We report measurements of isotopic ratios of C, N, Mg, Si, Ca, Ti, Cr, and Fe in bulk samples (aggregates of many grains) of up to seven different fractions of silicon carbide (SiC), ranging from 0.38 to 3.0 mu m in diameter, from the Murchison CM2 carbonaceous chondrite. Ratios of C-12/C-13 range from 37 to 42 and N-14/N-15 ratios from 370 to 520, within the range of single-grain measurements on coarser samples and in agreement with an asymptotic giant branch (AGB) star origin of most of the grains. Variations among size fractions do not show any simple trend and can be explained by varying contamination with isotopically normal material. Silicon isotopic ratios vary only little and, with one exception, lie to the right of the single-grain mainstream correlation line. This might indicate a higher percentage of the minor populations Y and Z among finer grain-size fractions. All bulk samples have large Mg-26 excesses attributed to the presence of short-lived Al-26 the time of grain formation. Inferred Al-26/Al-27 ratios are much larger than those measured in single larger mainstream grains. This is probably because of the presence of SiC grains of type X; we obtain an estimate of 0.4 for their Al-26/Al-27 ratio. Our Ca-isotopic measurements, the first made on presolar SiC grains, show excesses in C-42, and Ca-43, which is in general agreement with theoretical expectations for AGE stars. Calcium-44 excesses are much larger than expected and are probably because of X grains, which have high Ca-44 excesses because of the decay of short-lived Ti-44 Produced in supernova explosions. We arrive at an estimate of 0.014 for the initial Ti-44/Ti-48 ratio of the X grains, within the range obtained from previous single X grain measurements. The Ti-isotopic ratios of the bulk samples show a V-shaped pattern with excesses of all isotopes relative to Ti-48. Isotopes Ti-46, Ti-47, and Ti-50, show excesses relative to the correlation between Ti and Si ratios for single grains and are in general agreement with theoretical models of s-process nucleosynthesis in AGE stars. In contrast, Ti-49 does not show any excess relative to the single-grain data; it also fails to agree with theory, which predicts much larger excesses than observed. Measured Cr-53/Cr-52 and Fe-57/Fe-56 ratios are normal within errors. The first result is expected even for Cr in AGE star envelopes, but the second result suggests that most of the Fe analyzed originates from contamination. We have found no simple trends in isotopic composition with respect to grain size that can be interpreted in terms of nucleosynthetic origin, unlike the results for Kr, Xe, Ba, and Sr.