Final answer:
The calculations of the given expressions result in mixed numbers 10 13/15, 3 7/15, 2 1/2, and 4 1/3 in their lowest terms.
Step-by-step explanation:
The student's question involves performing addition with fractions, whole numbers, and mixed numbers and writing the result in lowest terms.
a) For the expression 54/10 + 82/15, we first find a common denominator, which is 30. We convert the fractions: 54/10 becomes 162/30 and 82/15 becomes 164/30. Adding these gives us 326/30, which simplifies to 10 26/30 or 10 13/15 in lowest terms.
b) In the case of 3 + 7/15, it is already a mixed number, and the fraction does not need to be altered, resulting in 3 7/15.
c) The fraction 5/2 can be written as the mixed number 2 1/2.
d) The fraction 13/3 simplifies to the mixed number 4 1/3.