What is 1 1/9 plus 3 5/8

I think the answer should be 4.7 but rounded up would be 5

3 5/8
You would take 1 1/9 and multiply 9x1 then add 1 so 10/9
8x3=24+5=29/8
The least common multiple (lcm) is 72
So then you multiply 10x8=80
29x9=261
Then you divide 261 by 72 and get 3.something
You multiply 72x3 which is 216
Then you divide that by 72 which is 3 45/72
If you simplify it you divide 45 and 72 by 9 to get 3 5/8