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Converting a percentage to a fraction is a straightforward process. Start by recognizing that any percentage can be expressed as a fraction with a denominator of 100. This is because 'percent' means 'per hundred'. For example, 50% means 50 out of 100. To convert 50% to a fraction, simply write it as \( \frac{50}{100} \) and you have your initial fraction form.

Another example could be converting 25% to a fraction. Following the same method, write 25% as \( \frac{25}{100} \). Now, the percentage is successfully turned into a fraction.

Simplifying fractions is a key skill in mathematics. It involves reducing the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

For instance, let's simplify the fraction \( \frac{50}{100} \). Start by identifying the GCD of 50 and 100. Then, use this GCD to divide both the numerator and the denominator. The GCD of 50 and 100 is 50. Hence, divide both the numerator and the denominator by 50:
\[ \frac{50 \div 50}{100 \div 50} = \frac{1}{2} \]

Now, the fraction is in its simplest form, \( \frac{1}{2} \). This method can simplify any fraction, making calculations and comparisons easier.

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD helps in simplifying fractions efficiently. There are different methods to find the GCD, such as listing the factors of both numbers and choosing the largest one, or using the Euclidean algorithm.

For example, to find the GCD of 50 and 100, list the factors of both numbers:

• Factors of 50: 1, 2, 5, 10, 25, 50
• Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

The common factors are 1, 2, 5, 10, 25, and 50. The greatest of these is 50, so the GCD is 50.

Another approach is the Euclidean algorithm. Start by dividing the larger number by the smaller number and finding the remainder. Repeat this process using the remainder and the smaller number until the remainder is zero. The last non-zero remainder is the GCD. This method is efficient for larger numbers.