TITLE: I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1?
QUESTION [8 upvotes]: 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?

REPLY [5 votes]: 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.)