To find out how far Clarissa traveled, we can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
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First, we need to convert the speed and time into improper fractions.
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Speed: \(12 \frac{1}{2}\) miles per hour can be converted to an improper fraction: \[ 12 \frac{1}{2} = \frac{25}{2} \text{ miles per hour} \]
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Time: \(2 \frac{1}{2}\) hours can also be converted to an improper fraction: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ hours} \]
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Now we can substitute these values into the distance formula: \[ \text{Distance} = \frac{25}{2} \times \frac{5}{2} \]
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Multiply the fractions: \[ \text{Distance} = \frac{25 \times 5}{2 \times 2} = \frac{125}{4} \]
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To ensure the answer is in simplest form, we check if the numerator (125) and the denominator (4) have any common factors. The greatest common divisor is 1, so \(\frac{125}{4}\) is already in simplest form.
Thus, the distance Clarissa traveled is:
\[ \boxed{\frac{125}{4}} \text{ miles} \]