Neither the decimal ".727272..." nor the decimal ".722222..." can be turned into a fraction.
Also to respond to CPhill's comment I'm pretty sure that he was saying that he needed the answer based on ".72 repeating" not what you assumed he meant. Also the answer you gave can be simplified to $${\frac{{\mathtt{18}}}{{\mathtt{25}}}}$$.
Do you meant
0.72727272.....
let x=0.727272.....
100x=72.727272
so
100x-x=72 The rest cancels out
99x=72
x=72/99
Thanks, Melody.......I see now what the questioner meant !!!!......disregard my answer !!!
BTW.....I liked the way you did that one....very clever......I haven't seen that technique before, but I intend to add it to my "tool chest".....!!!!!