To determine how many square yards 1 square inch on the map represents, we can set up the following proportion:

Let $x$ represent the number of square yards that corresponds to 1 square inch on the map. The given information tells us that 9,000 square yards corresponds to $6 \frac{2}{5}$ square inches on the map.

Step 1: Convert the mixed number to an improper fraction.

$6 \frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{32}{5} \text{ square inches}$

Step 2: Set up a proportion.

$\frac{9000 \text{ square yards}}{\frac{32}{5} \text{ square inches}} = \frac{x \text{ square yards}}{1 \text{ square inch}}$

Step 3: Solve for $x$.

To solve for $x$, multiply both sides of the equation by 1 square inch:

$x = \frac{9000 \text{ square yards}}{\frac{32}{5} \text{ square inches}} = 9000 \times \frac{5}{32}$

Now, calculate:

$9000 \times \frac{5}{32} = \frac{45000}{32} = 1406.25 \text{ square yards}$

Final Answer:

1 square inch on the map represents 1,406.25 square yards.

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Would you like more details or have any questions?

Here are some related questions for further practice:

1. How do you convert between different units of area, such as square yards to square inches?
2. If the map was rescaled, how would you calculate the new area each square inch represents?
3. How can you estimate the dimensions of the soccer field in yards, given the total area?
4. How would the problem change if the field was measured in square feet instead of square yards?
5. What would be the area in square miles that one square inch on the map represents?

Tip: Always remember to convert mixed numbers into improper fractions when setting up a proportion for easier calculations!