Let's analyze the situation step by step.
The mouse traveled a total distance of \( \frac{3}{24} \) of a mile in 3 hours. To find the distance the mouse traveled each hour, we need to divide the total distance by the total time:
\[ \text{Distance per hour} = \frac{\text{Total distance}}{\text{Total time}} = \frac{\frac{3}{24}}{3} \]
Matt's calculation shows:
\[ \frac{3}{24} \div 3 = \frac{3}{(24 \div 3)} = \frac{3}{8} \]
This calculation is incorrect because to divide a fraction by a whole number, we multiply the denominator by that whole number, not divide it:
\[ \frac{3}{24} \div 3 = \frac{3}{24} \times \frac{1}{3} = \frac{3 \cdot 1}{24 \cdot 3} = \frac{3}{72} \]
Now, simplifying \( \frac{3}{72} \):
\[ \frac{3}{72} = \frac{1}{24} \]
So the mouse traveled \( \frac{1}{24} \) of a mile each hour.
Looking at Matt’s conclusion, he incorrectly concluded that the distance per hour was \( \frac{3}{8} \) of a mile instead of \( \frac{1}{24} \) of a mile.
Now, let’s match the reasoning to the possible errors listed:
- Matt's error correctly relates to how he divided the total distance. He should have multiplied by the reciprocal of the 3, not divided.
Thus, the correct option is:
Matt should have multiplied \( \frac{3}{24} \) by 3 instead of dividing it by 3.
1 answer