60/360 simplified fraction

2 min read 11-03-2025

Fractions can seem daunting, but simplifying them is easier than you might think. This guide will walk you through the process of simplifying the fraction 60/360, explaining the concepts along the way. By the end, you'll be able to simplify other fractions with confidence.

Understanding Fractions

A fraction represents a part of a whole. The top number (60 in this case) is the numerator, representing the number of parts we have. The bottom number (360) is the denominator, representing the total number of parts the whole is divided into.

Finding the Greatest Common Factor (GCF)

Simplifying a fraction means finding the greatest common factor (GCF) of both the numerator and denominator and dividing both by it. The GCF is the largest number that divides evenly into both numbers.

Let's find the GCF of 60 and 360. One way is to list the factors of each number:

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
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 number that appears in both lists is 60. Therefore, the GCF of 60 and 360 is 60.

Another, often faster, method is to use prime factorization.

Prime Factorization Method

Prime factorization of 60: 2 x 2 x 3 x 5 = 2² x 3 x 5
Prime factorization of 360: 2 x 2 x 2 x 3 x 3 x 5 = 2³ x 3² x 5

Now, identify the common prime factors and their lowest powers:

Common prime factors: 2, 3, 5
Lowest powers: 2¹, 3¹, 5¹

Multiply these together: 2 x 3 x 5 = 30. This is another way to find that 60 is also a factor. The GCF is 60.

Simplifying 60/360

Now that we've found the GCF (60), we can simplify the fraction:

60/360 = (60 ÷ 60) / (360 ÷ 60) = 1/6

Therefore, the simplified form of 60/360 is 1/6.

Other Methods for Simplifying Fractions

While finding the GCF is the most efficient method, you can also simplify fractions step-by-step by dividing both the numerator and the denominator by any common factor until you reach the simplest form. For example:

60/360 = 30/180 = 15/90 = 5/30 = 1/6

This method takes more steps, but it's useful for understanding the simplification process.

Conclusion

Simplifying fractions, like 60/360, involves finding the greatest common factor of the numerator and denominator and dividing both by it. Whether you use the GCF directly or simplify step-by-step, the result remains the same: a simpler, equivalent fraction. In this case, 60/360 simplifies to the much easier-to-understand fraction 1/6. Remember to practice, and you'll master simplifying fractions in no time!