72/99 simplified

2 min read 28-02-2025

Fractions can seem daunting, but simplifying them is a straightforward process. This article will guide you through simplifying the fraction 72/99, explaining the steps involved and offering some helpful tips for future fraction simplification. We'll break down the process, making it easy to understand, even for beginners.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (top number) and the denominator (bottom number) and dividing both by it. The result is an equivalent fraction that's easier to understand and work with. This process doesn't change the value of the fraction; it just expresses it in a simpler form.

Finding the Greatest Common Divisor (GCD) of 72 and 99

The first step in simplifying 72/99 is to find the greatest common divisor (GCD) of 72 and 99. There are several ways to do this:

1. Listing Factors:

List all the factors of 72 and 99:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 99: 1, 3, 9, 11, 33, 99

The largest number that appears in both lists is 9. Therefore, the GCD of 72 and 99 is 9.

2. Prime Factorization:

Another method is prime factorization. Break down both numbers into their prime factors:

72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
99 = 3 x 3 x 11 = 3² x 11

The common prime factors are 3² (or 9). Therefore, the GCD is 9.

3. Euclidean Algorithm (for larger numbers):

For larger numbers, the Euclidean algorithm is a more efficient method. It involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is 0. The last non-zero remainder is the GCD. We won't go into detail here, as it's not necessary for this example.

Simplifying 72/99

Now that we know the GCD is 9, we can simplify the fraction:

72 ÷ 9 = 8 99 ÷ 9 = 11

Therefore, 72/99 simplified is 8/11.

Checking Your Work

It's always a good idea to check your work. You can verify that the simplified fraction is equivalent to the original by ensuring that the ratio remains the same:

72/99 = 8/11 (Both fractions are equal to approximately 0.727)

Conclusion: Mastering Fraction Simplification

Simplifying fractions, as shown with the example of 72/99, is a fundamental skill in mathematics. Mastering this process makes working with fractions easier and allows for a clearer understanding of their values. Remember to always find the greatest common divisor to get the fraction in its simplest form. Practice makes perfect, so keep working with different fractions to build your confidence and skill.