the soccer field at a park is 9,000 square yards. the soccer field takes up 6 2/5 square inches on the map of the park. how many square yards does 1 square inch on the map represent. show your work.

To find out how many square yards does 1 square inch on the map represent, we need to set up a proportion and solve for the unknown.

Let's denote the number of square yards that 1 square inch represents on the map as "x". The given information tells us that the soccer field takes up 6 2/5 square inches on the map, which we can represent as a fraction.

Using the proportion, we can set it up as follows:

(6 2/5 square inches) / (1 square inch) = (9,000 square yards) / (x square yards)

First, let's convert the mixed number (6 2/5) to an improper fraction. To do this, we multiply the whole number (6) by the denominator (5) and add the numerator (2), then place the result over the original denominator (5).

(32/5 square inches) / (1 square inch) = (9,000 square yards) / (x square yards)

Next, we can simplify the equation by canceling out the square inch units:

32/5 = 9,000 / x

To eliminate the fraction, we can cross-multiply:

32 * x = 5 * 9,000

32x = 45,000

Now, we solve for x by dividing both sides of the equation by 32:

x = 45,000 / 32

This can be simplified further by dividing both numerator and denominator by their greatest common divisor, which is 1:

x = 1406.25

So, 1 square inch on the map represents approximately 1406.25 square yards.

Math laws and steps used:
1. Converting mixed number to an improper fraction: (6 2/5) = (32/5)
2. Setting up a proportion: (6 2/5 square inches) / (1 square inch) = (9,000 square yards) / (x square yards)
3. Cross-multiplication: 32 * x = 5 * 9,000
4. Simplifying the expression: 32x = 45,000
5. Solving for x by dividing both sides by 32: x = 45,000 / 32
6. Simplifying the result: x = 1406.25

Please note that it's always important to check your work and ensure accuracy by double-checking calculations or using alternative methods.