The actual distance between two villages is 120 km. on a map of the area, 0.5 cm represents 2 km. what is the actual distance between the villages on the map?

On the map, the distance between the villages is 30 cm.
Since .5 cm represents 2 km, each cm on the map represents 4 km in actual distance, so to find the distance on the map, you divide 120 by 4 and you get 30. 
An alternative way to think of it is to set up a proportion. 
First, you would do .5/2 equals x/120
Next, you would cross multiply and get 2x equals 60
Then, you would solve and get x equals 30 
Your answer is 30 cm