What Percentage Of 75 Is 15

Introduction

Calculating percentages is a fundamental skill in mathematics and everyday life, helping us understand proportions, discounts, and statistical data. When faced with the question "what percentage of 75 is 15," we're essentially trying to determine what fraction of 75 equals 15, expressed as a percentage. This type of calculation is not only useful in academic settings but also in practical scenarios like shopping, finance, and data analysis. Understanding how to solve this problem will give you a valuable tool for interpreting numerical relationships in a variety of contexts.

Detailed Explanation

The question "what percentage of 75 is 15" is asking us to find what portion 15 represents out of 75, converted into a percentage. In mathematical terms, we're looking for the value of x in the equation: x% of 75 = 15. To solve this, we need to understand that "percentage" means "per hundred," so we're essentially finding what fraction of 75 equals 15, then multiplying that fraction by 100 to convert it to a percentage.

This type of calculation is based on the concept of ratios and proportions. When we say "what percentage," we're comparing two quantities to see how they relate to each other in terms of 100 parts. The formula for finding what percentage one number is of another is: (part/whole) × 100. In this case, 15 is the part, and 75 is the whole. By applying this formula, we can determine exactly what percentage 15 represents of 75.

Step-by-Step Solution

To solve "what percentage of 75 is 15," we follow these steps:

1. Set up the equation: x% of 75 = 15
2. Convert the percentage to a decimal: (x/100) × 75 = 15
3. Solve for x: x = (15 × 100) / 75
4. Simplify: x = 1500 / 75
5. Calculate: x = 20

Therefore, 15 is 20% of 75. This means that if you divide 75 into 100 equal parts, 15 would represent 20 of those parts.

Another way to think about it is that 15 is one-fifth of 75, and since one-fifth is equivalent to 20%, we arrive at the same answer. This method of cross-multiplication or using fractions can be helpful for quick mental calculations when dealing with percentages.

Real Examples

Understanding percentages is crucial in many real-life situations. For example, if a store offers a 20% discount on a $75 item, you would save $15, which is exactly the calculation we just performed. Similarly, in a class of 75 students, if 15 students are absent, that's 20% of the class not present.

In financial contexts, if you invest $75 and earn $15 in interest, your return on investment is 20%. This percentage helps you understand the proportion of your earnings relative to your initial investment. Percentages also play a significant role in statistics, where they help represent data in a more digestible format, such as survey results or demographic information.

Scientific or Theoretical Perspective

From a mathematical perspective, percentages are a way to express ratios as fractions of 100. This system makes it easier to compare different quantities and understand their relative sizes. The concept of percentage has been used for centuries, dating back to ancient civilizations that used fractions and proportions for trade and taxation.

In modern mathematics, percentages are fundamental in various fields, including statistics, economics, and science. They provide a standardized way to express proportions, making it easier to communicate and compare data across different contexts. The use of percentages allows for quick mental calculations and helps in understanding trends and patterns in numerical data.

Common Mistakes or Misunderstandings

One common mistake when dealing with percentages is confusing the part and the whole. In our example, it's crucial to remember that 75 is the whole, and 15 is the part we're comparing to it. Another error is forgetting to multiply by 100 to convert the fraction to a percentage, which would leave you with a decimal instead of the correct percentage value.

Some people also struggle with the concept of percentage increase or decrease, which involves calculating the difference between two values and then finding what percentage that difference represents of the original value. It's important to distinguish between finding what percentage one number is of another (as in our example) and calculating percentage change, which is a different concept.

FAQs

Q: How do I calculate what percentage one number is of another? A: To find what percentage one number is of another, divide the first number by the second, then multiply by 100. For example, to find what percentage 15 is of 75: (15 ÷ 75) × 100 = 20%.

Q: What if I need to find a percentage of a number, like 20% of 75? A: To find a percentage of a number, convert the percentage to a decimal (by dividing by 100) and multiply by the number. For 20% of 75: 0.20 × 75 = 15.

Q: Can percentages be more than 100%? A: Yes, percentages can exceed 100%. This occurs when the part is larger than the whole. For example, if you earn $150 on a $100 investment, that's a 150% return.

Q: How do I calculate percentage increase or decrease? A: To calculate percentage change, find the difference between the new and original values, divide by the original value, then multiply by 100. For an increase from 75 to 90: ((90 - 75) ÷ 75) × 100 = 20% increase.

Conclusion

Understanding how to calculate percentages, such as determining what percentage of 75 is 15, is a valuable skill with wide-ranging applications. In this case, we found that 15 is 20% of 75, a calculation that can be applied to various real-world scenarios, from shopping discounts to financial returns. By mastering the concept of percentages, you gain the ability to interpret numerical relationships, make informed decisions, and communicate data more effectively. Whether you're a student, professional, or simply someone looking to improve their numerical literacy, grasping the fundamentals of percentage calculations will serve you well in countless situations.