To determine how many meals Carmen can feed her dog with 24 pounds of dog food, we need to divide the total amount of dog food by the amount fed per meal.
Carmen has 24 pounds of dog food and feeds her dog \( \frac{3}{8} \) pounds for each meal.
The calculation is as follows:
\[ \text{Number of meals} = \frac{\text{Total dog food}}{\text{Dog food per meal}} = \frac{24 \text{ pounds}}{\frac{3}{8} \text{ pounds per meal}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{24}{\frac{3}{8}} = 24 \times \frac{8}{3} \]
Now, calculate \( 24 \times \frac{8}{3} \):
- Multiply \( 24 \times 8 = 192 \).
- Then divide by \( 3 \):
\[ 192 \div 3 = 64 \]
Thus, the food will last for 64 meals.