To find 55/77 (or any fraction) of a number , you simply multiply the fraction by the number!
(55/77)*(22/55)=(55*22)/(55*77)=1210/4325. Since 5 goes into 1210 242 times and into 4325 865 times, it's equal to 242/865 of a cup of flour, or around 0.28 of one