express 1/4 as a percentage of 52/9

The percentage is just a measure with respect to 100 so to represent any number as the percentage of other, consider the later to be the 100 %.

so in this example consider 52/9 : 100%

so                                              1/4 :  x?

so x=(1/4*100)/(52/9) = 100*9/52*4 = 4.32%