Which is the correct reasoning to use when simplifying this expression?
−200 ÷ −25
Responses
A The quotient of two even integers is always positive.The quotient of two even integers is always positive.
B The product of two even integers is always positive.The product of two even integers is always positive.
C The quotient of two negative integers is always negative.The quotient of two negative integers is always negative.
D The quotient of two negative integers is always positive.
C The quotient of two negative integers is always negative.
C The quotient of two negative integers is always negative.
The correct reasoning to use when simplifying the expression -200 ÷ -25 is:
C) The quotient of two negative integers is always negative.
To understand why this reasoning is correct, we need to understand the rules of integer division. When dividing two integers with the same sign (both positive or both negative), the result is always positive. However, when dividing two integers with different signs (one positive and one negative), the result is always negative.
In this case, both -200 and -25 are negative integers. Therefore, when we divide -200 by -25, the quotient will be negative.
To calculate the actual result, divide the absolute values of the numbers and assign a negative sign to the result: |-200| ÷ |-25| = 200 ÷ 25 = 8. However, since both numbers are negative, the final result is -8.