To find out how long Patricia studied for her science test, we start by determining how long she studied for her Social Studies test, which is \( 4 \frac{1}{2} \) hours.
First, we need to convert \( 4 \frac{1}{2} \) to an improper fraction: \[ 4 \frac{1}{2} = \frac{9}{2} \text{ hours} \text{ (since } 4 \times 2 + 1 = 9\text{)} \]
She studied half as long for her science test, so we calculate half of \( \frac{9}{2} \): \[ \text{Half of } \frac{9}{2} = \frac{1}{2} \times \frac{9}{2} = \frac{9}{4} \]
Now, we convert \( \frac{9}{4} \) back to a mixed number: \[ \frac{9}{4} = 2 \frac{1}{4} \text{ hours (since } 4 \text{ goes into } 9 \text{ two times with a remainder of } 1\text{)} \]
Therefore, Patricia studied \( 2 \frac{1}{4} \) hours for her science test.
The answer is 2 1/4 hours.
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