90 Is What Percent Of 120

90 is What Percent of 120? A Comprehensive Guide to Percentage Calculations

Percentage calculations are fundamental to numerous aspects of life, from calculating discounts and sales tax to understanding financial reports and statistical data. This comprehensive guide will delve into the question, "90 is what percent of 120?", providing not only the answer but also a detailed explanation of the process, variations of the problem, and practical applications.

Understanding Percentages

Before diving into the specific calculation, let's establish a firm understanding of percentages. A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" signifies "per hundred" or "out of 100." For instance, 50% represents 50 out of 100, or 50/100, which simplifies to 1/2 or 0.5.

Calculating "90 is What Percent of 120?"

To determine what percentage 90 represents of 120, we can employ a straightforward formula:

(Part / Whole) * 100% = Percentage

In this case:

• Part: 90 (the value we want to express as a percentage)
• Whole: 120 (the total value)

Substituting these values into the formula:

(90 / 120) * 100% = Percentage

This simplifies to:

(3/4) * 100% = 75%

Therefore, 90 is 75% of 120.

Different Ways to Solve Percentage Problems

While the above method is the most common and straightforward approach, there are alternative methods to solve percentage problems, particularly useful when dealing with more complex scenarios.

Method 2: Using Proportions

Proportions offer a visual and intuitive way to solve percentage problems. We can set up a proportion as follows:

90/120 = x/100

Where 'x' represents the percentage we're trying to find. To solve for 'x', we cross-multiply:

90 * 100 = 120 * x

9000 = 120x

x = 9000 / 120 = 75

Therefore, x = 75%, confirming our previous result.

Method 3: Using Decimal Equivalents

Percentages can be easily converted to decimals by dividing by 100. Conversely, decimals can be converted to percentages by multiplying by 100. This method is particularly useful when working with calculators or spreadsheets.

First, divide 90 by 120:

90 / 120 = 0.75

Then, multiply the decimal by 100 to convert it to a percentage:

0.75 * 100% = 75%

This method provides an alternative pathway to arrive at the same answer.

Practical Applications of Percentage Calculations

Understanding percentage calculations is crucial in various real-world scenarios. Here are a few examples:

1. Sales and Discounts:

Imagine a store offers a 25% discount on an item originally priced at $120. To calculate the discount amount, you'd find 25% of $120:

(25/100) * $120 = $30

The discount is $30, and the final price would be $120 - $30 = $90. This directly relates to our initial problem; the sale price ($90) represents 75% of the original price ($120).

2. Tax Calculations:

Sales tax is commonly expressed as a percentage. If the sales tax is 6% and you purchase an item for $120, you would calculate the tax amount as follows:

(6/100) * $120 = $7.20

The total cost, including tax, would be $120 + $7.20 = $127.20

3. Grade Calculation:

In education, percentage is often used to represent grades. If you answered 90 questions correctly out of a total of 120, your score would be 75%, as we've already established.

4. Financial Analysis:

Percentage change is frequently used in financial analysis to track growth or decline. For example, comparing profits from one year to the next. If profits increased from $90 to $120, the percentage increase would be:

((120 - 90) / 90) * 100% = 33.33%

5. Data Analysis and Statistics:

Percentages are fundamental to interpreting and presenting statistical data. For instance, if a survey of 120 people shows that 90 prefer a certain product, this translates to a 75% preference rate.

Advanced Percentage Problems

While the "90 is what percent of 120?" problem is relatively straightforward, let's explore some variations that require slightly more advanced techniques:

Finding the Whole When Given the Part and Percentage

Suppose you know that 75% of a certain amount is 90. How do you find the original amount (the whole)? You can use the following formula:

Whole = (Part / Percentage) * 100

Whole = (90 / 75) * 100 = 120

Finding the Part When Given the Whole and Percentage

If you know that a certain amount is 75% of 120, how do you find the part? Use this formula:

Part = (Percentage / 100) * Whole

Part = (75 / 100) * 120 = 90

Conclusion: Mastering Percentage Calculations

Understanding percentage calculations is a vital skill applicable in countless everyday situations. This guide has provided a comprehensive explanation of how to determine what percentage 90 represents of 120, along with alternative calculation methods and practical real-world applications. By mastering these fundamental concepts and formulas, you'll be well-equipped to tackle more complex percentage problems and confidently navigate situations involving percentages in various fields. Remember, consistent practice is key to solidifying your understanding and improving your problem-solving skills. The more you practice, the more intuitive percentage calculations will become.