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In a fraction, you’ll find two main parts: the numerator and the denominator. The numerator is the top number, and it represents how many parts of a whole we are considering. For example, in the fraction \(\frac{3}{4}\), the numerator is 3. It shows that we have 3 parts out of the total 4.

The denominator is the bottom number. It tells you how many equal parts the whole is divided into. In \(\frac{3}{4}\), the denominator is 4, meaning the whole is divided into 4 equal parts.

In the exercise we’re discussing, the fraction is \(\frac{-24}{8}\). Here, -24 is the numerator, and 8 is the denominator. Remember, both positive and negative numbers can be used in fractions, and they work the same way.

The Greatest Common Divisor (GCD) is a key concept when simplifying fractions. The GCD of two numbers is the largest number that can exactly divide both of them.

Finding the GCD helps in reducing fractions to their simplest form. For example, if we want to simplify \(\frac{-24}{8}\), we need to find the GCD of 24 and 8.

Here’s how to find the GCD:

• List the factors of each number. Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24. Factors of 8: 1, 2, 4, and 8.
• Identify the greatest factor that both lists share. In this case, it is 8.

So, the GCD of 24 and 8 is 8. We then use this GCD to divide both the numerator and the denominator.

Lastly, we use division to simplify the fraction. Using our example, \(\frac{-24}{8}\), we need to divide both the numerator and the denominator by their GCD.

Since we already know the GCD of 24 and 8 is 8, we proceed to divide:

• Divide the numerator: \(-24 \div 8 = -3\)
• Divide the denominator: \(\frac{8}{8} = 1\)

After dividing, the fraction \(\frac{-24}{8}\) simplifies to \(\frac{-3}{1}\), which is just -3.

This process works for any fraction, making it simpler and easier to understand.