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When we encounter percentages, we often need to convert them into fractions to perform various mathematical operations. Converting a percentage to a fraction involves placing the percentage number over 100. This is because 'percent' means 'per hundred'.

For example, turning 8% into a fraction involves writing 8 over 100, which gives us the fraction \( \frac{8}{100} \). However, our goal is to express this fraction in the simplest form, which requires finding the greatest common divisor (GCD) of both the numerator and the denominator and then dividing them by this number.

In our case, the GCD of 8 and 100 is 4. When we divide both the numerator and the denominator by 4, we get \( \frac{8}{4} \) over \( \frac{100}{4} \), which simplifies to \( \frac{2}{25} \). This simplified fraction represents the same value as the original percentage; it’s simply in a different form that might be more useful for further calculations or comparisons.

Reducing fractions, also known as simplifying fractions, is an important skill when working with numerical expressions. A fraction is considered fully reduced when the numerator and the denominator have no common factors other than 1. To reduce a fraction:

• First, identify the greatest common divisor (GCD) of the numerator and the denominator.
• Then, divide both the numerator and the denominator by the GCD.

In the 8% example, we found that the fraction equivalent \( \frac{8}{100} \) could be reduced. By dividing both the top and bottom by 4, the highest common factor, we simplified it to \( \frac{2}{25} \). It’s crucial to reduce fractions in order to work with the simplest form, which simplifies further operations like addition, subtraction, or comparison of fractions.

Converting percentages to decimals is another common practice in mathematics that allows for easier computation in many cases. The process is quite straightforward. Since a percentage represents a number out of 100, converting it to a decimal simply requires dividing the percentage by 100.

Thus, to convert the percentage 8% to a decimal, we remove the percent sign and divide 8 by 100. Doing this calculation, we obtain 0.08. This decimal form can be particularly helpful when you're working with decimal-based calculations, like in financial equations or measurements. It also lays the foundation for understanding that percentages can be expressed not just as fractions, but also as part of a whole number in decimal form, which sometimes provides a clearer picture of the proportion or ratio it represents.