What Is 20 Percent Of 85

What is 20 Percent of 85? A Deep Dive into Percentages and Their Applications

Finding 20 percent of 85 might seem like a simple arithmetic problem, but it opens the door to understanding a fundamental concept in mathematics and its widespread applications in various fields. This article will not only solve this specific problem but will also explore the broader context of percentages, offering practical examples and techniques to master this essential skill.

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "out of one hundred." The symbol "%" is used to denote percentages. For example, 20% means 20 out of 100, which can be written as the fraction 20/100 or the decimal 0.20.

Calculating 20% of 85: The Basic Method

The most straightforward way to calculate 20% of 85 is to convert the percentage to a decimal and then multiply it by the number.

1. Convert the percentage to a decimal: 20% = 20/100 = 0.20

2. Multiply the decimal by the number: 0.20 * 85 = 17

Therefore, 20% of 85 is 17.

Alternative Methods: Different Approaches for the Same Result

While the method above is efficient, understanding alternative approaches can enhance your grasp of percentages and provide flexibility in solving similar problems.

Method 2: Using Fractions

We can also solve this using fractions. Remember that 20% is equivalent to the fraction 20/100, which simplifies to 1/5.

1. Simplify the percentage to a fraction: 20% = 20/100 = 1/5

2. Multiply the fraction by the number: (1/5) * 85 = 85/5 = 17

This method reinforces the relationship between percentages, decimals, and fractions.

Method 3: Breaking it Down

Sometimes, breaking down the calculation into smaller, manageable parts can be helpful, especially for mental math. We can find 10% of 85 first, and then double the result to get 20%.

1. Find 10% of 85: 10% of 85 = (10/100) * 85 = 8.5

2. Double the result to find 20%: 8.5 * 2 = 17

Real-World Applications of Percentage Calculations

The ability to calculate percentages is crucial in various aspects of daily life and professional settings. Here are some examples:

• Shopping and Sales: Calculating discounts, sales tax, and tips are common applications. If a shirt costs $85 and is on sale for 20% off, you'll save $17 (20% of $85).

• Finance and Investments: Understanding interest rates, returns on investment, and loan calculations all rely heavily on percentage calculations. If you invest $85 and it yields a 20% return, you'll earn $17.

• Statistics and Data Analysis: Percentages are used extensively to represent data, show proportions, and analyze trends. For instance, if 20% of 85 survey respondents preferred a particular product, that equates to 17 respondents.

• Science and Engineering: Percentage calculations are important in many scientific fields, including chemistry, physics, and engineering, for expressing concentrations, efficiency, and error rates.

• Everyday Life: Calculating percentage increases or decreases in weight, temperature, or other quantities are often needed in everyday contexts.

Advanced Percentage Calculations: Going Beyond the Basics

While finding 20% of 85 is relatively straightforward, let's explore some more complex percentage problems to further solidify your understanding.

Finding the Original Value

Suppose you know that 20% of a certain number is 17. How can you find the original number?

This requires a slightly different approach. We can set up an equation:

0.20 * x = 17

To solve for x (the original number), divide both sides by 0.20:

x = 17 / 0.20 = 85

This demonstrates the reverse calculation, which is equally important in many practical situations.

Calculating Percentage Increase or Decrease

Let's say a value increases from 85 to 102. What is the percentage increase?

1. Find the difference: 102 - 85 = 17

2. Divide the difference by the original value: 17 / 85 = 0.20

3. Convert the decimal to a percentage: 0.20 * 100% = 20%

Therefore, there is a 20% increase from 85 to 102.

Similarly, if a value decreases from 85 to 68, the percentage decrease would be calculated as follows:

1. Find the difference: 85 - 68 = 17

2. Divide the difference by the original value: 17 / 85 = 0.20

3. Convert the decimal to a percentage: 0.20 * 100% = 20%

This represents a 20% decrease.

Mastering Percentages: Tips and Tricks

• Practice Regularly: The more you practice percentage calculations, the more comfortable and efficient you'll become.

• Use Online Calculators (Sparingly): While online calculators can be helpful, it's crucial to understand the underlying principles. Over-reliance on calculators can hinder your learning.

• Break Down Complex Problems: If you encounter a complex percentage problem, break it down into smaller, more manageable steps.

• Understand the Context: Always consider the context of the problem. This will help you choose the most appropriate method and interpret the results correctly.

• Check Your Work: Always verify your calculations to ensure accuracy.

Conclusion: The Power of Percentages

Understanding percentages is a valuable skill with widespread applications in various fields. While the seemingly simple question "What is 20 percent of 85?" provides a starting point, exploring the different methods and advanced applications highlights the importance and versatility of this fundamental mathematical concept. By mastering percentage calculations, you equip yourself with a powerful tool for navigating numerous situations in both your personal and professional life. Remember to practice regularly and explore different approaches to solidify your understanding and enhance your problem-solving abilities.