How to add a fraction and a mixed number together?

I know this sounds really stupid, but me and my mom are having an argument about how to do simple third grade math.I'm in 7th grade and never learned fractions right. Here's the question : 5/9 = 2 3/4. I thought you changed the mixed number into an improper fraction, add the fractions together, and then divide your numerator by the denominator (since the top on is bigger in this case) and what you got would be the whole number, then the number after the point would be the numerator, then the denominator would be the same.