15 Is What Percent Of 90

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

Understanding percentages is a fundamental skill applicable across numerous fields, from everyday budgeting to complex financial analyses. This comprehensive guide delves into the question, "15 is what percent of 90?", providing not only the solution but also a thorough exploration of the underlying concepts and practical applications. We'll cover different methods for solving percentage problems, explain the rationale behind each step, and offer real-world examples to solidify your understanding.

Understanding Percentages: The Basics

Before diving into the specific problem, let's establish a strong foundation in percentage concepts. A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" represents "per cent," meaning "out of one hundred." For instance, 50% signifies 50 out of 100, or ½.

Key Terms and Concepts:

• Percentage: The proportion of a whole, represented as a number out of 100.
• Base: The total amount or whole from which the percentage is calculated.
• Part: The portion of the base that represents the percentage.

Method 1: Using the Formula

The most direct method to determine what percentage 15 represents of 90 is using the standard percentage formula:

(Part / Base) x 100 = Percentage

In this case:

• Part: 15
• Base: 90

Substituting these values into the formula:

(15 / 90) x 100 = Percentage

Simplifying the fraction:

(1/6) x 100 = Percentage

Calculating the result:

16.666...% ≈ 16.67%

Therefore, 15 is approximately 16.67% of 90. The recurring decimal ".666..." is typically rounded to two decimal places for practicality.

Method 2: Using Proportions

Another effective approach involves setting up a proportion. A proportion equates two ratios. We can represent the problem as:

15/90 = x/100

Where 'x' represents the unknown percentage. To solve for 'x', we cross-multiply:

15 * 100 = 90 * x

1500 = 90x

Now, solve for x by dividing both sides by 90:

x = 1500 / 90

x ≈ 16.67

Again, we arrive at the solution: 15 is approximately 16.67% of 90.

Method 3: Using Decimal Equivalents

Percentages can also be expressed as decimals. To convert a percentage to a decimal, divide by 100. Conversely, to convert a decimal to a percentage, multiply by 100.

We can solve the problem by first converting the percentage to a decimal:

Let 'x' be the percentage. The equation becomes:

x/100 * 90 = 15

Solving for 'x':

x = (15 * 100) / 90

x = 1500 / 90

x ≈ 16.67

Therefore, 15 is approximately 16.67% of 90.

Real-World Applications: Illustrative Examples

Percentage calculations are integral to various aspects of daily life and professional fields. Here are some examples illustrating the practical applications of understanding percentage problems like "15 is what percent of 90?":

1. Sales and Discounts:

Imagine a store offers a discount on an item originally priced at $90. The discounted price is $15 less. To calculate the discount percentage:

(Discount Amount / Original Price) x 100 = Discount Percentage

($15 / $90) x 100 = 16.67%

The store is offering a 16.67% discount.

2. Grades and Scores:

A student scores 15 out of 90 points on a test. To find their percentage score:

(Score Obtained / Total Possible Score) x 100 = Percentage Score

(15 / 90) x 100 = 16.67%

The student achieved a 16.67% on the test.

3. Financial Calculations:

Suppose you invest $90 and earn a profit of $15. To determine the percentage return on your investment:

(Profit / Investment) x 100 = Return on Investment Percentage

($15 / $90) x 100 = 16.67%

Your investment yielded a 16.67% return.

4. Surveys and Statistics:

In a survey of 90 people, 15 responded positively to a particular question. To calculate the percentage of positive responses:

(Positive Responses / Total Responses) x 100 = Percentage of Positive Responses

(15 / 90) x 100 = 16.67%

16.67% of respondents gave positive answers.

5. Tax Calculations:

If a sales tax of $15 is applied to a $90 purchase, the tax rate can be calculated as:

(Tax Amount / Purchase Price) x 100 = Tax Rate

($15/$90) x 100 = 16.67%

The sales tax rate is 16.67%.

Beyond the Basics: More Complex Percentage Problems

While this article focuses on a relatively straightforward percentage problem, the principles discussed are applicable to more complex scenarios. These can involve multiple percentages, compound interest calculations, or percentage change over time. Mastering the fundamental concepts outlined here provides a solid base for tackling these more advanced problems.

Tips and Tricks for Solving Percentage Problems:

• Simplify Fractions: Before performing calculations, simplify fractions whenever possible. This makes the arithmetic easier and reduces the risk of errors.
• Use a Calculator: For more complex calculations, utilize a calculator to ensure accuracy and save time.
• Check Your Work: Always double-check your answer to ensure it aligns with the context of the problem. Does the percentage seem reasonable given the values?
• Practice Regularly: Consistent practice is key to mastering percentage calculations. Work through various examples to build your confidence and understanding.

Conclusion: Mastering Percentages for Success

The question, "15 is what percent of 90?", serves as a springboard for understanding a fundamental mathematical concept with widespread applicability. By understanding the different methods for solving percentage problems and practicing their application in diverse contexts, you equip yourself with a valuable skill applicable across numerous aspects of life, from personal finance to professional pursuits. Remember, mastering percentages is not just about getting the right answer; it's about developing a deeper understanding of ratios, proportions, and their significance in quantifying relationships between numbers.