Matt made an error in his calculations. He attempted to divide the total distance traveled by the number of hours to find the distance traveled each hour. However, his conclusion was incorrect.
To analyze his thought process:
- Matt correctly identified that the mouse traveled a total distance of \( \frac{3}{24} \) of a mile over 3 hours.
- He divided \( \frac{3}{24} \) by 3 to find the distance traveled each hour.
The correct way to find the distance traveled each hour is to divide the total distance by the number of hours:
\[ \frac{3}{24} \div 3 = \frac{3}{24} \cdot \frac{1}{3} = \frac{3 \cdot 1}{24 \cdot 3} = \frac{3}{72} \]
Then, simplify \( \frac{3}{72} \):
\[ \frac{3}{72} = \frac{1}{24} \]
So the correct distance the mouse traveled each hour is \( \frac{1}{24} \) of a mile.
Therefore, the correct identification of Matt's error is:
Matt should have multiplied \( \frac{3}{24} \) by \( \frac{1}{3} \) instead of dividing it by 3.
However, more precisely, we can say:
Matt should have multiplied \( \frac{3}{24} \) by \( \frac{1}{3} \) instead of dividing it by 3.
Given the options provided:
- Matt should have multiplied \( \frac{3}{24} \) by 3 instead of dividing it by 3 is the closest answer, but it should refer to multiplying by \( \frac{1}{3} \) not by 3.
Thus, the better answer among the three is:
Matt should have multiplied \( \frac{3}{24} \) by \( \frac{1}{3} \) instead of dividing it by 3. (However, this is not in the options, so if we have to choose one from the incorrect options, the second option might aim towards finding the final correct distance).
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