Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was shown that sparse-arrays are really 3 dense-arrays (dense-shape, index-array, and data-array). Dense-array manipulations of these constituent arrays are used to determine the resulting partial-trace. Because computational arrays are used in a verity of different studies, these methods are broadly applicable.