60/360 simplified fraction

Charlotte

2 min read

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28-02-2025

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The fraction 60/360 might seem daunting at first, but simplifying it is easier than you think! This guide will walk you through the process step-by-step, explaining the concepts involved. By the end, you'll be able to simplify similar fractions with confidence.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (the top number) and the denominator (the bottom number) and dividing both by that number. The result is an equivalent fraction that's easier to work with.

Finding the Greatest Common Divisor (GCD) of 60 and 360

The first step in simplifying 60/360 is to find the greatest common divisor (GCD) of 60 and 360. The GCD is the largest number that divides both 60 and 360 without leaving a remainder.

There are several ways to find the GCD:

• Listing Factors: List all the factors of 60 and 360. The largest number that appears in both lists is the GCD.

• Prime Factorization: Break down both numbers into their prime factors. The GCD is the product of the common prime factors raised to the lowest power.

• Euclidean Algorithm: This is a more efficient method for larger numbers, involving repeated division.

Let's use prime factorization for this example:

• 60: 2 x 2 x 3 x 5 = 2² x 3 x 5
• 360: 2 x 2 x 2 x 3 x 3 x 5 = 2³ x 3² x 5

The common prime factors are 2, 3, and 5. The lowest power of 2 is 2², the lowest power of 3 is 3, and the lowest power of 5 is 5. Therefore, the GCD is 2² x 3 x 5 = 60.

Simplifying the Fraction

Now that we know the GCD is 60, we can simplify the fraction:

60/360 = (60 ÷ 60) / (360 ÷ 60) = 1/6

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

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and use in calculations. A simplified fraction provides the same value as the original fraction, but in a more concise and manageable form. This is crucial for various mathematical operations and real-world applications.

Practice Problems

Try simplifying these fractions using the same method:

• 12/48
• 25/100
• 15/75

By mastering fraction simplification, you'll improve your mathematical skills and solve problems more efficiently. Remember, finding the GCD is the key to simplifying any fraction.