What Is 20 Of 85

What is 20% of 85? A Comprehensive Guide to Percentages

Finding a percentage of a number is a fundamental skill in mathematics with wide-ranging applications in everyday life, from calculating discounts and tips to understanding financial reports and statistical data. This article will delve into the calculation of 20% of 85, explaining the process in detail, providing multiple approaches, and exploring the broader concept of percentages. We'll also look at how this seemingly simple calculation can be applied in various real-world scenarios and address frequently asked questions. This guide aims to not just provide the answer but to empower you with a solid understanding of percentage calculations.

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "out of 100" ( per centum in Latin). Therefore, 20% represents 20 out of 100, or 20/100, which simplifies to 1/5. Understanding this fundamental concept is crucial for all percentage calculations.

Method 1: Using the Decimal Equivalent

This is perhaps the most straightforward method. To find 20% of 85, we first convert the percentage to its decimal equivalent. We do this by dividing the percentage by 100:

20% ÷ 100 = 0.20 or simply 0.2

Now, we multiply this decimal by the number we want to find the percentage of:

0.2 x 85 = 17

Therefore, 20% of 85 is $\boxed{17}$.

Method 2: Using Fractions

As mentioned earlier, 20% can be expressed as the fraction 20/100, which simplifies to 1/5. We can use this fraction to calculate 20% of 85:

(1/5) x 85 = 85/5 = 17

This method provides an alternative approach, showcasing the equivalence between percentages, decimals, and fractions. This method is particularly useful when dealing with percentages that can be easily expressed as simple fractions, like 25% (1/4), 50% (1/2), and 75% (3/4).

Method 3: Proportion Method

This method uses the concept of proportions to solve for the unknown value. We can set up a proportion as follows:

20/100 = x/85

Here, 'x' represents the value we want to find (20% of 85). To solve for x, we cross-multiply:

20 x 85 = 100x

1700 = 100x

x = 1700/100

x = 17

Again, we find that 20% of 85 is $\boxed{17}$. This method is helpful for visualizing the relationship between the percentage and the whole number.

Real-World Applications

The ability to calculate percentages is invaluable in numerous real-world situations. Consider these examples:

Discounts: A store offers a 20% discount on an item priced at $85. Using our calculation, the discount is $17, meaning the final price would be $85 - $17 = $68.
Taxes: If a sales tax is 20%, the tax amount on an $85 purchase would be $17.
Tips: Calculating a 20% tip on an $85 restaurant bill involves the same calculation, resulting in a tip of $17.
Commission: A salesperson earns a 20% commission on sales. If they sell $85 worth of goods, their commission would be $17.
Statistical Analysis: Percentages are fundamental in statistical analysis, representing proportions within a data set. Understanding percentages is crucial for interpreting various statistical measures and charts.

Expanding on Percentage Calculations: Beyond 20% of 85

While this article focuses on calculating 20% of 85, understanding the underlying principles allows you to calculate any percentage of any number. The key is to consistently apply the methods outlined above: converting the percentage to a decimal or fraction, and then multiplying by the target number.

For example, let's calculate 35% of 120:

Decimal Method: 35% = 0.35; 0.35 x 120 = 42
Fraction Method: 35% = 35/100 = 7/20; (7/20) x 120 = 42
Proportion Method: 35/100 = x/120; 35 x 120 = 100x; x = 42

Therefore, 35% of 120 is 42. This demonstrates the adaptability of these methods to a wide variety of percentage calculations.

Advanced Percentage Calculations

Beyond simple percentage calculations, there are more complex scenarios to consider:

Calculating the percentage increase or decrease: This involves finding the difference between two numbers and expressing it as a percentage of the original number. For instance, if a price increases from $85 to $102, the percentage increase is calculated as: ((102-85)/85) x 100% = 20%.
Finding the original number when a percentage is known: If you know that a certain percentage of a number is a specific value, you can work backward to find the original number. For example, if 20% of a number is 17, the original number is 17 / 0.20 = 85.
Compound interest: This involves calculating interest on both the principal amount and accumulated interest. This requires more advanced calculations and understanding of exponential growth.

Mastering these advanced concepts builds a more robust understanding of percentages and their applications in finance and other fields.

Frequently Asked Questions (FAQ)

Q1: What is the easiest way to calculate percentages?

A1: The decimal method is generally considered the easiest for most people. Converting the percentage to a decimal and multiplying is a straightforward process.

Q2: Can I use a calculator for percentage calculations?

A2: Yes, calculators have a percentage function (%) that simplifies these calculations significantly. However, understanding the underlying principles remains crucial for problem-solving and avoiding errors.

Q3: Are there any online tools or apps to calculate percentages?

A3: Numerous online calculators and apps are available for calculating percentages. These tools can be helpful for quick calculations, but learning the manual methods ensures a deeper understanding of the concept.

Q4: Why is understanding percentages important?

A4: Percentages are used extensively in everyday life, from financial transactions and budgeting to understanding statistics and data analysis. A strong grasp of percentages is essential for informed decision-making in various aspects of life.

Q5: How can I improve my skills in percentage calculations?

A5: Practice is key! Work through various problems with different percentages and numbers. Start with simple examples and gradually increase the complexity.

Conclusion

Calculating 20% of 85, as demonstrated, yields a result of 17. This seemingly simple calculation highlights the fundamental importance of understanding percentages. By mastering the different methods – decimal, fraction, and proportion – you equip yourself with versatile tools applicable across numerous real-world situations. The ability to confidently work with percentages is a valuable asset, enhancing your understanding of numerical data and your ability to make informed decisions in various aspects of life, from personal finance to professional endeavors. Remember that consistent practice and a firm grasp of the underlying principles are key to mastering percentage calculations and unlocking their practical applications.