I know to turn the numbers into improper fractions, , flip the second fraction, change the division symbol to a multiplication symbol; simplify, and multiple across...but what do I do with the negative symbol?
Treat the negative symbol as a negative 1 (-1) that is being multiplied at the same time. If there is one negative symbol, and the operation is multiplication or division, you will have a negative answer. If there are none or two negatives, you will end up with a positive answer.
In your case, follow the strategy you outlined, but keep the negative symbol. Your answer will be negative.
(-1 1/5) / (2 1/5)
= (-6/5) / (11/5)
= (-6/5) * (5/11)
= - 30/55