4. The scale on a map reads inch \( \frac{1}{4}=50 \) miles. If the distance between two cities on the map is \( 2 \frac{3}{4} \) inches, find the actual distance between the cities.

To find the actual distance, we first convert \( 2 \frac{3}{4} \) inches to an improper fraction: \( 2 \frac{3}{4} = \frac{11}{4} \) inches. Since the scale indicates that \( \frac{1}{4} \) inch represents 50 miles, we can calculate how many \( \frac{1}{4} \) inch segments are in \( \frac{11}{4} \) inches. This is done by dividing \( \frac{11}{4} \) by \( \frac{1}{4} \): \[ \frac{11}{4} \div \frac{1}{4} = 11 \] Next, we multiply the number of \( \frac{1}{4} \) inch segments (11) by the number of miles each segment represents (50 miles): \[ 11 \times 50 = 550 \text{ miles} \] Thus, the actual distance between the two cities is 550 miles. Now you can pack your bags for a road trip!