Final answer:
To add the fractions 5/11, 9/11, 14/22, and 10/11, we first simplify 14/22 to 7/11 and then add the numerators of the like fractions to get a sum of 31/11.
Step-by-step explanation:
The question requires performing the indicated operation: adding fractions with like denominators and simplifying the result. When adding fractions with the same denominator, we simply add the numerators and keep the denominator the same. Here, we have 5/11, 9/11, and 10/11 which all share the same denominator, so we can add them directly. Additionally, the term 14/22 can be simplified by dividing both the numerator and the denominator by 2, to yield 7/11, which also has the same denominator as the other terms.
So, the addition becomes 5/11 + 9/11 + 7/11 + 10/11. Adding the numerators together, we get 5 + 9 + 7 + 10, which equals 31. Therefore, the sum of all fractions is 31/11.