This problem follows on from Twisting and Turning in which twisting has the effect of adding 1 and turning transforms any number into the negative of its reciprocal.

It would be nice to have a strategy for disentangling any tangled ropes...
I wonder if it is always possible to disentangle them...

Before reading on, select a few fractions and try to get back to 0.

You could consider ropes that have been tangled up and have left you with a negative fraction containing a 2 as the denominator.
eg:

$- \frac{5}{2} or - \frac{17}{2} or - \frac{23}{2}$

How would you disentangle them?

Try to describe an efficient strategy for disentangling any fraction of the form

$- \frac{n}{2}$

Can this help you disentangle any positive fraction containing a 2 as the numerator?
eg:

$\frac{2}{7} or \frac{2}{15} or \frac{2}{32}$

Next, you could consider ropes that have been tangled up and have left you with a negative fraction containing a 3 as the denominator.
eg:

$- \frac{5}{3} or - \frac{17}{3} or - \frac{23}{3}$

Try to describe an efficient strategy for disentangling any fraction of the form

$- \frac{n}{3}$

and use this to suggest a strategy for disentangling any fraction of the form

$\frac{3}{n}$

Next, you could consider ropes that have been tangled up and have left you with negative fractions containing 4, 5, 6 ... as the denominator, or positive fractions containing 4, 5, 6 ... as the numerator.

Can you develop a strategy for disentangling any tangled ropes, irrespective of the fraction you have ended up with?

You may want to take a look at All Tangled Up after this.