The fastest way to compare negative fractions is by using cross multiplication. Simply multiply the numerator (top number) of the first fraction with the denominator (bottom number) of the second fraction. This sum will give you the value of the first fraction. Then multiply the denominator of the first fraction with the numerator of the second fraction. This will give you the value of the second fraction. It doesn't matter how you order your fractions when comparing them, just ignore the negative sign for now.
After you have converted your fractions into integers, put a negative sign in front of them. When looking at your fractions on the number line, they will always be on the left side of zero. The only time a value will be on the right side of zero is when you multiply two positive numbers. As long as one of the numbers is negative, the sum will have a negative value.
When comparing positive fractions, the bigger number is the bigger value (i.e., 20 is larger than 10). It's the other way around when comparing negative fractions (i.e., -10 is larger than -20). This is because the smaller number is closer to zero than the larger number. It may be easiest to compare fractions on a number line. When dealing with negative fractions, the value closest to zero is the largest.
If your fractions have like denominators, you don't have to perform cross multiplication. All you have to do is compare the numerators of the fractions. If the numerators are positive, the bigger number has the bigger value. If the numerators are negative, the smaller number is the bigger value. Don't be surprised to see fractions with positive denominators and negative numerators and vice versa.