simplify 35/48

Daniel Parker

2 min read

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21-02-2025

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Meta Description: Learn how to simplify the fraction 35/48 to its simplest form. This easy-to-follow guide provides a step-by-step explanation, helping you master fraction simplification. Discover the greatest common divisor (GCD) and understand the process of reducing fractions. Perfect for students and anyone needing a refresher on fraction basics!

Introduction:

Simplifying fractions, also known as reducing fractions, is a fundamental skill in mathematics. It involves finding an equivalent fraction with smaller numbers. Today, we'll explore how to simplify the fraction 35/48. We'll break down the process step-by-step, making it easy to understand, even if you're new to fraction simplification. Simplifying 35/48 might seem daunting at first, but with the right method, it's straightforward.

Finding the Greatest Common Divisor (GCD)

The key to simplifying any fraction is finding the greatest common divisor (GCD) of the numerator (35) and the denominator (48). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

There are several ways to find the GCD. One common method is to list the factors of each number and identify the largest factor they share.

Factors of 35: 1, 5, 7, 35 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Looking at the lists, we see that the largest number that appears in both lists is 1.

Another method to find the GCD is using the Euclidean algorithm. This is particularly useful for larger numbers.

Euclidean Algorithm

1. Divide the larger number (48) by the smaller number (35): 48 ÷ 35 = 1 with a remainder of 13.
2. Replace the larger number with the smaller number (35) and the smaller number with the remainder (13): Now we have 35 and 13.
3. Repeat: 35 ÷ 13 = 2 with a remainder of 9.
4. Repeat: 13 ÷ 9 = 1 with a remainder of 4.
5. Repeat: 9 ÷ 4 = 2 with a remainder of 1.
6. Repeat: 4 ÷ 1 = 4 with a remainder of 0.

The last non-zero remainder is the GCD. In this case, the GCD of 35 and 48 is 1.

Simplifying the Fraction

Since the GCD of 35 and 48 is 1, we can't simplify the fraction any further. This means that 35/48 is already in its simplest form.

Therefore, the simplified form of 35/48 is $\boxed{35/48}$.

Conclusion

While we initially aimed to simplify 35/48, we discovered that it's already in its simplest form because the greatest common divisor of 35 and 48 is 1. Understanding how to find the GCD is crucial for simplifying fractions effectively. This process ensures that you always express a fraction in its most concise representation. Remember to always check for common factors to simplify fractions whenever possible. Mastering this skill is fundamental to success in further mathematical studies.