Multiplying , , , and with Counters
The two-color counter model effectively demonstrates integer multiplication by interpreting it as repeated addition or subtraction. For , adding positive counters three times gives positives. For , adding negative counters three times gives negatives. Conversely, multiplying by a negative number designates taking away. To model , we must subtract positive counters three times. Starting from a blank workspace, we insert neutral pairs, then remove the positive counters, leaving negatives (yielding ). Similarly, for , we must take away negative counters three times. After introducing neutral pairs, removing the negative counters leaves positive counters (yielding ). This illustrates why taking away a negative quantity mirrors adding a positive value.
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Multiplying , , , and with Counters
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