400 pounds per 340 square feet” as a rate in simplest form

400lbs/340ft^2

Factor out largest common factor.  LCF is the product of shared primes of the numbers prime factorization.

400=2*2*2*2*5*5,  340=2*2*5*17

So the product of the shared primes is 2*2*5=20, so divide the numerator and denominator by 40.

(400/20)lbs/(340/20)ft^2

20lbs/17ft^2  or if you prefer

(20/17)lbs/ft^2

(1 3/17)lbs/ft^2 or approximately

1.18 lbs/ft^2