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When you are dealing with fractions, simplifying them makes them easier to understand and work with. Essentially, simplifying a fraction means reducing it to its simplest form. This involves finding a common factor, which is a number that divides both the numerator (top number) and the denominator (bottom number) without leaving a remainder.

For example, in the fraction \( \frac{84}{100} \), both 84 and 100 can be divided by their greatest common divisor (GCD), which is 4. By dividing both the numerator and the denominator by 4, we get \( \frac{21}{25} \).

The simplified fraction \( \frac{21}{25} \) is in its simplest form because there are no numbers other than 1 that can divide both 21 and 25 evenly. Simplifying fractions helps make calculations easier and results more understandable.

The Greatest Common Divisor (GCD) is the largest number that can exactly divide both the numerator and the denominator of a fraction. Finding the GCD is crucial for simplifying fractions.

To find the GCD of two numbers, you can list their divisors and choose the largest one that both numbers share. For example, the divisors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The divisors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common divisor they both share is 4. Hence, the GCD of 84 and 100 is 4.

Using the GCD, you can reduce fractions easily. In our example: \( \frac{84}{100} \) becomes \( \frac{21}{25} \), once both the numerator and the denominator are divided by their GCD of 4.

Basic arithmetic consists of simple mathematical operations: addition, subtraction, multiplication, and division. For percent to fraction conversion, we mainly use division.

First, convert the percentage to a fraction by placing the percent value over 100. For instance, 84% becomes \( \frac{84}{100} \). This is because percent means per hundred.

Then, use division to simplify the fraction. Find the greatest common divisor (GCD) of the numerator and denominator to do this efficiently. Divide both the numerator and the denominator by the GCD. In our problem, the GCD is 4; hence, \( \frac{84}{100} \) simplifies to \( \frac{21}{25} \).

Basic arithmetic is the foundation for all other mathematical operations and is used extensively in various mathematical processes, including simplifying fractions.