what is 20 of 84

less than a minute read 24-12-2024

So, you want to know what 20 out of 84 is? This seemingly simple question touches upon fundamental mathematical concepts like fractions, decimals, and percentages. Let's break it down and explore different ways to understand this relationship.

Calculating the Fraction

The most straightforward approach is to express "20 of 84" as a fraction. This fraction represents the part (20) relative to the whole (84). Therefore, the fraction is 20/84.

Simplifying the Fraction

This fraction can be simplified by finding the greatest common divisor (GCD) of 20 and 84. The GCD of 20 and 84 is 4. Dividing both the numerator (20) and the denominator (84) by 4, we get the simplified fraction 5/21. This means 20 out of 84 is equivalent to 5 out of 21.

Converting to a Decimal

To express 20/84 (or its simplified form 5/21) as a decimal, we simply divide the numerator by the denominator:

20 ÷ 84 ≈ 0.238

5 ÷ 21 ≈ 0.238

As you can see, both fractions yield the same decimal approximation.

Expressing as a Percentage

A percentage represents a fraction out of 100. To convert the decimal 0.238 to a percentage, we multiply by 100:

0.238 x 100 = 23.8%

Therefore, 20 out of 84 is approximately 23.8%.

Real-World Applications

Understanding how to calculate fractions, decimals, and percentages is crucial in many real-world scenarios:

Discounts: Calculating sale prices based on percentage discounts.
Surveys and Polls: Interpreting survey results and understanding proportions.
Financial Calculations: Determining interest rates, loan payments, and investment returns.
Data Analysis: Representing and interpreting data using percentages and fractions.

Conclusion: 20 out of 84 Explained

In summary, 20 out of 84 can be represented as the fraction 20/84, which simplifies to 5/21. This fraction is approximately equal to 0.238 or 23.8%. This knowledge is applicable across various mathematical and real-world contexts. Understanding these calculations empowers you to tackle similar problems confidently.