75/360 simplified

2 min read 28-02-2025

Understanding fractions can sometimes feel overwhelming, especially when dealing with seemingly complex numbers like 75/360. This article will break down 75/360 in a simple, easy-to-understand way, exploring its simplification and practical applications. We'll explore how to simplify this fraction, its decimal equivalent, and its percentage representation. By the end, you'll confidently work with this fraction and similar ones.

Understanding the Basics: Simplifying Fractions

Before diving into 75/360, let's refresh the concept of simplifying fractions. Simplifying, or reducing, a fraction means finding an equivalent fraction with smaller numbers. This is done by finding the greatest common divisor (GCD) of the numerator (top number) and denominator (bottom number) and dividing both by it.

Key Concept: A simplified fraction represents the same value as the original fraction, but with smaller, more manageable numbers.

Finding the Greatest Common Divisor (GCD)

The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. Several methods exist for finding the GCD. A common method is to list the factors of each number and find the largest factor they share.

For 75 and 360:

Factors of 75: 1, 3, 5, 15, 25, 75
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 15.

Simplifying 75/360

Now that we know the GCD of 75 and 360 is 15, we can simplify the fraction:

75 ÷ 15 = 5

360 ÷ 15 = 24

Therefore, 75/360 simplifies to 5/24.

Converting to Decimal and Percentage

Simplified fractions are easier to work with. Let's convert 5/24 to a decimal and a percentage:

Decimal: Divide the numerator (5) by the denominator (24): 5 ÷ 24 ≈ 0.2083

Percentage: Multiply the decimal by 100: 0.2083 x 100 ≈ 20.83%

Practical Applications

Understanding how to simplify fractions like 75/360 has many practical applications. It's useful in various fields, including:

Finance: Calculating interest rates, proportions, and ratios.
Construction: Measuring materials and proportions in blueprints.
Cooking: Adjusting recipes and understanding ingredient ratios.
Data Analysis: Interpreting data and presenting results clearly.

Conclusion

Simplifying 75/360 to 5/24 makes it significantly easier to understand and use. Remember, the key is finding the greatest common divisor and dividing both the numerator and denominator by that number. This simple process unlocks a better grasp of fractions, making calculations and interpretations much more straightforward. Mastering this skill enhances your understanding of mathematical concepts and improves your ability to solve real-world problems.