Computational facility and the relationship between automaticity or efficient processing of addition facts and success in more complex tasks were examined in a cross-sectional study of 109 children from Grades 3 through 6. Latency data and interview protocols enabled identification of speed and strategy use on the addition facts, grouped into eight fact bundles (e.g. zeroes, small doubles), as a parsimonious procedure for exploring processing efficiency. Profiles of children based on latency performance on the fact bundles were clustered. The slowest cluster reported use of counting strategies on many bundles; the fastest cluster reported use of retrieval or efficient-thinking strategies. Cluster group was the best predictor of performance on multidigit tasks. Addition fact accuracy contributed only for tasks without carrying, and grade level was not significant. Analysis by error type showed most errors on the multidigit sums were due to fact inaccuracy, not algorithmic errors. The implication is that the cognitive demands caused by inefficient solutions of basic facts made the multidigit sums inaccessible. Suggestions for instruction of students who have problems learning basic arithmetic are made.