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Percentages are a way to express numbers as parts of a whole. Imagine that whole as being divided into 100 equal parts. When we say 24%, we mean 24 out of those 100 parts.

Percentages are very useful because they give us a quick way to compare values. For instance, if you score 75% on a test, you know you got 75 out of every 100 points right, regardless of the total points.

To convert a percentage into a more flexible format like a fraction, the conceptual leap is realizing that 'percent' literally means 'per one hundred'.

So, 24% can be directly translated into the fraction \( \frac{24}{100} \).

Fractions represent parts of a whole too, but sometimes they can look complicated. That's where simplification comes in. Simplifying a fraction makes it easier to understand and use.

To simplify, we need to find a common number that both the numerator (top number) and the denominator (bottom number) can be divided by without leaving a remainder. This simplifies the fraction without changing its value.

For example, with \( \frac{24}{100} \), we look for a number that divides both 24 and 100. Simplifying it, we find the greatest common divisor (GCD). Dividing both the numerator and the denominator by their GCD, we get a simpler fraction. This is how \( \frac{24}{100} \) becomes \( \frac{6}{25} \).

The greatest common divisor (GCD) is the largest number that can divide both the numerator and the denominator of a fraction exactly, without leaving a fraction. Knowing how to find the GCD is essential for simplifying fractions.

For instance, to convert 24% to a simplified fraction, we start with \( \frac{24}{100} \). Next, we find the GCD of 24 and 100. To do this, start by listing the factors of each number:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

The largest number common to both lists is 4. Therefore, 4 is the GCD.

By dividing both the numerator and the denominator of \( \frac{24}{100} \) by 4, we simplify it to \( \frac{6}{25} \).

Using the GCD ensures we get the simplest form of the fraction, making it easier to work with in calculations and comparisons.