Evaluate: $9\frac{1}{2}+11\frac{3}{4}-5\frac{3}{8}$

The correct option is 15 $\frac{7}{8}$.

To evaluate the given mathematical expression involving mixed fractions, we can conveniently separate the whole number parts from the fractional parts.

Given expression:
$9\frac{1}{2}+11\frac{3}{4}-5\frac{3}{8}$

Step 1: Separate the whole numbers and the fractions.
We can regroup the expression by collecting all the whole numbers together and all the fractional parts together:
$(9+11-5)+(\frac{1}{2}+\frac{3}{4}-\frac{3}{8})$

Step 2: Simplify the whole number part.
Perform addition and subtraction on the whole numbers:
$9+11-5=15$

Step 3: Find a common denominator for the fractions.
The denominators of the fractions are 2, 4, and 8. The least common multiple (LCM) of 2, 4, and 8 is 8.
Now, convert each fraction into an equivalent fraction with a denominator of 8:
$\frac{1}{2}=\frac{1\times 4}{2\times 4}=\frac{4}{8}$

$\frac{3}{4}=\frac{3\times 2}{4\times 2}=\frac{6}{8}$

$\frac{3}{8}=\frac{3}{8}$

Step 4: Combine the fractional parts.
Add and subtract the numerators over the common denominator 8:
$\frac{4}{8}+\frac{6}{8}-\frac{3}{8}=\frac{4+6-3}{8}=\frac{7}{8}$

Step 5: Combine the whole number result and the fractional result.
Add the whole number sum and the fractional sum to get the final answer:
$15+\frac{7}{8}=15\frac{7}{8}$

Hence, the evaluated value of the expression is 15 $\frac{7}{8}$.