To find the distance Clarissa traveled, we can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Clarissa's speed is \( 12 \frac{1}{2} \) miles per hour, which can be converted to an improper fraction:
\[ 12 \frac{1}{2} = \frac{25}{2} \text{ miles per hour} \]
Next, we need to convert her time of \( 2 \frac{1}{2} \) hours into an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \text{ hours} \]
Now we can plug these values into the distance formula:
\[ \text{Distance} = \left(\frac{25}{2}\right) \times \left(\frac{5}{2}\right) \]
To multiply these fractions, we multiply the numerators and the denominators:
\[ \text{Distance} = \frac{25 \times 5}{2 \times 2} = \frac{125}{4} \text{ miles} \]
Now, \( \frac{125}{4} \) is already in improper fraction form and is also in simplest form since 125 and 4 have no common factors other than 1.
Thus, the distance Clarissa traveled is
\[ \boxed{\frac{125}{4}} \text{ miles.} \]
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