100/360 simplified

Charlotte

2 min read

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28-02-2025

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Understanding fractions can sometimes feel overwhelming, especially when dealing with less common denominators like 360. This article simplifies the fraction 100/360, explaining how to reduce it to its simplest form and exploring its practical applications.

Reducing 100/360 to its Simplest Form

The first step in simplifying 100/360 is to find the greatest common divisor (GCD) of both the numerator (100) and the denominator (360). The GCD is the largest number that divides both numbers without leaving a remainder.

One way to find the GCD is through prime factorization. Let's break down 100 and 360 into their prime factors:

• 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. Multiplying these together gives us the GCD: 2² x 5 = 20.

Now, we divide both the numerator and the denominator by the GCD (20):

100 ÷ 20 = 5 360 ÷ 20 = 18

Therefore, the simplified fraction is 5/18.

Alternative Methods for Simplification

While prime factorization is a reliable method, you can also simplify using a step-by-step approach. Notice that both 100 and 360 are divisible by 10:

100 ÷ 10 = 10 360 ÷ 10 = 36

Now we have 10/36. Both are divisible by 2:

10 ÷ 2 = 5 36 ÷ 2 = 18

This also leads us to the simplified fraction of 5/18. This illustrates that you don't always need to find the greatest common divisor in one step; repeated simplification with smaller common factors works just as well.

Practical Applications of 100/360 (or 5/18)

The fraction 100/360, and its simplified equivalent 5/18, can appear in various contexts. Here are a few examples:

• Percentage Calculations: To express 100/360 as a percentage, divide the numerator by the denominator and multiply by 100: (5/18) * 100 ≈ 27.78%. This could represent a score on a test, a discount, or progress towards a goal.

• Geometry and Angles: Since 360 represents the total degrees in a circle, 100/360 represents a specific angle within a circle. This is equivalent to 5/18 of a full circle.

• Probability and Statistics: The fraction could represent the probability of a specific event occurring, or a proportion within a larger dataset. For instance, if you have 100 successes out of 360 trials, the success rate is approximately 27.78%.

Converting to Decimal and Percentage

To further illustrate the fraction's value, let's convert it to a decimal and percentage:

• Decimal: 5 ÷ 18 ≈ 0.2778
• Percentage: 0.2778 x 100% ≈ 27.78%

This shows that 100/360 represents roughly 28% of a whole.

Conclusion

Simplifying fractions like 100/360 is a fundamental skill in mathematics. By understanding the process of finding the greatest common divisor and reducing the fraction to its simplest form (5/18), you can easily work with this fraction in various practical applications, from calculating percentages to understanding proportions and probabilities. Remember that choosing the method that's easiest for you is key – whether prime factorization or a step-by-step approach. The result remains the same: a simplified and easily understandable representation of the original fraction.