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?
On
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.
On
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)
On
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 $-2 = (-1)+(-1)$.
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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!
On
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.)
When you multiply by a negative number the inequality sign switches.
For example
$$-1>-a \implies 1 < a$$