100/360 as a fraction

2 min read 07-02-2025

The fraction 100/360 might seem daunting at first, but simplifying it is easier than you think. This guide will walk you through the process, explaining the steps involved and showing you how to arrive at the simplest form of this fraction. Understanding fraction simplification is crucial for various mathematical applications.

Understanding Fraction Simplification

Before we dive into simplifying 100/360, let's quickly review the concept of simplifying fractions. Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (the top number) and the denominator (the bottom number) and dividing both by that GCD. The result is an equivalent fraction that is simpler and easier to work with.

Finding the Greatest Common Divisor (GCD) of 100 and 360

The first step in simplifying 100/360 is to find the greatest common divisor (GCD) of 100 and 360. There are several ways to do this:

Method 1: Listing Factors

List all the factors of both 100 and 360. The largest number that appears in both lists is the GCD.

Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 Factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The largest common factor is 20.

Method 2: Prime Factorization

Another method is to find the prime factorization of both numbers. The GCD is the product of the common prime factors raised to the lowest power.

Prime factorization of 100: 2² x 5² Prime factorization of 360: 2³ x 3² x 5

The common prime factors are 2 and 5. The lowest power of 2 is 2², and the lowest power of 5 is 5¹. Therefore, the GCD is 2² x 5 = 20.

Method 3: Euclidean Algorithm

The Euclidean algorithm is a more efficient method for finding the GCD, especially for larger numbers. It involves repeatedly applying the division algorithm until the remainder is 0. The last non-zero remainder is the GCD.

Divide 360 by 100: 360 = 3 x 100 + 60
Divide 100 by 60: 100 = 1 x 60 + 40
Divide 60 by 40: 60 = 1 x 40 + 20
Divide 40 by 20: 40 = 2 x 20 + 0

The last non-zero remainder is 20, so the GCD is 20.

Simplifying the Fraction

Now that we know the GCD of 100 and 360 is 20, we can simplify the fraction:

100 ÷ 20 = 5 360 ÷ 20 = 18

Therefore, 100/360 simplifies to 5/18.

Conclusion

Simplifying 100/360 to its lowest terms results in the fraction 5/18. We achieved this by finding the greatest common divisor of 100 and 360, which is 20, and then dividing both the numerator and the denominator by 20. This process is fundamental in mathematics and helps in making calculations easier and more efficient. Remember to always look for common factors to simplify fractions.