35/48 in simplest form

Charlotte

2 min read

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28-02-2025

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Fractions are a fundamental part of mathematics, representing parts of a whole. Simplifying, or reducing, a fraction means expressing it in its lowest terms—making it easier to understand and work with. This article will guide you through the process of simplifying the fraction 35/48 to its simplest form. We'll explore the concept of greatest common divisors (GCD) and demonstrate a step-by-step approach that you can apply to other fractions.

Understanding Fraction Simplification

Simplifying a fraction involves finding the greatest common divisor (GCD) of the numerator (the top number) and the denominator (the bottom number). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once you find the GCD, you divide both the numerator and the denominator by it to obtain the simplified fraction.

Finding the GCD of 35 and 48

To find the greatest common divisor (GCD) of 35 and 48, we can use a few different methods. The most common is the prime factorization method:

1. Prime Factorization of 35: 35 can be broken down into its prime factors as 5 x 7.

2. Prime Factorization of 48: 48 can be broken down as 2 x 2 x 2 x 2 x 3 = 2⁴ x 3.

3. Identifying Common Factors: Examining the prime factorizations of 35 and 48, we see that they share no common prime factors. This means their greatest common divisor (GCD) is 1.

Simplifying 35/48

Since the GCD of 35 and 48 is 1, we divide both the numerator and denominator by 1:

35 ÷ 1 = 35

48 ÷ 1 = 48

Therefore, the simplified form of 35/48 is 35/48. Because there are no common factors other than 1, this fraction is already in its simplest form.

Other Methods for Finding the GCD

While prime factorization is a reliable method, the Euclidean algorithm provides another way to find the GCD, particularly useful for larger numbers. This involves repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder until the remainder is 0. The last non-zero remainder is the GCD.

Conclusion: 35/48 in Simplest Form

In conclusion, the fraction 35/48 is already in its simplest form. There are no common factors between 35 and 48 besides 1, making further simplification impossible. Understanding the concept of the greatest common divisor is crucial for simplifying fractions efficiently. This process, whether using prime factorization or the Euclidean algorithm, ensures the fraction is expressed in its most concise and manageable form.