Question

The scale of a map is 1:3,000,000. What is the actual distance in km corresponding to 12 cm on the map?

3600 km
360 km
36 km
3.6 km

Answer 1

Explanation:

The scale number can be interpreted as (1cm/3,000,000 km), a conversion factor. Since it is a conversion factor, we can invert it to the form:

(3,000,000 km/1cm)

A measure of 12cm on the map would correspond to:

(12cm)*((3,000,000 km/1cm) = 42,000,000 km

Wow - a long trek, if you need water.

Note that inverting the conversion factor isn't totally necessary, since we could use the original form and divide:

12 cm/(1cm/(3,000,000km)) = 42,000,000 km

But I dislike division, so I always invert a conversion factor if it makes the calculation more convenient, for me.