What Is 75 Percent Of 90

What is 75 Percent of 90? A Deep Dive into Percentages and Their Applications

Calculating percentages is a fundamental skill with wide-ranging applications in various aspects of life. From understanding sales discounts and interest rates to analyzing statistical data and making financial decisions, the ability to swiftly and accurately calculate percentages is invaluable. This article delves into the question, "What is 75 percent of 90?", exploring the different methods for calculating percentages, demonstrating the solution, and showcasing the practical relevance of percentage calculations in real-world scenarios.

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The term "percent" is derived from the Latin words "per centum," meaning "out of a hundred." Therefore, 75 percent (75%) signifies 75 parts out of 100 equal parts of a whole. This concept is crucial in understanding how percentages work and how to calculate them.

Key Concepts:

• The Whole: This represents the total value or quantity from which a percentage is being calculated (in this case, 90).
• The Percentage: This is the rate or proportion expressed as a percentage (75%).
• The Part: This is the result of calculating the percentage of the whole (the answer we're seeking).

Methods for Calculating 75% of 90

There are several ways to calculate 75% of 90. We'll explore three common approaches:

Method 1: Using the Fraction Method

75% can be expressed as the fraction 75/100, which simplifies to 3/4. To find 75% of 90, we multiply 90 by the fraction 3/4:

(3/4) * 90 = 270/4 = 67.5

Therefore, 75% of 90 is 67.5.

Method 2: Using Decimal Conversion

Converting the percentage to a decimal is another effective approach. To convert 75% to a decimal, divide by 100:

75% / 100 = 0.75

Now, multiply 0.75 by 90:

0.75 * 90 = 67.5

Again, we find that 75% of 90 is 67.5.

Method 3: Using Proportion

We can set up a proportion to solve this problem. We know that 75 is to 100 as x is to 90. This can be written as:

75/100 = x/90

To solve for x, we cross-multiply:

75 * 90 = 100 * x

6750 = 100x

x = 6750/100 = 67.5

This method confirms that 75% of 90 is 67.5.

Real-World Applications of Percentage Calculations

Understanding percentage calculations is essential in numerous real-world situations. Let's explore some examples:

1. Sales and Discounts:

Retail stores frequently offer discounts on their products. For instance, a 75% discount on a $90 item would mean a reduction of $67.50 (75% of 90), resulting in a final price of $22.50 ($90 - $67.50).

2. Interest Calculations:

Interest rates on loans and investments are expressed as percentages. If you invest $90 and earn 75% annual interest, you would earn $67.50 in interest after one year.

3. Tax Calculations:

Sales tax is a percentage of the purchase price. If a 75% sales tax (a very high rate used here for illustrative purposes) applied to a $90 item, the tax would be $67.50.

4. Statistical Analysis:

Percentages are crucial for interpreting data in surveys, polls, and other statistical analyses. For example, if 75% of 90 respondents answered "yes" to a survey question, it means 67.5 respondents said "yes." (Note: in real-world surveys, we'd typically round this to 68, as we can't have half a respondent).

5. Grade Calculation:

In many educational systems, grades are expressed as percentages. If a student scored 75% on a test with a total of 90 points, their score would be 67.5 out of 90.

6. Financial Planning:

Budgeting and financial planning often require percentage calculations. For example, determining the percentage of your income allocated to savings or determining the percentage of your expenses related to housing, food, or transportation.

7. Tip Calculation:

When dining at a restaurant, it's customary to tip the server a certain percentage of the bill. If you want to tip 75% on a $90 bill, you would leave a tip of $67.50.

Advanced Percentage Calculations

While the example of calculating 75% of 90 is relatively straightforward, understanding percentage calculations extends to more complex scenarios. These include:

• Calculating the Percentage Increase or Decrease: Determining the percentage change between two values requires understanding the difference between the values and then expressing that difference as a percentage of the original value.

• Finding the Original Value: If you know the percentage and the resulting value (the "part"), you can work backward to calculate the original value (the "whole").

• Compound Interest Calculations: These calculations involve interest accumulating not only on the principal amount but also on previously earned interest.

Mastering these advanced percentage calculations requires a solid understanding of fundamental percentage concepts and often involves utilizing formulas and algebraic equations.

Conclusion: The Importance of Percentage Literacy

The ability to calculate percentages accurately and efficiently is a vital life skill. From managing personal finances to understanding complex data analyses, percentage literacy empowers individuals to make informed decisions and navigate the quantitative aspects of various aspects of daily life. While the seemingly simple question "What is 75 percent of 90?" serves as a foundation, the true value lies in grasping the underlying principles and applying these skills to a wide array of practical situations. This ability to work with percentages will continue to be valuable throughout your personal and professional life.