help! how to deal with negative fractions?

This problem completely confuses me as it had negative fractions. The answer that I worked out is different from the answer key.

Simplify:

(3a/-b) (b^2/6b) (b/-a)

= (3/6) (a/-a) (b^3/-b^2)

= (1/2) (-a^0) (-b^1)

= (1/2) (1) (-b)

= **-**b/2

The answer key gives **+**b/2 as the answer.

Should the negative sign in (3a/-b) be applied to 3 as well, such that step 2 would be:

(**-**3/6) (a/-a) (b^3/-b^2)

By having a -3, I could simplify the expression to +b/2. Does this mean that the negative sign in -b should be applied to 3 as well?

Please help, I can't find any resource that discusses simplifying negative fractions. Thanks in advance.