I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1? Because technically, the numerator is smaller than the denominator as $-2 < -1$
I know it's an extremely stupid question. 
I mean I know that I can just multiply $-1$ to the numerator and the denominator and I'll get $\frac 2 1$ which is greater than one.
But what exactly is happening here?
 A: If you regard $\dfrac82=4$ as true because $8 = 2+2+2+2$, i.e. you can write $8$ as the sum of four $2$s, 
then you can regard $\dfrac{-2}{-1}=2$ as being equally true because $-2 = (-1)+(-1)$.
A: What happens is that what you were taught (or found out) does not apply to negative numbers. If you multiply a negative number $a$ with a number $b > 1$, the result is not larger than $a$, but smaller. Essentially, multiplying $a$ by $b > 1$ "amplifies" $a$: if $a$ is negative, then the result is "more negative" than $a$ (i.e., smaller). Now, $a/b$ can be said to be the "amplification factor" you need to apply to $b$ in order to obtain $a$. In your case of $\frac{-2}{-1}$, $-2$ is "more negative" than $-1$, so you need to apply a factor which is larger than $1$.
The correct rule to remember if you want to account for negative numbers is that if the numerator of a fraction is smaller than its denominator in absolute value, then the fraction is smaller than $1$ again in absolute value. (The sign of the fraction is then determined by the usual sign rules.)
A: The fact that the numerator is smaller than the denominator does not imply that the fraction is smaller than $0$. Consider for example $\frac{1}{2
}$, where the exact same situation occurs, while obviously $0 < \frac{1}{2}$.
Rather, a fraction $\frac{a}{b}$ (with $b\neq 0$) should be interpreted as: what number do I have to multiply with $b$ to obtain $a$? In this case: which number should I multiply with $-1$ to obtain $-2$? Clearly, this number equals $2$. Therefore, $\frac{-2}{-1} = 2$.
Edit: Since OP has edited the question, the first paragraph of my answer is not relevant anymore. The second paragraph still is.
A: When you multiply by a negative number the inequality sign switches.
For example 
$$-1>-a \implies 1 < a$$
A: Whether the fraction is less than zero or not is independent of the magnitude of the numerator and denominator. It only depends on their signs.(unlike signs = less than zero) 
A: In my early days I used to interpret it as how many of the denominators can you fit in the numerator. I need 2 '-1's to get one '-2'. So 2 is your answer. Also your premise is an incorrect way of defining division. Leave this idea. Good luck!
