IGH – multiply or divide?

[Vargas]

I don't know how they work and I am trying to understand it. Please help me!

Given a 3 speeds IGH rated for example 75%, 100% and 133%.
I suppose I use the difference between gears and divide when going up and multiply when going down. Is it correct?
Thus the differences are:
1st to 2nd : 1.25 (25%)
2nd to 3rd: 1.33 (33%)
Supposing I am running a 16T cog.
16T cog going from 1st to 2nd would be equivalent to moving to a 12.8T cog (16T/1.25).
16T cog going from 2nd to 3rd would be equivalent to moving to a 12T cog (16T/1.33).
16T cog going from 3rd to 2nd would be equivalent to moving to a 21.3T cog (16T*1.33).
16T cog going from 2nd to 1st would be equivalent to moving to a 20T cog (16T*1.25).
Is my understanding correct?

 

[Vargas]

Or to make it easier

Starting with a 16T cog at 2nd gear (100%).

16T cog going from 2nd to 1st would be equivalent to moving to a 20T cog (16T*1.25).
16T cog returning from 1st to 2nd would be equivalent to moving to a 16T cog (20T/1.25).
16T cog going from 2nd to 3rd would be equivalent to moving to a 12T cog (16T/1.33).
16T cog returning from 3rd to 2nd would be equivalent to moving to a 16T cog (12T*1.33).

Is that correct?

 

[John Tolhurst]

Maybe fractions is easier. 
1

Maybe fractions is easier.

1 to 2: 4/3
2 to 3: 4/3 the same!

changing down:
16 * 3/4 = 12
changing up:
16 * 4/3 = 21.3

 

[Vargas]

I got it!
Crystal clear.

I got it!
Crystal clear. Thanks!