Brain systems involved in arithmetic with positive versus negative numbers

Positive number arithmetic is based on combining and separating sets of items, with systematic differences in brain activity in specific regions depending on operation. In contrast, arithmetic with negative numbers involves manipulating abstract values worth less than zero, possibly involving different operation-activity relationships in these regions. Use of procedural arithmetic knowledge, including transformative rules like "minus a negative is plus a positive," may also differ by operand sign. Here, we examined whether the activity evoked in negative number arithmetic was similar to that seen in positive problems, using region of interest analyses (ROIs) to examine a specific set of brain regions. Negative-operand problems demonstrated a positive-like effect of operation in the inferior parietal lobule with more activity for subtraction than addition, as well as increased activity across operation. Interestingly, while positive-operand problems demonstrated the expected addition > subtraction activity difference in the angular gyrus, negative problems showed a reversed effect, with relatively more activity for subtraction than addition. Negative subtraction problems may be understood after translation to addition via rule, thereby invoking more addition-like activity. Whole-brain analyses showed increased right caudate activity for negative-operand problems across operation, indicating a possible overall increase in usage of procedural rules. Arithmetic with negative numbers may thus shows some operation-activity relationships similar to positive numbers, but may also be affected by strategy. This study examines the flexibility of the mental number system by exploring to what degree the processing of an applied usage of a difficult, abstract mathematical concept is similar to that for positive numbers.