Carmen is the youngest and Katie is the oldest. Anthony's age difference from Katie's is going to be the difference between the two age differences given.
First, convert both to fraction form 11 and 1/2 is 23/2; 5 and 1/4 is 21/4.
(23/2)-(21/4)=(46/4)-(21/4)=25/4
25/4 is 6 and 1/4.
Katie is 6 and 1/4 years older than Anthony.