Empirical and conceptual relations of the carry effect in addition and the borrow effect in subtraction: An inversion account [Author Accepted Manuscript]

When multi-digit numbers are added or subtracted, the numbers are decomposed into digits, separate calculations are performed, and in some cases operations across place-values are necessary. The carry operation in addition (carrying a decade when the sum of the units exceeds 9) and the borrow operation in subtraction (borrowing a decade when the unit of the minuend is smaller than the unit of the subtrahend) increase the difficulty of arithmetic. This paper reviews the carry effect in addition and the borrow effect in subtraction and proposes a theoretical framework for the carry and borrow effects. First, the domain-general (working memory) and domain-specific processing demands (place-value processing) for the carry and borrow effects are characterized. Next, interindividual influences and heterogeneity of mathematics (math development and math ability), cognition (working memory and language), and emotion (math anxiety and attitudes) on the carry and borrow effects are summarized. Finally, the relation between the carry and borrow effects was analyzed to address the question whether the borrow effect is identical, inverse or different to the carry effect. The effects were found to be similar but the borrow effect is larger than the carry effect – suggesting an inverse relation between the effects.