Hey there! I'm happy to help!
Let's call our fraction x.
x=1.55555.....
We want to get rid of the repeating stuff. If we multiply our fraction by 10, we will have 10x=15.5555555.....
10x=15.5555.....
x=1.5555....
Now we subtract these equations to get rid of the repeating stuff.
9x=14
We divide both sides by 9.
x=14/9 or 1 5/9.
Have a wonderful day! :D