According to a map, the distance between Hilltop and Valleyfloor is 1 3/4 inches. If the map uses a scale of ¼ inch to represent 1 mile, what is the actual distance in miles from Hilltop to Valleyfloor?

If 1/4 inch represents 1 mile, then

1 inch represents 4 miles , and
1 3/4 inches or 7/4 inches will represent
(7/4)(4) miles
= 7 miles

or

just use a ratio:
(7/4)/(1/4) = x/1
(1/4)x = 7/4
x = 4(7/4) = 7