Final answer:
The correct addition problem with a common denominator of 16 is 31/16 + 11/16. When added and simplified, the result is 21/8, which can also be expressed as the mixed number 2 and 5/8.
Step-by-step explanation:
The question asks to select an addition problem with unlike mixed numbers and a least common denominator of 16, and then to find the sum in the simplest form. The provided options do not include unlike mixed numbers; they are fractions. However, from the given choices, (a) 31/16 + 11/16 is the only valid operation where the fractions share a common denominator of 16. Therefore, we can proceed to add the fractions directly.
To add 31/16 and 11/16, we simply add the numerators while keeping the denominator the same: (31 + 11) / 16 = 42/16. To simplify 42/16 to its simplest form, we divide both the numerator and the denominator by their greatest common divisor, which is 2. Therefore, 42/16 simplified is 21/8.
In conclusion, the sum of 31/16 and 11/16 in simplest form is 21/8, which is equal to 2 and 5/8 when expressed as a mixed number.