What Is 90 Percent Of 75

What is 90 Percent of 75? A Comprehensive Guide to Percentage Calculations

Finding 90 percent of 75 might seem like a simple task, but understanding the underlying principles of percentage calculations is crucial for various applications in daily life, academics, and professional settings. This comprehensive guide will not only answer the question directly but also delve into the methodology, provide practical examples, and explore related concepts to solidify your understanding of percentages.

Understanding Percentages

A percentage is a fraction or ratio expressed as a number out of 100. The term "percent" literally means "out of one hundred". The symbol % is used to denote percentages. For example, 50% means 50 out of 100, which is equivalent to the fraction ½ or the decimal 0.5.

Key Concepts

• Fraction: A percentage can be represented as a fraction. For instance, 90% can be written as 90/100.
• Decimal: Percentages can also be expressed as decimals. To convert a percentage to a decimal, divide the percentage by 100. 90% is equivalent to 0.9 (90 ÷ 100).
• Ratio: A percentage represents a ratio between two numbers. In the context of "90% of 75," we're finding the ratio of 90 to 100 applied to the number 75.

Calculating 90% of 75: Three Methods

There are several ways to calculate 90% of 75. Let's explore three common methods:

Method 1: Using the Decimal Equivalent

This is arguably the most straightforward method. We convert the percentage to its decimal equivalent and then multiply it by the number.

1. Convert the percentage to a decimal: 90% = 0.9
2. Multiply the decimal by the number: 0.9 * 75 = 67.5

Therefore, 90% of 75 is 67.5.

Method 2: Using the Fraction Equivalent

This method involves converting the percentage to a fraction and then multiplying it by the number.

1. Convert the percentage to a fraction: 90% = 90/100
2. Simplify the fraction (optional): 90/100 simplifies to 9/10
3. Multiply the fraction by the number: (9/10) * 75 = 675/10 = 67.5

Again, 90% of 75 is 67.5.

Method 3: Using Proportions

This method utilizes the concept of proportions to solve for the unknown value.

We set up a proportion:

90/100 = x/75

Where 'x' represents 90% of 75.

To solve for 'x', we cross-multiply:

90 * 75 = 100 * x

6750 = 100x

x = 6750 / 100

x = 67.5

Once again, we find that 90% of 75 is 67.5.

Practical Applications of Percentage Calculations

Understanding percentage calculations is essential in numerous real-world scenarios:

• Sales and Discounts: Calculating discounts on sale items. For example, a 20% discount on a $100 item.
• Taxes: Determining the amount of sales tax or income tax.
• Tips and Gratuities: Calculating tips in restaurants or service industries.
• Financial Calculations: Calculating interest on loans or investments. Understanding percentage changes in stock prices or investment portfolios.
• Statistics and Data Analysis: Expressing data as percentages for easier interpretation and comparison. Understanding statistical significance and confidence intervals which often use percentages.
• Academic Assessments: Calculating grades based on percentages of correct answers on exams.
• Scientific Measurements and Experiments: Expressing experimental error or results as percentages.

Advanced Percentage Calculations: Beyond the Basics

While finding 90% of 75 is a relatively simple calculation, let's explore some more advanced scenarios:

Calculating the Percentage Increase or Decrease

Determining the percentage change between two numbers requires the following formula:

[(New Value - Old Value) / Old Value] * 100%

For example, if a stock price increases from $50 to $60, the percentage increase is:

[(60 - 50) / 50] * 100% = 20%

Finding the Original Value After a Percentage Change

If you know the final value after a percentage increase or decrease, and the percentage change itself, you can work backward to find the original value. This involves a bit of algebra.

Let's say a price increased by 15% to reach $80. To find the original price:

Let 'x' be the original price. Then:

x + 0.15x = 80

1.15x = 80

x = 80 / 1.15

x ≈ $69.57

Working with Multiple Percentages

Sometimes you need to apply multiple percentage changes sequentially. Remember that these percentages don't simply add together. Each percentage change is applied to the result of the previous change.

For example, a 10% increase followed by a 20% decrease does not result in a net 10% decrease.

Let's start with $100:

• 10% increase: $100 + ($100 * 0.10) = $110
• 20% decrease (applied to $110): $110 - ($110 * 0.20) = $88

The net result is an 12% decrease from the original $100.

Conclusion: Mastering Percentage Calculations

This comprehensive guide has demonstrated multiple methods for calculating 90% of 75 and expanded on the broader application of percentage calculations. Mastering these concepts is invaluable for navigating various aspects of daily life, academic pursuits, and professional endeavors. Remember to practice regularly, and you'll soon find yourself confidently tackling percentage problems of all complexities. The seemingly simple question of "What is 90 percent of 75?" serves as a springboard to understanding a much wider range of mathematical applications. By solidifying your understanding of percentages, you'll be better equipped to analyze data, make informed decisions, and excel in various fields. Further exploration into compound interest, statistical analysis, and financial modeling will build upon this foundation, enhancing your numerical literacy and problem-solving skills.