A precise measurement of the total reaction cross sections in a model independent way was made using the sum-of-differences (SOD) method in 1 2 C, 1 3 C, 1 5 N, 1 6 O+ 2 8 Si elastic scattering at incident energies much higher than the Coulomb barrier. Cross Sections have been measured in an angular range of θ l a b =0.6°∼2.0° with high accuracy. The scattering amplitudes at θ=0° and the total reaction cross sections were deduced from the present observation by the SOD method. These total reaction cross sections were compared with the results obtained from optical model analyses. Furthermore, it was shown that the contribution of the complete-fusion process to the total-reaction cross section in the 1 2 C+ 2 8 Si scattering system was 75% at E c m =45.5 MeV.