Final answer:
The sum of the mixed numbers 3 1/2 and 2 1/4 is 5 3/4, which does not match any of the provided options. The process involves adding whole numbers and finding a common denominator for fractional parts.
Step-by-step explanation:
The question asks about the result of adding the mixed numbers 3 1/2 and 2 1/4. When adding mixed numbers, it's necessary to add the whole numbers separately from the fractional parts. To begin, we have 3 (from 3 1/2) plus 2 (from 2 1/4), which equals 5. Next, we need to add the fractional parts, which are 1/2 and 1/4.
To add fractions, they must have the same denominator. In this case, the common denominator for 2 and 4 is 4. We can convert 1/2 to the equivalent fraction 2/4, which allows us to add the fractions: 2/4 (equivalent to 1/2) plus 1/4 equals 3/4.
So, the sum of the whole numbers is 5 and the sum of the fractions is 3/4. Combining these, we get a mixed number of 5 3/4. This mixed number cannot be simplified further, and none of the provided options (a. 7/4, b. 5/6, c. 11/8, d. 13/9) match our result.