Abstract: In the field of cognitive arithmetic, the representation format for addition and multiplication facts is one of the most important problems. Researchers argued that generally there is a single-format representation for addition and multiplication facts. A new hypothesis was proposed in the present study. The hypothesis emphasized that people basically develop visual-Arabic codes for addition facts and auditory-verbal codes for multiplication facts, which can be called hypothesis of dissociated representation for addition and multiplication facts. In experimental research, undergraduates were asked to solve one-digit addition and multiplication problems (e.g., 2＋3，2×3) in which the operands were presented with Arabic digits(such as 1～9) or Chinese number( such as 壹～玖). There was much variation for the two physical formats of number in the visual dimension, but was invariable auditory dimension. According to the hypothesis, the manipulation of physical faces on number would bring much more influences on children’s solving addition problems. The experimental results were consistent with the prediction. Importantly, the result can’t be explained in terms of the relative difficulty level of Arabic-digit addition and multiplication. Present research supports Campbell’s complex-coding hypothesis, however, giving some constraints to it and further development

Key words: words addition, multiplication, arithmetic facts, multiplication rhymes, visual-arabic digit codes, auditory-verbal codes