I think you should use unit multipliers.

In order to be able to get rid of an "old" unit in a NUMERATOR 
(DENOMINATOR) and bring in a "new" unit in its place:

Create a unit multiplier such that:

1. The unit multiplier has the "old" unit in its DENOMINATOR
(NUMERATOR) and the "new" unit in its NUMERATOR (DENOMINATOR).

2. The numerical coefficients of the numerator and denominator
of the unit multiplier must be such that the numerator and 
denominator are equal.  



Then cancel all the units that will cancel:



And we are left with this:

 

Edwin