75/360 simplified

Charlotte

2 min read

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27-02-2025

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Understanding fractions can sometimes feel like navigating a maze. But fear not! This guide will simplify the fraction 75/360, explaining how to reduce it to its simplest form and providing context for its use in various applications, particularly in the world of finance and date calculations. We'll explore different methods and ensure you leave with a clear understanding.

Understanding the Fraction 75/360

The fraction 75/360 represents 75 parts out of a total of 360 parts. This is a common fraction encountered in financial calculations, especially those involving interest calculations using the 75/360 day-count convention.

Simplifying 75/360: Step-by-Step Guide

The key to simplifying fractions is finding the greatest common divisor (GCD) of both the numerator (75) and the denominator (360). The GCD is the largest number that divides both numbers without leaving a remainder.

Method 1: Finding the GCD

1. List the factors: Find the factors of 75 (1, 3, 5, 15, 25, 75) and the 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).

2. Identify the GCD: The largest number that appears in both lists is 15. Therefore, the GCD of 75 and 360 is 15.

3. Divide both numerator and denominator by the GCD: Divide both 75 and 360 by 15:

   75 ÷ 15 = 5 360 ÷ 15 = 24

Therefore, 75/360 simplified is 5/24.

Method 2: Prime Factorization

This method is particularly useful for larger numbers.

1. Find the prime factorization of 75: 75 = 3 x 5 x 5 = 3 x 5²

2. Find the prime factorization of 360: 360 = 2 x 2 x 2 x 3 x 3 x 5 = 2³ x 3² x 5

3. Identify common factors: Both numbers share one 3 and one 5.

4. Cancel out common factors: (3 x 5²) / (2³ x 3² x 5) simplifies to 5 / (2³ x 3) = 5/24

The Significance of 75/360 in Finance

The 75/360 day-count convention is a method used to calculate the number of days in a period for interest calculations. While it doesn't accurately reflect the actual number of days in a year (which varies), its simplicity makes it widely used. The fraction 75/360 might represent a portion of a year when calculating accrued interest. For example, 75 days out of a 360-day year.

Decimal Equivalent

To express 5/24 as a decimal, divide 5 by 24: 5 ÷ 24 ≈ 0.2083

Conclusion: Mastering 75/360

Simplifying 75/360 to 5/24 is a straightforward process once you understand the concept of finding the greatest common divisor. This simplified fraction provides a more manageable and easily understood representation of the original fraction, particularly useful in financial calculations employing the 75/360 day-count convention. Remember, mastering fractions is crucial for various applications, and understanding how to simplify them is a fundamental skill.