Question

chaya has a map that shows the lengths of some hiking trails. the scale is shown in the drawing. what number can you multiply each distance in the scale drawing by to find the actual distance? (the scale is 3 cm : 1.5 km, with distances like waterfall (6 cm), parking (3 cm), ranger tower, renc ano (9 cm) shown in the drawing.)

Explanation:

Step1: Understand the scale

The scale is given as \(3\) cm : \(1.5\) km. We need to find the conversion factor from cm (drawing) to km (actual).

Step2: Calculate the factor

To find how many km is represented by 1 cm in the drawing, we divide the actual distance by the drawing distance. So, \(\frac{1.5\space km}{3\space cm} = 0.5\space km/cm\). This means we multiply each distance in the scale drawing (in cm) by \(0.5\) (or \(\frac{1}{2}\)) to get the actual distance in km. Alternatively, if we consider the scale as a ratio, \(3\) cm corresponds to \(1.5\) km, so the multiplier is \(\frac{1.5}{3}= 0.5\) (or \(\frac{1}{2}\)) when converting cm to km. If we want to convert to meters, \(1.5\) km \( = 1500\) m, so \(\frac{1500\space m}{3\space cm}=500\space m/cm\), but since the question is about the number to multiply each distance in the scale drawing (probably in cm) to get actual distance (maybe in km as per the scale), the multiplier is \(0.5\) (or \(\frac{1}{2}\)) in km per cm or \(500\) in meters per cm. But looking at the scale \(3\) cm : \(1.5\) km, simplifying the ratio \(\frac{1.5}{3}=0.5\), so the number is \(0.5\) (if actual distance is in km) or \(500\) (if in meters, since \(1.5\) km \( = 1500\) m, \(1500\div3 = 500\)). But let's check the scale: \(3\) cm represents \(1.5\) km. So for 1 cm, it's \(1.5\div3 = 0.5\) km. So the multiplier is \(0.5\) (or \(\frac{1}{2}\)) when the drawing distance is in cm and actual in km.

Answer:

The number is \(0.5\) (or \(\frac{1}{2}\)) (if actual distance is in kilometers per centimeter of drawing) or \(500\) (if actual distance is in meters per centimeter of drawing). Commonly, based on the scale \(3\) cm : \(1.5\) km, the multiplier is \(0.5\) (km per cm) or \(500\) (m per cm). If we take the scale as \(3\) cm \( = 1.5\) km, then the conversion factor (multiplier) is \(\frac{1.5}{3}=0.5\) (km/cm) or \(500\) (m/cm). So the answer is \(0.5\) (or \(500\) depending on units, but likely \(0.5\) for km or \(500\) for meters).