how do you simlify 20/110

Charlotte

2 min read

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28-02-2025

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Simplifying fractions like 20/110 might seem daunting at first, but it's a straightforward process involving finding the greatest common divisor (GCD) of the numerator (20) and the denominator (110). This article will guide you through the process, explaining the steps clearly and concisely. Let's learn how to simplify 20/110 to its simplest form.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the largest number that divides both the numerator and the denominator without leaving a remainder. This number is the greatest common divisor (GCD). The simplified fraction represents the same value as the original fraction, but in a more concise and manageable form.

Finding the Greatest Common Divisor (GCD)

Several methods exist for finding the GCD. Here are two common approaches:

Method 1: Listing Factors

1. List the factors of the numerator (20): 1, 2, 4, 5, 10, 20
2. List the factors of the denominator (110): 1, 2, 5, 10, 11, 22, 55, 110
3. Identify the greatest common factor: The largest number appearing in both lists is 10. Therefore, the GCD of 20 and 110 is 10.

Method 2: Prime Factorization

1. Find the prime factorization of 20: 2 x 2 x 5 = 2² x 5
2. Find the prime factorization of 110: 2 x 5 x 11
3. Identify common prime factors: Both 20 and 110 share a 2 and a 5.
4. Calculate the GCD: Multiply the common prime factors: 2 x 5 = 10. The GCD is 10.

Simplifying the Fraction

Now that we've found the GCD (10), we can simplify the fraction:

1. Divide the numerator (20) by the GCD (10): 20 ÷ 10 = 2
2. Divide the denominator (110) by the GCD (10): 110 ÷ 10 = 11

Therefore, the simplified form of 20/110 is 2/11.

Checking Your Work

It's always a good idea to verify your answer. You can do this by checking if the simplified fraction is equivalent to the original fraction. In this case, if you multiply both the numerator and denominator of 2/11 by 10, you get back to 20/110, confirming that 2/11 is the correct simplified form.

Conclusion

Simplifying fractions is a fundamental skill in mathematics. By understanding how to find the greatest common divisor and applying the steps outlined above, you can confidently simplify fractions like 20/110 to their simplest form, 2/11. Remember to practice these methods to build your proficiency!