We examined the contribution of a major predictor of basic literacy ability--phoneme awareness--to individual differences in two arithmetic computation tasks: a speeded task consisting of simple computation problems (arithmetic fluency) and an untimed, more complex computation task involving multi-digit operands (numerical operations). The contribution of phoneme awareness to word-reading fluency, untimed word-reading accuracy, and untimed spelling accuracy also was evaluated. Participants were 134 Brazilian Portuguese-speaking 4th and 5th grade students aged 8.67 to 11.75 years (M = 10.13 years; SD = 0.58). Individual differences in phoneme awareness accounted for significant and unique variance in performance on the arithmetic fluency task even after taking into account individual differences in grade in school, verbal ability, nonverbal ability, rapid naming, and verbal working memory. In contrast, phoneme awareness did not contribute uniquely to variance in performance on the more complex, untimed numerical operations task. In keeping with De Smedt's (2018) argument regarding the role of phoneme awareness in arithmetic ability, our findings suggest that the contribution of phoneme awareness is primarily restricted to the ability to solve very simple arithmetic problems for which the solution is likely to be retrieved directly and automatically from long-term memory. As expected, phoneme awareness and rapid naming were the two strongest predictors of individual differences in all literacy measures.