The reciprocal of a number is a value that when multiplied by the original number is equal to one, mathematically, if we let n=number and r=reciprocal:
nr=1
Now in this case the number is 9 1/4, which is equal to 37/4.
37r/4=1 multiply both sides by 4
37r=4 divide both sides by 37
r=4/37
So the reciprocal of 9 1/4 is 4/37