And if the participation rate was the same as it was under Eisenhower, the unemployment rate would be negative.
All you’re saying is the if there were more unemployed, then the unemployment rate would be higher. But the fact is that fewer people want to work, and that’s why participaton is down. No. I don't think you understand.
Under Eisenhower, the Labor Force Participation rate was actually much lower than now. That was before the mass influx of women into the American labor force which began around the tail end of the Eisenhower administration.
The Labor Force participation rate simply takes the size of the labor force and tells us how many of those people are actually participating (working). 
SO...
our current labor force is about 157 million people.
62.7% of them are working.
It seems you don’t understand. The Labor Force is Employed plus Unemployed, and the Labor Force Participation Rate is the Labor Force as a percent of the Adult Civilian non-institutional population.
In short, the participation rate is the percent of the population that is doing something about work.
The participation rate has been going down since 2015...mostly due to an aging population, but also due to more students and more disabled and more stay-home spouses.
When you say “if the participation rate were as high as it was under President X then the UE rate would by Y” then what you’re saying is that if there were more people in the labor force looking for work (unemployed) then the unemployment rate would be higher. But the fact is that not as many people want to work.
And the current labor force is 157,028,000. 149,120,000 are employed and 7,908,000 are unemployed, giving an unemployment rate of 5.0%. The adult civilian non-institutional population is 251,541,000 giving us a labor force participation rate of 157,028,000/251,541,000 = 62.4%