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:

- 5
2
or - 17
2
or - 23
2

How would you disentangle them?

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

- n
2

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

2
7
or 2
15
or 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:

- 5
3
or - 17
3
or - 23
3

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

- n
3

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

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.