\(3\times1\frac{1}{8}=3\times\frac{1\times8+1}{8}=3\times\frac{9}{8}=\frac{3\times9}{8}=\frac{27}{8}=\frac{24+3}{8}=\frac{24}{8}+\frac{3}{8}=\boxed{3\frac{3}{8}}\\\\other\ way:\\\\3\times1\frac{1}{8}=3\times(1+\frac{1}{8})=3\times1+3\times\frac{1}{8}=3+\frac{3}{8}=\boxed{3\frac{3}{8}}\)