# Behavioural evidence for sex differences in the overlap between subtraction and multiplication

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## Abstract

The present study aims to identify factors that may influence the dissociability of number magnitude processing and arithmetic fact retrieval at the behavioural level. To that end, we assessed both subtraction and multiplication performance in a within-subject approach and evaluated the interdependence of unit-decade integration measures on the one hand as well as sex differences in the interdependence of performance measures on the other hand. We found that subtraction items requiring borrowing (e.g. 53–29 = 24, 3 < 9) are more error prone than subtraction items not requiring borrowing (e.g. 59–23 = 34, 9 > 3), thereby demonstrating a borrowing effect, which has been suggested as a measure of unit-decade integration in subtraction. Furthermore, we observed that multiplication items with decade-consistent distractors (e.g. 6 × 4 = 28 instead of 24) are more error prone that multiplication items with decade-inconsistent distractors (e.g. 6 × 4 = 30 instead of 24), thereby demonstrating a decade-consistency effect, which has been suggested as a measure of unit-decade integration in simple multiplication. However, the borrowing effect in subtraction was not correlated with the effect of decade consistency in simple multiplication in either men or women. This indicates that unit-decade integration arises from different systems in subtraction and multiplication. Nevertheless, men outperformed women not only in subtraction, but also in multiplication. Furthermore, subtraction and multiplication performance on correct solution probes were correlated in women, but unrelated in men. Thus, the view of differential systems for number magnitude processing and arithmetic fact retrieval may not be universal across sexes.

## Keywords

Number magnitude processing Arithmetic fact retrieval Subtraction Multiplication Unit-decade integration Sex differences## Notes

### Acknowledgments

We wish to acknowledge all participants for their time and willingness to contribute to this study. We thank Maria Leitner and Laura Popovic for their help with data collection.

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