In order to calculate the quotient 100÷(-50), you consider that you first calculate the quotient between the numbers, in this case 100÷50 and then you also take into accoun the rules for the division of signs. You add the result of the division of signs to the number that results of the division of the numbers.
Thus, you have:
100 ÷ 50 = 2
plus (+) divided minus (-) is equal to minus (-)
Then, the result of the quotient is:
100÷(-50) = -2