Do you mean the product? The product is 1/4*4/5 means a quarter of four fifths. A quarter of 4 is 1 so a quarter of 4/5 is 1/5.
Quotient means division, so 1/4 divided by 4/5 is the same as 1/4*5/4 (just invert the divisor)=5/16.
4/5 divided by 1/4 is the same as 4/5 times 4=16/5 or 3 1/5.