what is 20 of 192

Natashya

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23-12-2024

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Knowing how to calculate fractions like 20/192 is a fundamental math skill. This article will guide you through simplifying this fraction and understanding its equivalent percentage. We'll also explore different methods for solving similar problems.

Simplifying the Fraction 20/192

The fraction 20/192 represents 20 parts out of a total of 192 parts. To simplify this, we need to find the greatest common divisor (GCD) of both 20 and 192. The GCD is the largest number that divides both numbers evenly.

Finding the GCD:

One way to find the GCD is through prime factorization.

• Prime factorization of 20: 2 x 2 x 5
• Prime factorization of 192: 2 x 2 x 2 x 2 x 2 x 2 x 3 = 2⁶ x 3

The common factors are two 2s, meaning the GCD is 4 (2 x 2 = 4).

Simplifying:

Now, we divide both the numerator (20) and the denominator (192) by the GCD (4):

20 ÷ 4 = 5 192 ÷ 4 = 48

Therefore, the simplified fraction is 5/48.

Converting the Fraction to a Percentage

To express 5/48 as a percentage, we divide the numerator by the denominator and multiply the result by 100:

(5 ÷ 48) x 100 ≈ 10.42%

So, 20/192 is approximately 10.42%.

Alternative Methods for Simplification

While prime factorization is a reliable method, there are other ways to simplify fractions:

• Dividing by common factors: You can repeatedly divide both the numerator and denominator by common factors until you reach the simplest form. For example, you could notice that both 20 and 192 are divisible by 2, giving you 10/96. Then you can divide both by 2 again, resulting in 5/48.

• Using a calculator: Many calculators have a function to simplify fractions directly. Just enter the fraction and the calculator will provide the simplified form.

Real-World Applications

Understanding fractions and percentages is essential in various aspects of daily life, including:

• Calculating discounts: Determining the price after a discount involves working with percentages.
• Measuring ingredients: Recipes often use fractions to specify ingredient quantities.
• Analyzing data: Representing data in fractional or percentage form helps in understanding proportions and trends.

Conclusion

20/192 simplifies to the fraction 5/48, which is approximately 10.42%. Mastering fraction simplification and percentage conversion is crucial for various mathematical applications and everyday problem-solving. Remember to utilize the methods described above to tackle similar problems confidently. Understanding these concepts provides a solid foundation for more complex mathematical concepts in the future.