Imputing # of unemployed from Labor Force Survey

I am working on state-level data, where one state has recently stopped publishing the absolute figures for the number of the unemployed. Instead, it currently only releases U and LFP rates.

Specifically, the unemployment rate went down from 12% in Q4, 2019, to 11.8% in Q1, 2020, and the labor force survey had the following data:

Q4, 2019
Employed Persons =                            3,170,272
LFPR(15) years and above=                     46.7%
Unemp Rate                                    12%


Q1, 2020
Employed Persons =                          3,203,423
LFPR(15) years and above=                   46.2%
Unemp Rate                                  11.8%

Therefore, I algebraically rearranged the figures as follows:

Q4, 2019    Q4 2019
LFPR = (# of workers + #of unemployed)/population 

0.467 = (3,170,272+#unemployed)/population
So total individuals in the LF ==  3,170,272/0.467
==6,788,591 
And the Unemployed individuals are == Unemp rate *6,788,591 or .12* 6,788,591 
==814,630.92    
Q1, 2020
LFPR = (# of workers + #of unemployed)/population
0.462 = (3203423+#unemployed)/p
So total individuals in the LF == 3,203,423/0.462
                 ==  6,933,816 

And the Unemployed individuals are == Unemp rate * 6,933,816 or .118* 6,933,816 
= 
818,190.29 

Assuming the imputation method above is correct, then the number of the unemployed has increased
by approximately 4,000 workers between Q4, 2019 and Q1, 2020, despite the apparent decline in the U rate.
Is this a correct imputation approach?