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Express the ratio in its reduced form.

500 yards : 10 yards

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To express the ratio of 500 yards to 10 yards in its reduced form, follow these steps:

1. Identify the initial ratio values:
- Numerator: 500 yards
- Denominator: 10 yards

2. Find the greatest common divisor (GCD) of the numerator and the denominator:
- The GCD is the largest positive integer that divides both numbers without leaving a remainder. In this case, the greatest common divisor of 500 and 10 is 10.

3. Divide both numbers by the GCD to simplify the ratio:
- Divide 500 by 10: [tex]\( \frac{500}{10} = 50 \)[/tex]
- Divide 10 by 10: [tex]\( \frac{10}{10} = 1 \)[/tex]

4. Express the simplified ratio:
- After dividing both numbers by the GCD, we get the simplified ratio as 50 yards : 1 yard.

Therefore, the ratio 500 yards : 10 yards expressed in its reduced form is 50 yards : 1 yard.
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