21/60 simplest form

Daniel Parker

2 min read

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28-02-2025

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Fractions can seem daunting, but simplifying them is a straightforward process. Let's break down how to simplify the fraction 21/60 to its simplest form. This guide will walk you through the steps, explaining the concepts along the way. Understanding this process will help you tackle any fraction simplification problem.

Understanding Fraction Simplification

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

Finding the Greatest Common Divisor (GCD) of 21 and 60

The first step in simplifying 21/60 is to find the greatest common divisor (GCD) of 21 and 60. The GCD is the largest number that divides evenly into both 21 and 60. There are several ways to find the GCD:

Method 1: Listing Factors

1. List the factors of 21: 1, 3, 7, 21
2. List the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
3. Identify the greatest common factor: The largest number that appears in both lists is 3.

Method 2: Prime Factorization

1. Find the prime factorization of 21: 3 x 7
2. Find the prime factorization of 60: 2 x 2 x 3 x 5
3. Identify common prime factors: Both numbers share a single '3'.
4. Multiply the common prime factors: 3 (This is our GCD).

Simplifying 21/60

Now that we know the GCD of 21 and 60 is 3, we can simplify the fraction:

1. Divide the numerator (21) by the GCD (3): 21 ÷ 3 = 7
2. Divide the denominator (60) by the GCD (3): 60 ÷ 3 = 20

Therefore, the simplified form of 21/60 is 7/20.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and use in calculations. 7/20 is a much simpler fraction than 21/60. It's easier to visualize and compare to other fractions. Simplified fractions are also essential for more advanced mathematical operations.

Practice Problems

Try simplifying these fractions using the methods described above:

• 15/25
• 18/24
• 36/48

By mastering fraction simplification, you'll build a strong foundation for more complex mathematical concepts. Remember to always find the greatest common divisor to ensure the fraction is in its simplest form.