a Write the ratio that compares the actual distance and the distance on the map.
B
b Write the ratio that compares the actual distance and the distance on the map.
C
c We can get the distance from Town A to Town C by adding the distance from Town A to Town B to the distance from Town B to Town C.
A
a True.
B
b False.
C
c False.
Practice makes perfect
a We know that the distance from Town A to Town B on a map is 6 inches and the scale of the map is 1 in: 4 mi. Using this information we can write the ratio that compares the actual distance and the distance on the map. actual distance/map distance =
4/1
If we let d represent the actual distance from A to B, we can write a second ratio.
actual distance/map distance =
d/6
Since these ratios are comparing the same objects, we can form a proportion.
4/1 = d/6
Let's solve the proportion for d.
The actual distance from Town A to Town B is 24 miles.
Therefore, the statement is true.
b Now, we are asked for the distance on the map from Town B to Town C. Since the scale of the map is the still 1 in: 4 mi, and we know that the actual distance between these two towns is 12 miles we can write the ratios just like we did before. actual distance/map distance =
4/1
If we let m represent the distance from B to C on the map, we can write a second ratio.
actual distance/map distance =
12/m
Since these ratios are comparing the same objects, we can form a proportion.
4/1 = 12/m
Let's solve the proportion for m.
The distance on the map from Town B to Town C is 3 inches and not 36 inches. Therefore, the statement is false.
c Since we calculated that the actual distance from Town A to Town B is 24 miles, and we know the actual distance from Town B to Town C is 12 miles, we can calculate the distance from Town A to Town C by adding them.
