Mathematician: Consider what would happen if when we multiplied a positive number by a negative number we got a positive number. More intuitively though, why should we expect that negative numbers multiplying positive ones should lead to negative numbers? If we denote positive amounts of dollars with positive numbers (i.e. money owned), it makes sense that negative numbers would correspond to money owed (i.e. Of course, this only works if multiplying the positive number 3 with the negative number -20 leads to a negative number (in this case -60).