What Is 75 Of 90

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

Finding 75% of 90 might seem like a simple arithmetic problem, but it opens the door to understanding a fundamental concept in mathematics: percentages. This seemingly straightforward calculation has far-reaching applications in various fields, from everyday budgeting and shopping to complex financial modeling and scientific analysis. This article will not only show you how to calculate 75% of 90 but will also explore the underlying principles of percentages, different methods for calculating them, and real-world examples to solidify your understanding.

Understanding Percentages: The Basics

A percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "out of one hundred" ( per centum in Latin). So, 75% means 75 out of 100, which can be written as the fraction 75/100 or the decimal 0.75. Understanding this fundamental concept is crucial for tackling any percentage problem.

Method 1: Converting to a Fraction

The most intuitive way to calculate 75% of 90 is to convert the percentage to a fraction and then multiply.

• Step 1: Convert the percentage to a fraction: 75% is equivalent to 75/100. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 25. This simplifies to 3/4.

• Step 2: Multiply the fraction by the whole number: Now, multiply the simplified fraction (3/4) by 90: (3/4) * 90 = 270/4

• Step 3: Simplify the result: Divide 270 by 4 to get the final answer: 270/4 = 67.5

Therefore, 75% of 90 is 67.5.

Method 2: Using Decimal Equivalents

Another common approach involves converting the percentage to its decimal equivalent before multiplying.

• Step 1: Convert the percentage to a decimal: To convert 75% to a decimal, divide it by 100: 75 / 100 = 0.75

• Step 2: Multiply the decimal by the whole number: Multiply the decimal (0.75) by 90: 0.75 * 90 = 67.5

Again, the result is 67.5. This method is often faster and more convenient, especially when dealing with larger numbers or more complex percentage calculations.

Method 3: Using Proportions

The concept of percentages can also be understood through proportions. We can set up a proportion to solve for the unknown value (x), which represents 75% of 90.

• Step 1: Set up the proportion: We can express the problem as a proportion: 75/100 = x/90

• Step 2: Cross-multiply: Cross-multiply the terms to get: 75 * 90 = 100 * x

• Step 3: Solve for x: This simplifies to 6750 = 100x. Divide both sides by 100 to solve for x: x = 6750 / 100 = 67.5

Once again, we find that 75% of 90 is 67.5. This method is particularly useful for understanding the underlying relationship between percentages and proportions.

Real-World Applications of Percentage Calculations

Understanding percentage calculations is essential for navigating various aspects of daily life and professional endeavors. Here are some examples:

• Shopping and Sales: Calculating discounts is a common application. If a $90 item is on sale for 25% off, you can calculate the discount amount (25% of $90) and the final price.

• Finance and Budgeting: Percentages are used extensively in finance, from calculating interest on loans and savings accounts to determining tax rates and investment returns. Understanding percentage change is crucial for tracking financial performance.

• Science and Statistics: Percentages are used to represent data in various scientific fields, from expressing experimental results to analyzing survey data. For instance, scientists might report that 75% of participants in a study showed a particular response.

• Grades and Assessments: Grading systems often use percentages to represent student performance. A score of 75% on a test typically indicates that the student answered 75 out of 100 questions correctly.

• Data Analysis and Interpretation: Percentages are used extensively to present data in a clear and concise way, making it easier to understand and interpret trends and patterns.

Beyond the Basics: More Complex Percentage Problems

While finding 75% of 90 is a relatively simple calculation, percentage problems can become more complex. For instance, you might encounter scenarios that involve calculating percentage increase or decrease, finding the original value after a percentage change, or dealing with compound percentages. These require a more nuanced understanding of percentage principles and potentially the use of algebraic equations.

Frequently Asked Questions (FAQ)

• Q: How do I calculate a percentage increase or decrease?

A: To calculate a percentage increase, find the difference between the new and original values, divide the difference by the original value, and multiply by 100. For a percentage decrease, follow the same steps, but the difference will be negative.

• Q: What if I need to find the original value after a percentage change?

A: This involves working backward. If you know the final value and the percentage change, you can use algebraic equations to solve for the original value.

• Q: How do I calculate compound percentages (like compound interest)?

A: Compound percentages involve applying a percentage change repeatedly over time. This requires using exponential formulas.

• Q: Are there online calculators or tools to help with percentage calculations?

A: Yes, many online calculators are available that can help with various percentage calculations, simplifying the process.

Conclusion: Mastering Percentages – A Lifelong Skill

Mastering percentage calculations is a valuable skill applicable across numerous disciplines. While the calculation of 75% of 90 might appear elementary, the underlying principles are crucial for various real-world applications. By understanding the different methods of calculating percentages and their practical applications, you'll be well-equipped to tackle more complex problems and confidently navigate situations involving percentages in your daily life and professional career. Remember to practice regularly and explore different approaches to solidify your understanding and build confidence in your abilities. The more you practice, the easier and more intuitive percentage calculations will become.