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A fraction represents a part of a whole or, in this case, a ratio. When we see a situation like 200 miles traveled in 4 hours, we can express it as a fraction to make it easier to understand. In this scenario, the fraction is written as \( \frac{200 \text{ mi}}{4 \text{ hr}} \).
By converting the ratio into a fraction, we can simplify it if necessary. Simplification involves finding the most reduced form of the fraction.
In the example given, we simplified \( \frac{200 \text{ mi}}{4 \text{ hr}} \) to \( \frac{50 \text{ mi}}{1 \text{ hr}} \) by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). This makes the fraction easier to understand and use.

The greatest common divisor (GCD) of two or more numbers is the largest number that divides all of them without leaving a remainder. In our example of simplifying the fraction \( \frac{200 \text{ mi}}{4 \text{ hr}} \), we need to find the GCD of 200 and 4.
To do this, list the factors of both numbers:

• The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
• The factors of 4 are 1, 2, 4.

From the lists above, we see that the largest number that appears in both lists is 4. Thus, the GCD of 200 and 4 is 4.
With the GCD identified, we can simplify the fraction by dividing both the numerator and the denominator by the GCD, making the fraction \( \frac{50 \text{ mi}}{1 \text{ hr}} \).

Unit conversion involves changing the unit of a measurement to another unit. In the given problem, the original units were miles (mi) and hours (hr).
When simplifying ratios, it's crucial to ensure the units remain consistent. Otherwise, the simplified ratio might lose its meaning. In the provided solution, we did not need to change units because the ratio was already in the appropriate units for simplification.
However, if different units are involved in a ratio (e.g., miles to kilometers or hours to minutes), it's important first to convert all units to a consistent form before beginning the simplification process. This ensures accuracy and clarity in your final simplified ratio.