How do you calculate labor force participation rate when given people employed unemployment rate and labor force?

If you mean employment rate, then it is employment/labor force.

the participation rate is the labor force/non-institutionalized population over 16, I believe.

A participation rate generally implies that what the data is explaining is overall how many people are working out of an entire population.

Labor force participation rate= (number of people in the labor force) divided by total adult population

note adult population in the work force is considered to start at age 15

number of people in the work force is the sum of unemployed and employed adults