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what is 20 of 108

what is 20 of 108

less than a minute read 05-02-2025
what is 20 of 108

What is 20/108 Simplified? Understanding Fractions

What is 20/108? This seemingly simple question involves understanding fractions and how to simplify them to their lowest terms. Let's break it down step-by-step.

Understanding Fractions

A fraction represents a part of a whole. The top number (20 in this case) is called the numerator, and the bottom number (108) is the denominator. The fraction 20/108 means 20 out of 108 equal parts.

Simplifying Fractions

To simplify a fraction, we need to find the greatest common divisor (GCD) of both the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

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 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The largest number that appears in both lists is 4. Therefore, the GCD of 20 and 108 is 4.

Reducing the Fraction

Now, we divide both the numerator and the denominator by the GCD (4):

20 ÷ 4 = 5 108 ÷ 4 = 27

Therefore, 20/108 simplified is 5/27.

Alternative Methods for Finding the GCD

While listing factors works well for smaller numbers, the Euclidean algorithm is a more efficient method for larger numbers. This algorithm 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.

Let's illustrate this with 20 and 108:

  1. 108 ÷ 20 = 5 with a remainder of 8
  2. 20 ÷ 8 = 2 with a remainder of 4
  3. 8 ÷ 4 = 2 with a remainder of 0

The last non-zero remainder is 4, confirming our GCD.

Converting to a Decimal

To express 5/27 as a decimal, we simply divide 5 by 27:

5 ÷ 27 ≈ 0.185

Conclusion

Therefore, 20/108 simplified to its lowest terms is 5/27, which is approximately equal to 0.185. Understanding how to simplify fractions is a fundamental skill in mathematics, with applications in various fields. Remember to always find the greatest common divisor to ensure the fraction is in its simplest form.

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