100/360 simplified

wmissh

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17-02-2025

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Fractions are a fundamental part of mathematics, representing parts of a whole. Simplifying fractions, also known as reducing fractions, means finding an equivalent fraction with smaller numbers. This article will guide you through simplifying the fraction 100/360, explaining the process step-by-step. Learning to simplify fractions like 100/360 is crucial for understanding mathematical concepts and solving problems more efficiently.

What is 100/360?

The fraction 100/360 represents 100 parts out of a total of 360 parts. Imagine a pizza cut into 360 slices; 100/360 represents having 100 of those slices. This fraction can be simplified to a smaller, equivalent fraction using the greatest common divisor (GCD).

Finding the Greatest Common Divisor (GCD)

The GCD is the largest number that divides both the numerator (100) and the denominator (360) without leaving a remainder. There are several ways to find the GCD, including:

• Listing factors: List all the factors of 100 and 360 and find the largest common factor. This method works well for smaller numbers, but becomes less efficient with larger ones.
• Prime factorization: Break down both numbers into their prime factors and find the common prime factors. The product of these common factors is the GCD.
• Euclidean algorithm: A more efficient method for larger numbers. This involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The last non-zero remainder is the GCD.

Let's use prime factorization for 100/360:

• 100: 2 x 2 x 5 x 5 = 2² x 5²
• 360: 2 x 2 x 2 x 3 x 3 x 5 = 2³ x 3² x 5

The common prime factors are 2² and 5. Therefore, the GCD of 100 and 360 is 2² x 5 = 20.

Simplifying 100/360

To simplify 100/360, divide both the numerator and the denominator by their GCD (20):

100 ÷ 20 = 5 360 ÷ 20 = 18

Therefore, the simplified fraction is 5/18.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and work with. It helps in:

• Easier calculations: Performing operations (addition, subtraction, multiplication, division) with smaller numbers is simpler and less prone to errors.
• Better visualization: A simplified fraction provides a clearer representation of the proportion.
• Problem-solving: Simplified fractions make it easier to identify patterns and solve problems.

Other Examples of Fraction Simplification

Let's look at a few more examples to solidify your understanding:

• 24/36: The GCD of 24 and 36 is 12. Simplifying gives 2/3.
• 15/25: The GCD of 15 and 25 is 5. Simplifying gives 3/5.
• 42/63: The GCD of 42 and 63 is 21. Simplifying gives 2/3.

Mastering fraction simplification is a valuable skill that will benefit you in various mathematical applications. Understanding the concept of the greatest common divisor and applying the appropriate method will significantly aid in reducing fractions to their simplest form, like simplifying 100/360 to 5/18. Remember to always check your answer by multiplying the simplified fraction by the GCD to ensure it's equivalent to the original fraction.