What Is 75 Of 90

What is 75% of 90? A Comprehensive Guide to Percentages and Their Applications

Finding 75% of 90 might seem like a simple calculation, but understanding the underlying concepts of percentages and their applications is crucial in various aspects of life, from everyday budgeting to complex financial analysis. This comprehensive guide will not only solve this specific problem but also delve into the broader world of percentages, explaining different methods of calculation and providing real-world examples.

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The term "percent" literally means "out of one hundred" (per centum in Latin). Therefore, 75% means 75 out of 100, which can also be represented as the fraction 75/100 or the decimal 0.75. Percentages are incredibly useful for comparing quantities, showing proportions, and representing changes or growth. They are prevalent in various fields, including:

• Finance: Interest rates, discounts, tax calculations, investment returns.
• Statistics: Representing data, analyzing trends, probability calculations.
• Science: Measuring concentrations, expressing experimental results.
• Everyday life: Sales, tips, grades, surveys.

Calculating 75% of 90: Three Methods

There are several ways to calculate 75% of 90. Here are three common methods:

Method 1: Using the Decimal Equivalent

This is often the quickest and most straightforward method. First, convert the percentage to its decimal equivalent by dividing by 100. 75% divided by 100 is 0.75. Then, multiply this decimal by the number you want to find the percentage of:

90 * 0.75 = 67.5

Therefore, 75% of 90 is 67.5.

Method 2: Using Fractions

Percentages can also be represented as fractions. 75% is equivalent to the fraction 75/100, which can be simplified to 3/4. To find 75% of 90, multiply 90 by the fraction 3/4:

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

Again, we arrive at the answer: 75% of 90 is 67.5. This method is particularly useful when dealing with percentages that have simple fractional equivalents.

Method 3: Using Proportions

This method involves setting up a proportion. We know that 75 is to 100 as x is to 90, where x is the value we want to find. This can be written as:

75/100 = x/90

To solve for x, cross-multiply:

100x = 75 * 90 100x = 6750 x = 6750 / 100 x = 67.5

Thus, using proportions, we confirm that 75% of 90 is 67.5.

Real-World Applications of Percentage Calculations

Understanding how to calculate percentages is essential in numerous real-life situations. Here are a few examples:

• Sales and Discounts: If a store offers a 75% discount on an item priced at $90, the discount amount would be $67.50 ($90 * 0.75). The final price after the discount would be $22.50 ($90 - $67.50).

• Tax Calculations: If a sales tax is 7.5%, the tax on a $90 item would be $6.75 ($90 * 0.075). The total cost, including tax, would be $96.75 ($90 + $6.75).

• Grade Calculations: If a test is worth 90 points, and a student scores 75% on the test, their score would be 67.5 points ($90 * 0.75).

• Investment Returns: If an investment of $90 yields a 75% return, the profit would be $67.50 ($90 * 0.75).

• Survey Results: If 75% of 90 respondents in a survey answered "yes" to a question, then 67.5 respondents answered "yes". While you can't have half a respondent, this represents a strong majority.

• Tip Calculations: In many cultures, tipping is customary. If you want to leave a 75% tip on a $90 bill, you would leave $67.50.

• Understanding Growth and Decline: Percentages are essential when expressing growth (increase) or decline (decrease) in various quantities. For example, a 75% increase in a company's profits or a 75% decrease in unemployment rate.

Beyond the Basics: Advanced Percentage Calculations

While finding 75% of 90 is a straightforward calculation, more complex scenarios may arise. These could involve:

• Calculating the percentage increase or decrease: This involves finding the difference between two values and expressing it as a percentage of the original value. For instance, if a quantity increases from 90 to 150, the percentage increase is [(150-90)/90] * 100% = 66.67%.

• Finding the original value given a percentage and a result: If 75% of a certain number is 67.5, you can find the original number by dividing 67.5 by 0.75: 67.5 / 0.75 = 90.

• Working with multiple percentages: This involves performing several percentage calculations sequentially. For example, applying a discount followed by a tax.

• Compounding percentages: This occurs when a percentage change is applied repeatedly over time, such as compound interest.

Using Technology for Percentage Calculations

While manual calculations are beneficial for understanding the concepts, technology significantly simplifies the process. Calculators, spreadsheets (like Microsoft Excel or Google Sheets), and online percentage calculators can perform these calculations quickly and accurately, especially for more complex problems. Spreadsheets, in particular, are powerful tools for handling large datasets and performing numerous percentage calculations simultaneously.

Conclusion:

Calculating 75% of 90, resulting in 67.5, is a fundamental percentage calculation. Understanding this concept, however, extends far beyond this simple example. The ability to work with percentages is a vital skill applicable across various fields and daily situations. Mastering different calculation methods and utilizing available technology can make percentage calculations efficient and accurate, enabling informed decision-making in personal and professional contexts. From understanding financial transactions to interpreting statistical data, the ability to confidently work with percentages empowers you to navigate a wide range of situations successfully.