What Is 90 Of 75

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

Finding 90% of 75 might seem like a simple calculation, easily solvable with a calculator. However, understanding the underlying principles of percentages is crucial for various applications in everyday life, from calculating discounts and taxes to comprehending statistical data and financial reports. This article will not only answer the question "What is 90% of 75?" but will also delve into the meaning of percentages, different methods for calculation, and real-world examples.

Introduction: Understanding Percentages

A percentage is a fraction or ratio expressed as a number out of 100. The term "percent" literally means "per hundred." So, 90% means 90 out of 100, or 90/100, which simplifies to 9/10. This representation is fundamental to understanding how percentages work. They offer a standardized way to compare proportions and fractions, making them immensely useful in various fields.

Method 1: The Direct Calculation Method

The most straightforward way to find 90% of 75 is to convert the percentage into a decimal and then multiply it by the number.

• Step 1: Convert the Percentage to a Decimal: To convert 90% to a decimal, divide 90 by 100: 90 ÷ 100 = 0.9

• Step 2: Multiply by the Number: Now, multiply the decimal (0.9) by the number you want to find the percentage of (75): 0.9 x 75 = 67.5

Therefore, 90% of 75 is 67.5.

Method 2: The Fraction Method

As mentioned earlier, 90% can be represented as the fraction 90/100 or its simplified form, 9/10. This method involves multiplying the fraction by the number.

• Step 1: Express the Percentage as a Fraction: 90% = 90/100 = 9/10

• Step 2: Multiply the Fraction by the Number: Multiply the fraction (9/10) by 75: (9/10) x 75 = (9 x 75) / 10 = 675 / 10 = 67.5

This method yields the same result: 90% of 75 is 67.5.

Method 3: Using Proportions

This method utilizes the concept of ratios and proportions to solve percentage problems. It's particularly helpful for understanding the underlying relationship between percentages and whole numbers.

• Step 1: Set up a Proportion: We can set up a proportion as follows:

  x / 75 = 90 / 100

  Where 'x' represents the value we want to find (90% of 75).

• Step 2: Solve for x: To solve for x, we can cross-multiply:

  100x = 90 x 75

  100x = 6750

  x = 6750 / 100

  x = 67.5

Again, the result confirms that 90% of 75 is 67.5.

Why Different Methods? Understanding the Nuances

While all three methods provide the same answer, each offers a different perspective on percentage calculations. The direct calculation method is the quickest and most efficient for simple problems. The fraction method helps to reinforce the concept of percentages as fractions, which is crucial for more complex calculations. The proportion method, while potentially longer, provides a deeper understanding of the underlying mathematical relationship and is particularly useful when dealing with more intricate percentage problems.

Real-World Applications of Percentage Calculations

The ability to calculate percentages is invaluable in many real-world scenarios:

• Sales and Discounts: Stores frequently offer discounts like "90% off." Knowing how to calculate percentages helps you determine the final price after the discount.

• Taxes: Sales tax, income tax, and other taxes are often expressed as percentages. Understanding percentages allows you to calculate the total cost including taxes.

• Tips and Gratuities: Calculating tips at restaurants or service charges often involves percentages.

• Finance: Interest rates on loans and investments are expressed as percentages. Understanding percentages is crucial for managing personal finances and making sound investment decisions.

• Statistics and Data Analysis: Percentages are extensively used in statistics to represent proportions and trends in data. For example, understanding the percentage of a population that supports a particular candidate or the percentage change in a company's profits requires calculating and interpreting percentages.

• Science and Engineering: Percentages are used in various scientific and engineering applications, such as expressing concentrations of solutions or efficiency rates of machines.

Frequently Asked Questions (FAQs)

• What if I need to find a different percentage of 75? The same methods described above can be applied by simply substituting the desired percentage for 90%. For instance, to find 25% of 75, you would replace 0.9 with 0.25 in the direct calculation method, or 90/100 with 25/100 in the fraction method.

• Can I use a calculator for these calculations? Absolutely! Calculators are a convenient tool for quickly computing percentages. However, understanding the underlying methods is crucial for problem-solving and to avoid relying solely on technology.

• What if the result isn't a whole number? Many percentage calculations result in decimal values, as we saw with 90% of 75 (67.5). These decimal values are perfectly valid and often represent a more precise result. In real-world applications, you might round the result to the nearest whole number depending on the context (e.g., you can't give a 67.5% tip, but 68% might be rounded up).

• Are there online percentage calculators? Yes, numerous online calculators are readily available to calculate percentages. However, understanding the underlying principles remains essential.

Conclusion: Mastering Percentages – A Key Skill for Life

Understanding percentages is a fundamental skill with broad applications across various fields. While finding 90% of 75 might seem straightforward, the underlying principles explained in this article—including the various methods of calculation and their applications—equip you with a deeper understanding and a more versatile approach to percentage problems. This knowledge will be invaluable in navigating everyday life, making informed decisions, and enhancing your problem-solving skills in both academic and professional settings. So, the next time you encounter a percentage problem, remember the different methods presented here and choose the approach that best suits your needs and understanding. Remember, mastering percentages is not just about getting the right answer; it's about understanding the “why” behind the calculations and how they apply to the world around you.