1 1/9 + 3 5/8 is 4 53/72.
My reason is you must equalize 1 1/9 to 1 8/72.
Then equalize 3 5/8 to 3 45/72.
Now add them together and do not add the denominators. Add the numerators, and the whole numbers. Simplifying is unnecessary. The answer should be 4 53/72.