Question

what number can you multiply each distance in the scale drawing by to find the actual distance? image of a map with labeled distances (6 cm, 3 cm, 9 cm) and scale “3 cm : 1.5 km”

Explanation:

Step1: Understand the scale

The scale given is \( 3 \, \text{cm} : 1.5 \, \text{km} \). We need to find the number (scale factor) to multiply the map distance (in cm) to get the actual distance (in km).

Step2: Calculate the scale factor

To find the factor, we divide the actual distance by the map distance. So, \( \frac{1.5 \, \text{km}}{3 \, \text{cm}} = 0.5 \, \text{km/cm} \). This means for each cm on the map, the actual distance is \( 0.5 \) km. So we multiply the map distance (in cm) by \( 0.5 \) (or \( \frac{1.5}{3} \)) to get the actual distance in km.

Answer:

\( 0.5 \) (or \( \frac{1}{2} \) if we consider \( 1.5\div3 = 0.5 \), and also \( 1.5\) km is \( 1500\) meters, \( 3\) cm is \( 0.03\) meters, \( 1500\div0.03 = 50000\) if we convert to same units, but based on the scale \( 3 \, \text{cm} : 1.5 \, \text{km} \), the multiplier is \( \frac{1.5}{3}=0.5 \) km per cm)