Simple mathematics and the US unemployment rate

Look, maybe I'm missing something here. I'm quite happy to be wrong about gut-feelings (as per my last post) but I'm not happy to be wrong when I could have done the work to prove myself wrong in the first place.

The unemployment rate dropped from 4.9% to 4.8%, but the amount of people out of work increased, thus spooking the markets only slightly. At issue here is the "participation rate", which decreased from 66.1% to 65.9%. This is the thesis argued by those at Angry Bear, who also point out that the employment to population ratio dropped as well (another way of measuring participation).

The problem here is with basic mathematics, so if anyone can correct me here I would oblige deeply.

First of all, the data:
  1. Unemployment rate: 4.9% in January, 4.8% in February.
  2. Participation rate: 66.1% in January, 65.9% in February.
  3. Civilian Employment-Population Ratio.: 62.9% in January, 62.7% in February.
(The links above are to the data figures from the St Louis Fed)

Okay, so maybe I'm making an error here, but this is how I see it:

Is there a way to determine what the unemployment rate would have been if the participation rate or civilian employment-population ratio remained the same. Surely it would simply be a matter of a simple equation:

(February Unemployment Rate)
----------------------------------------- x (January Participation Rate)
(February Participation Rate)

So, in this case, it would be (4.8/65.9) x 66.1

Which equals 4.81%

A similar equation using the employment-population ratio comes up with the same result.

Again, maybe I've got this wrong. Can anyone help?

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