Why is the quotient of two negative integers is positive?

because when multiplying or dividing two negatives equal a positive.

Let me try to explain it using Words and an example from everyday life.

Imagine you say "I am not going to school." The not is a negative and means you are not going! Now say "I am not not going to school." Since there are two nots they actually cancel each other out and in this sentence. It is called a double negative. Your first not is actually cancelling out your second not which then makes you say that you are going to school. This is the same idea in math when multiplying and dividing. When you have two negatives they cancel each other out do not count just like in the "not not" idea.

if this makes no sense i am sry. its the way how i was taught in 8th grade to under stand double negatives and it made sense to me.