Understanding Percentages: The Percentage of 12 out of 20 and 15

In this article, we#8217;ll explore how to calculate the percentage of 12 out of 20 and 15. Understanding these calculations is crucial for various applications in mathematics, finance, and everyday life. We'll provide step-by-step solutions, clear explanations, and practical examples to help you grasp the concept.

Percentage of 12 out of 20

To find the percentage of 12 out of 20, we start by setting up the problem as a fraction: 12/20. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.

Step 1: Simplify 12/20 by dividing both by 4:

12 ÷ 4 3, 20 ÷ 4 5

Step 2: Convert the simplified fraction to a percentage by multiplying by 100:

3/5 * 100 60%

Therefore, 12 out of 20 is 60%.

Percentage of 12 out of 15

The calculation for finding the percentage of 12 out of 15 is similar. We can directly set up the fraction as 12/15.

Step 1: Simplify 12/15 by dividing both the numerator and the denominator by their GCD, which is 3:

12 ÷ 3 4, 15 ÷ 3 5

Step 2: Convert the simplified fraction to a percentage by multiplying by 100:

4/5 * 100 80%

Thus, 12 out of 15 is 80%.

Alternative Method: Cross-Multiplication

A more intuitive method for finding percentages is using cross-multiplication. We can set up the equation to find the percentage directly:

15 - 100

To find the percentage of 12 out of 15, we set up the proportion:

15 100

12 x

Solving for x, we get:

x (12 * 100) / 15 80%

This method provides a straightforward way to find percentages without the need for simplification steps.

Methods and Techniques

To convert a fraction to a percentage, follow these steps:

Divide the numerator by the denominator: For 12/15, this is 12 ÷ 15 0.8 (for 12/20, this is 12 ÷ 20 0.6). Multiply the result by 100: For 0.8, this is 0.8 * 100 80% (for 0.6, this is 0.6 * 100 60%).

These methods can be applied to any fraction to find the corresponding percentage.

Practice and Application

Understanding percentages is crucial for practical applications like discounts, taxes, and financial planning. By mastering these calculations, you can make informed decisions and manage resources effectively.

We hope this detailed guide helps you understand and apply the concept of percentages in various contexts. If you have any questions or need further assistance, feel free to reach out!