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Converting a percent to a fraction is a common task in math. Here’s a simple way to understand it:

Percent means out of 100. So, if we are given a percentage, like 2.5%, we can directly write it as a fraction where the numerator is the percent value and the denominator is 100. For example:

• 2.5% becomes \(\frac{2.5}{100}\)

To make calculations easier and to get rid of the decimal in the numerator, we multiply both the numerator and denominator by 10 (since 2.5 has one digit after the decimal). This gives us:

\( \frac{2.5 \times 10}{100 \times 10} = \frac{25}{1000} \)
This way we have converted the percent into a simple fraction that can be easily managed in further calculations.

Fractions often need to be simplified to their lowest terms for better understanding and ease of use. Simplifying a fraction means making the numerator and denominator as small as possible. This is done by finding and dividing both by their greatest common divisor (GCD).

Let's use our fraction from above: \( \frac{25}{1000} \)

The GCD here is 25 because it is the largest number that divides evenly into both 25 and 1000. So, we divide the numerator and the denominator by 25:

• Numerator: \( 25 \div\ 25 = 1 \)
• Denominator: \( 1000 \div\ 25 = 40 \)

This simplifies our fraction to:

\( \frac{1}{40} \)
Simplifying fractions is important because it makes them easier to work with and understand, especially in further mathematical operations.

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), is the largest number that can exactly divide two or more numbers without leaving a remainder. Finding the GCD is crucial for simplifying fractions.

To find the GCD of two numbers, such as 25 and 1000, use these steps:

• List the factors of both numbers.
• Identify the common factors.
• Select the greatest factor that appears in both lists.

For instance, the factors of 25 are 1, 5, and 25. The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. The common factors are 1, 5, and 25. Hence, the GCD is 25.

Using the GCD, you can then simplify the fraction \( \frac{25}{1000} \) by dividing both the numerator and the denominator by 25, giving \( \frac{1}{40} \).

Learning how to find and use the GCD helps you simplify fractions with confidence, enhancing your math skills overall.