Question

The scale of a map of Pennsylvania is 1 inch: 25 miles. The actual distance from Ambridge to Pittsburgh is 20 miles. What is the distance on the map?

Answer 1

Explanation:

1 inch = 25 miles

or as ratio

1 inch : 25 miles

1 : 25 or 1/25

a ratio is nothing else than a fraction (just with special meaning, but the handling, calculation, transformation and simplification is the same).

the checked distance is 20 miles.

so, we need to transform the ratio (in the same way as we transform fractions) to show 20 instead of 25 in the denominator.

25 × f = 20

f = 20/25 = 4/5

remember, we need to multiply 1/25 by f/f to keep the original value of the ratio unchanged.

1/25 × 4/5/4/5 = (4/5)/(25×4/5) = (4/5)/20

so, the distance on the map is 4/5 in.