Question

Using a different map that is missing any indication of scale, you measure the distance from Point C

to Point D as five inches, but it is 500 miles on the ground. Prepare the following two expressions
of scale for the map:
(a) Fractional
(b) Written
SHOW YOUR WORK! This includes the potential for partial value, if incorrect.
Simplify your scale (e.g., reduce to 1 inch = x miles, not 5 inches = 250 miles).

Answer 1

To calculate the scale of the map, we can use the following formula:

Scale = Actual distance / Map distance

(a) Fractional scale:

The actual distance between Point C and Point D is 500 miles, and the distance on the map is 5 inches. Therefore, the fractional scale can be calculated as:

Scale = 500 miles / 5 inches

Scale = 100 miles per inch

So the fractional scale of the map is 1 inch = 100 miles.

(b) Written scale:

To express the scale in written form, we can use the ratio of inches to miles. Since 1 inch represents 100 miles, we can write the scale as:

1 inch represents 100 miles

Alternatively, we can simplify the scale to a more common ratio by dividing both sides by 100:

1/100 inch represents 1 mile

Therefore, the written scale of the map is 1/100 inch = 1 mile.