To find Leah's walking speed in miles per hour, we need to divide the distance she walked by the time it took her to walk that distance.
Leah walked \( \frac{4}{5} \) of a mile in \( \frac{3}{8} \) of an hour.
Her walking speed \( S \) in miles per hour is given by:
\[ S = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{4}{5}}{\frac{3}{8}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ S = \frac{4}{5} \times \frac{8}{3} \]
Now, we can multiply the fractions:
\[ S = \frac{4 \times 8}{5 \times 3} = \frac{32}{15} \]
Now we can convert \( \frac{32}{15} \) into a mixed number:
- Divide 32 by 15. \( 32 \div 15 = 2 \) with a remainder of 2.
- Thus, we can write this as \( 2 \frac{2}{15} \).
Therefore, Leah’s walking speed is:
\[ \boxed{2 \frac{2}{15}} \text{ mph} \]
The correct answer is option D: \( 2 \frac{2}{15} \) mph.
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