what is 20 of 102

Natashya

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26-12-2024

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Finding the simplest form of a fraction like 20/102 is a fundamental math skill. This article will walk you through how to solve this problem and explain the underlying concepts of fraction simplification. We'll explore the steps involved and show you how to arrive at the correct answer. Understanding how to simplify fractions is essential for various mathematical calculations and problem-solving.

Simplifying Fractions: A Step-by-Step Guide

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (top number) and the denominator (bottom number) and dividing both by it. Let's break down how to simplify 20/102:

1. Find the Greatest Common Divisor (GCD): The GCD is the largest number that divides evenly into both 20 and 102. One way to find the GCD is to list the factors of each number:

   • Factors of 20: 1, 2, 4, 5, 10, 20
   • Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102

   The largest number that appears in both lists is 2. Therefore, the GCD of 20 and 102 is 2.

2. Divide Both the Numerator and Denominator by the GCD: Divide both the numerator (20) and the denominator (102) by the GCD (2):

   • 20 ÷ 2 = 10
   • 102 ÷ 2 = 51

3. Simplified Fraction: The simplified fraction is 10/51.

Therefore, 20/102 simplified is 10/51.

Understanding Fraction Simplification

Simplifying fractions doesn't change the value of the fraction; it just makes it easier to work with. 10/51 represents the same proportion as 20/102. This process is crucial for:

• Easier Calculations: Simplified fractions make addition, subtraction, multiplication, and division much simpler.
• Clearer Understanding: A simplified fraction gives a clearer representation of the proportion.
• Problem Solving: Many mathematical problems require simplifying fractions to arrive at the correct solution.

Alternative Methods for Finding the GCD

While listing factors works well for smaller numbers, for larger numbers, the Euclidean algorithm is a more efficient method for finding the GCD. This algorithm involves repeatedly applying the division algorithm until the remainder is zero. The last non-zero remainder is the GCD.

Conclusion

Simplifying fractions is a valuable skill in mathematics. By understanding the concept of the greatest common divisor and applying the steps outlined above, you can easily simplify fractions like 20/102 to their simplest form, which is 10/51. Mastering this skill will enhance your understanding of fractions and make various mathematical operations much easier. Remember to always look for the greatest common divisor to ensure the fraction is in its simplest form.