Unveiling the Mystery: 15 Percent of 90 – A Deep Dive into Percentage Calculations
Percentages are fundamental to everyday life, cropping up in sales discounts, interest rates, tax calculations, and countless other scenarios. Understanding how to calculate percentages efficiently is a crucial skill. This article delves into the specific calculation of "15 percent of 90," explaining the process in detail and exploring different methods to arrive at the solution. We'll go beyond a simple answer, providing a solid understanding of the underlying principles and their practical applications.
Understanding Percentages: A Foundational Review
A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" signifies "per cent" or "out of one hundred." To calculate a percentage of a number, we essentially find that fractional part of the number. For example, 15% means 15/100 or 0.15. Therefore, calculating 15% of 90 means finding 15/100 of 90.
Method 1: The Fraction Method
This method directly applies the definition of percentage. We can express 15% as a fraction: 15/100. To find 15% of 90, we multiply the fraction by 90:
(15/100) 90 = 1350/100 = 13.5
Therefore, 15% of 90 is 13.5.
Practical Example: Imagine a store offers a 15% discount on an item priced at $90. Using this method, we determine the discount amount to be $13.50.
Method 2: The Decimal Method
This is a more streamlined approach. We convert the percentage to its decimal equivalent. 15% is equal to 0.15 (simply divide 15 by 100). Then, multiply this decimal by the number:
0.15 90 = 13.5
This method is generally faster and preferred for larger calculations.
Practical Example: Suppose you earn a 15% commission on sales. If your sales total $90, your commission would be $13.50.
Method 3: Using Proportions
This method uses the concept of ratios. We can set up a proportion:
15/100 = x/90
Where 'x' represents the unknown value (15% of 90). To solve for x, we cross-multiply:
100x = 15 90
100x = 1350
x = 1350/100
x = 13.5
This method reinforces the underlying relationship between percentages and proportions.
Practical Example: If 15 out of every 100 students in a school participate in a particular club, and the school has 90 students, how many students participate in the club? The answer, using this method, is 13.5 students. (In reality, the number of students would be rounded to the nearest whole number.)
Expanding the Concept: Applications Beyond Simple Calculations
Understanding percentage calculations opens doors to more complex scenarios. For example, we can use this knowledge to calculate percentage increase or decrease, compound interest, or even analyze statistical data. Mastering the basics allows for a smoother transition into these more advanced applications.
Conclusion
Calculating 15% of 90, whether through the fraction, decimal, or proportion method, consistently yields the result of 13.5. The choice of method depends primarily on personal preference and the context of the problem. However, the underlying principle remains the same: converting the percentage to a fraction or decimal and multiplying it by the given number. This fundamental concept has far-reaching implications across various fields, emphasizing the importance of understanding and applying percentage calculations effectively.
FAQs
1. Can I use a calculator for these calculations? Absolutely! Calculators are efficient tools, especially for more complex percentage calculations.
2. What if I need to calculate a percentage that isn't a whole number (e.g., 12.5% of 90)? The same methods apply; simply convert the percentage to its decimal equivalent (12.5% = 0.125) and multiply.
3. How do I calculate the percentage one number represents of another? Divide the smaller number by the larger number and multiply by 100. For example, to find what percentage 13.5 is of 90: (13.5/90) 100 = 15%.
4. Are there any online tools or calculators to help with percentage calculations? Yes, numerous online percentage calculators are readily available. A simple web search will reveal several options.
5. Why is understanding percentages important? Percentages are essential for comprehending data, making financial decisions (budgets, investments, discounts), and interpreting information across various fields, from science to business.
Note: Conversion is based on the latest values and formulas.
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