Effects of problem format on division and multiplication performance: division facts are mediated via multiplication-based representations.

In 2 experiments participants solved division problems presented in multiplication-based formats (e.g., 8 x _ = 72) more quickly than division problems presented in division-based formats (e.g., 72 / 8 = _). In contrast, participants solved multiplication problems presented in a division-based format (e.g., _ / 8 = 9) slowly and made many errors. In both experiments, the advantage for multiplication-based formats on division problems was found only for large problems (i.e., those with products or dividends greater than 25). These findings provide support for the view that large single-digit division facts are mediated via multiplication-based representations and that multiplication is the primary mode of representation for both division and multiplication facts.