Allison,
Parvis gave you a correct solution; but I thought I'd share another way to look at the problem.
3-1/9=3 8/9
3 8/9 is a mixed number that = 3 + 8/9.
Always look at the given problem and assess if it makes sense or not.
In this case, on the left side something is taken away from 3 and on the right side something is added to 3; how can the two sides be equal? Start with two stacks of 3 pennies that are equal height. Take one penny away from one stack and add a penny to the other; are the stacks equal in height now?
Another thing, be very careful when you write and use mixed numbers. They are the only place in math where the absence of an arithmetic operator means something other than multiply. And it's easy to miss the space and interpret 3 8/9 as 38/9. I always rewrite mixed numbers with a + sign; 3 8/9 = 3 + 8/9.