how do you simlify 20/110

Daniel Parker

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 and denominator. Let's break it down step-by-step.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the largest number that divides evenly into both the numerator (top number) and the denominator (bottom number). This number is the greatest common divisor (GCD). Dividing both the numerator and the denominator by the GCD results in a simplified, equivalent fraction.

Finding the GCD of 20 and 110

To simplify 20/110, we need to find the greatest common divisor (GCD) of 20 and 110. There are several ways to do this:

Method 1: Listing Factors

1. List the factors of 20: 1, 2, 4, 5, 10, 20
2. List the factors of 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 numbers share a 2 and a 5.
4. Multiply the common prime factors: 2 x 5 = 10. This is the GCD.

Method 3: Euclidean Algorithm (for larger numbers)

The Euclidean algorithm is a more efficient method for finding the GCD of larger numbers. It involves repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder until the remainder is 0. The last non-zero remainder is the GCD.

1. Divide 110 by 20: 110 = 5 x 20 + 10
2. Divide 20 by the remainder 10: 20 = 2 x 10 + 0
3. The last non-zero remainder is 10, so the GCD is 10.

Simplifying the Fraction

Now that we know the GCD is 10, we can simplify the fraction:

20/110 = (20 ÷ 10) / (110 ÷ 10) = 2/11

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

Practice Problems

Try simplifying these fractions using the methods above:

• 15/45
• 28/35
• 36/60

By mastering these methods, you'll be able to confidently simplify any fraction you encounter. Remember, the key is finding the greatest common divisor of the numerator and denominator.