absolutely sure. As for the tubes,tubes are designed to fit a range of tire widths(they're rubber,they stretch). For example,the tubes in my cargo bike's 2" tires are for 1.5-2" tires. As long as the tires are within the tube's range,you'll be fine.
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C'dale BBU('05 and '09)/Super Six/Hooligan8and 3,Kona Dew Deluxe,Novara Buzz/Safari,Surly Big Dummy,Marin Pt Reyes,Giant Defy 1,Schwinn DBX SuperSport,Dahon Speed Pro TT,Brompton S6L/S2E-X