This is the trick of the puzzle! it seems the rate should be 1 egg in 1 day huh? but that is not right.

if four chickens (denominator) laid 16 eggs (numerator) in 2 days that would be (16/4) / 2 = 2 eggs per day. Right?

so if instead of 16 eggs it was 1.5 eggs, and 4 chickens it was 1.5 chickens, and 1.5 days then it would be:

(1.5 / 1.5) / 1.5 = 1/1.5 eggs per day

To understand this intuitively think about 1.5 chickens. in your mind imagine that 1/2 chicken standing next to the whole chicken. Now the whole chicken "in charge" of laying a whole egg, while the 1/2 chicken is laying the 1/2 egg. And how long does this take? well it says 1.5 days.

ok so if that is true, then how long did it take the whole chicken to lay its whole egg? 1.5 days. just as long as it took the 1/2 chicken to lay its 1/2 egg.

weird, but that is how I understand the math at an intuitive level. (but of course I have a weird head, so not sure if that will help you. ;-) )