Two cities on a map are 2 and 1/4 inches apart. The cities are actually 112.5 miles apart. How many miles is represented by one inch? What is the actual distance between two cities that are 4 and 3/4 inches apart? Use proportions
112.5/2.25 = ? miles = 1 inch
To find the number of miles represented by one inch, we can set up a proportion using the given information.
Let's denote the number of miles represented by one inch as "x". We can set up the proportion as follows:
2 1/4 inches / 112.5 miles = 1 inch / x
Now, let's solve for x:
To divide a fraction by a whole number, we need to convert the whole number into a fraction. We can do this by writing it over a denominator of 1:
2 1/4 inches / 112.5 miles = 1 inch / (9/4) miles
Now, we can rewrite the proportion using the reciprocal of the denominator:
2 1/4 inches / 112.5 miles = 1 inch * (4/9 miles)
To multiply fractions, we multiply the numerators together and the denominators together:
(9/4) * (4/9) = 1 inch * (4/9 miles)
The numerator and denominator of the left side will cancel out, leaving us with:
1 = 1 inch * (4/9 miles)
Now, we can solve for x by multiplying both sides of the equation by (4/9 miles):
x = 1 inch * (4/9 miles)
By simplifying the expression on the right side, we get:
x = (4/9) miles
Therefore, one inch on the map represents (4/9) miles.
Now, let's determine the actual distance between two cities that are 4 3/4 inches apart using the proportion we found:
4 3/4 inches / 1 inch = x miles / (4/9) miles
Again, we need to convert the whole number into a fraction by writing it over a denominator of 1:
4 3/4 inches / 1 inch = x miles / (19/4) miles
We can rewrite the proportion using the reciprocal of the denominator:
4 3/4 inches / 1 inch = x miles * (4/19 miles)
Multiplying the fractions gives us:
(19/4) * (4/19) = x miles * (4/19 miles)
The numerator and denominator on the left side cancel out, leaving us with:
1 = x miles * (4/19 miles)
Now, we can solve for x by multiplying both sides of the equation by (4/19 miles):
x = 1 inch * (4/19 miles)
By simplifying the expression on the right side, we get:
x = (4/19) miles
Therefore, the actual distance between the two cities that are 4 3/4 inches apart is (4/19) miles.