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The Greatest Common Divisor, often abbreviated as GCD, is a key concept in simplifying fractions. When we talk about simplifying fractions like \( \frac{90}{120} \), finding the GCD of the numerator and denominator is essential.
The GCD is the largest number that divides both numbers without leaving a remainder.
This means it's the biggest number that fits evenly into both the numerator and denominator of a fraction.
To determine the GCD, you can list the factors of both numbers involved. For example, if we list the factors of 90, we get:

• 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Factors of 120 are:

• 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Looking through these factors, we see that the largest shared factor is 30.
This, therefore, is the GCD of 90 and 120. Knowing how to find the GCD is fundamental as it directly allows you to simplify a fraction to its lowest form.

Understanding factors is vital when simplifying fractions. Factors are numbers you multiply together to get another number.
For instance, when simplifying \( \frac{90}{120} \), we need to know the factors of both the numerator and the denominator.
For 90, the factors are:

• 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

For 120, the factors include:

• 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Identifying common factors is the first step in simplifying fractions.
The more you practice, the easier it becomes to spot the factors and the greatest common divisor.
Using these common factors, especially the largest one, helps to break down the fraction into its simplest form.

A fraction consists of two parts: the numerator and the denominator. These two elements are crucial in working with fractions.
The numerator is the number on top, showing how many parts we have. The denominator is the number below, displaying the total parts of the whole.
For example, in the fraction \( \frac{90}{120} \), 90 is the numerator, and 120 is the denominator.
To simplify a fraction, you must divide both the numerator and the denominator by their GCD. This process reduces the fraction to its simplest form.
Once we know that the GCD of 90 and 120 is 30, we divide both parts of the fraction by this number:

• \( 90 \div 30 = 3 \)
• \( 120 \div 30 = 4 \)

Simplifying \( \frac{90}{120} \) in this method results in \( \frac{3}{4} \).
Understanding the roles of the numerator and denominator is essential when simplifying fractions. It helps in applying the GCD effectively to achieve a simplified fraction swiftly. This understanding also provides a foundation for solving more complex fraction problems.