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Understanding how to convert a percentage to a fraction is a fundamental skill in mathematics. A percentage represents a number out of 100. So when we need to convert a percentage to a fraction, we place that number over 100. For example, if we take 35%, we write it as \( \frac{35}{100} \). This is based on the idea that 'percent' means 'per hundred'.

Once you have the initial fraction, it often needs to be simplified to make it easier to work with. Simplifying fractions, which we will discuss next, allows us to express the fraction in its simplest form, helping us with further calculations and comparisons.

Simplifying a fraction is the process of reducing it to its simplest form. The simplest form of a fraction is achieved when the numerator and the denominator have no common factors other than 1. To simplify a fraction, we look for the greatest common divisor (GCD) that both numbers share. In our example, we have the fraction \( \frac{35}{100} \), and upon examining the numerator and denominator, we identify that they both share a GCD of 5.

Divide both the numerator and denominator by this GCD: \( \frac{35 \div 5}{100 \div 5} = \frac{7}{20} \). The fraction \( \frac{7}{20} \) is in its simplest form because there are no common factors between 7 and 20 anymore. It's important to always simplify fractions to ensure that they are in their most straightforward and easily understandable state.

Converting a percentage to a decimal is a simple process that requires dividing the percentage value by 100. This is because percentages are inherently base 100, and decimals are base 10, so dividing by 100 effectively shifts the decimal point two places to the left. For instance, converting 35% to a decimal involves the calculation \(35 \div 100 = 0.35\).

Remember, the decimal form is often used when we need to perform calculations that involve percentages, as decimals are congruent with our base-10 number system. This makes addition, subtraction, multiplication, and division of percentages straightforward when they're in decimal form. Therefore, mastering the conversion of percentages to decimals is a vital skill in various mathematical applications.